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    <link:label id="lab_ecd_TradingArrByIndTable_label_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual [Table]</link:label>
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    <link:label id="lab_ecd_TradingArrAxis_label_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement [Axis]</link:label>
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    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum [Member]</link:label>
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    <link:label id="lab_gemi_WarrantLiabilityMember_label_en-US" xlink:label="lab_gemi_WarrantLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrant Liability [Member]</link:label>
    <link:label id="lab_gemi_WarrantLiabilityMember_documentation_en-US" xlink:label="lab_gemi_WarrantLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Warrant Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_WarrantLiabilityMember" xlink:href="gemi-20260930.xsd#gemi_WarrantLiabilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_WarrantLiabilityMember" xlink:to="lab_gemi_WarrantLiabilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoAssetsCollateralPayableCurrent_01a015a8-8b08-7ba3-8872-3cd422af01df_terseLabel_en-US" xlink:label="lab_gemi_CryptoAssetsCollateralPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto asset collateral payable</link:label>
    <link:label id="lab_gemi_CryptoAssetsCollateralPayableCurrent_label_en-US" xlink:label="lab_gemi_CryptoAssetsCollateralPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Assets, Collateral Payable, Current</link:label>
    <link:label id="lab_gemi_CryptoAssetsCollateralPayableCurrent_documentation_en-US" xlink:label="lab_gemi_CryptoAssetsCollateralPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Assets, Collateral Payable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoAssetsCollateralPayableCurrent" xlink:href="gemi-20260930.xsd#gemi_CryptoAssetsCollateralPayableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoAssetsCollateralPayableCurrent" xlink:to="lab_gemi_CryptoAssetsCollateralPayableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_01a015a8-8b08-7af7-8fc1-44f3006755df_terseLabel_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement</link:label>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ExecutiveDeparturesMember_01a015a8-8b8d-7d3f-8e51-e280862d541b_terseLabel_en-US" xlink:label="lab_gemi_ExecutiveDeparturesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Executive Departures</link:label>
    <link:label id="lab_gemi_ExecutiveDeparturesMember_label_en-US" xlink:label="lab_gemi_ExecutiveDeparturesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Executive Departures [Member]</link:label>
    <link:label id="lab_gemi_ExecutiveDeparturesMember_documentation_en-US" xlink:label="lab_gemi_ExecutiveDeparturesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Executive Departures</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ExecutiveDeparturesMember" xlink:href="gemi-20260930.xsd#gemi_ExecutiveDeparturesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ExecutiveDeparturesMember" xlink:to="lab_gemi_ExecutiveDeparturesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShortTermDebtTypeAxis_01a015a8-8b08-707f-8837-96cdbc54fa8f_terseLabel_en-US" xlink:label="lab_us-gaap_ShortTermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Short-Term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_ShortTermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_ShortTermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShortTermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortTermDebtTypeAxis" xlink:to="lab_us-gaap_ShortTermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_Security12bTitle_01a015a8-8b08-7728-a9f4-4bca21bdcfc4_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:label id="lab_dei_Security12bTitle_label_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_Security12bTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_Security12bTitle" xlink:to="lab_dei_Security12bTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventMember_01a015a8-8b8d-744b-ab37-501409fc8480_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event</link:label>
    <link:label id="lab_us-gaap_SubsequentEventMember_label_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventMember" xlink:to="lab_us-gaap_SubsequentEventMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_01a015a8-8a6b-7e25-94c4-c79abd8deaab_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net loss attributable to common stockholders, diluted</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ProceedsFromRepurchaseAgreements_01a015a8-8b8d-7b4a-bb24-eb8efd830e4f_terseLabel_en-US" xlink:label="lab_gemi_ProceedsFromRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash proceeds</link:label>
    <link:label id="lab_gemi_ProceedsFromRepurchaseAgreements_label_en-US" xlink:label="lab_gemi_ProceedsFromRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From Repurchase Agreements</link:label>
    <link:label id="lab_gemi_ProceedsFromRepurchaseAgreements_documentation_en-US" xlink:label="lab_gemi_ProceedsFromRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds From Repurchase Agreements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ProceedsFromRepurchaseAgreements" xlink:href="gemi-20260930.xsd#gemi_ProceedsFromRepurchaseAgreements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ProceedsFromRepurchaseAgreements" xlink:to="lab_gemi_ProceedsFromRepurchaseAgreements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable_01a015a8-8b8d-78b2-ac8e-c68c20809ac5_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Table]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable" xlink:to="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation, Amount</link:label>
    <link:label id="lab_ecd_AdjToCompAmt_label_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAmt" xlink:to="lab_ecd_AdjToCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_01a015a8-8b08-788e-b659-6e2fb34f9620_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentAxis" xlink:to="lab_us-gaap_FinancialInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ComputerAndOtherEquipmentMember_01a015a8-8a6b-767b-8f7b-9bc973a96639_terseLabel_en-US" xlink:label="lab_gemi_ComputerAndOtherEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Computers and other equipment</link:label>
    <link:label id="lab_gemi_ComputerAndOtherEquipmentMember_label_en-US" xlink:label="lab_gemi_ComputerAndOtherEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Computer And Other Equipment [Member]</link:label>
    <link:label id="lab_gemi_ComputerAndOtherEquipmentMember_documentation_en-US" xlink:label="lab_gemi_ComputerAndOtherEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Computer And Other Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ComputerAndOtherEquipmentMember" xlink:href="gemi-20260930.xsd#gemi_ComputerAndOtherEquipmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ComputerAndOtherEquipmentMember" xlink:to="lab_gemi_ComputerAndOtherEquipmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CreditCardReceivablesPostedReturnedAsCollateralForFundingDebtNet_01a015a8-8b8d-7f92-928d-cd67899255b8_terseLabel_en-US" xlink:label="lab_gemi_CreditCardReceivablesPostedReturnedAsCollateralForFundingDebtNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit card receivables posted (returned) as collateral for funding debt, net</link:label>
    <link:label id="lab_gemi_CreditCardReceivablesPostedReturnedAsCollateralForFundingDebtNet_label_en-US" xlink:label="lab_gemi_CreditCardReceivablesPostedReturnedAsCollateralForFundingDebtNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Card Receivables Posted (Returned) As Collateral For Funding Debt, Net</link:label>
    <link:label id="lab_gemi_CreditCardReceivablesPostedReturnedAsCollateralForFundingDebtNet_documentation_en-US" xlink:label="lab_gemi_CreditCardReceivablesPostedReturnedAsCollateralForFundingDebtNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Credit Card Receivables Posted (Returned) As Collateral For Funding Debt, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CreditCardReceivablesPostedReturnedAsCollateralForFundingDebtNet" xlink:href="gemi-20260930.xsd#gemi_CreditCardReceivablesPostedReturnedAsCollateralForFundingDebtNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CreditCardReceivablesPostedReturnedAsCollateralForFundingDebtNet" xlink:to="lab_gemi_CreditCardReceivablesPostedReturnedAsCollateralForFundingDebtNet" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_MarketBasedStockOptionsMember_01a015a8-8a6b-754c-8302-26a6deeb2f77_terseLabel_en-US" xlink:label="lab_gemi_MarketBasedStockOptionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Market-Based Stock Options</link:label>
    <link:label id="lab_gemi_MarketBasedStockOptionsMember_label_en-US" xlink:label="lab_gemi_MarketBasedStockOptionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Market Based Stock Options [Member]</link:label>
    <link:label id="lab_gemi_MarketBasedStockOptionsMember_documentation_en-US" xlink:label="lab_gemi_MarketBasedStockOptionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Market Based Stock Options</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_MarketBasedStockOptionsMember" xlink:href="gemi-20260930.xsd#gemi_MarketBasedStockOptionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_MarketBasedStockOptionsMember" xlink:to="lab_gemi_MarketBasedStockOptionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_01a015a8-8b8d-7478-ac41-96ae2239106a_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Expected Future Amortization Expense for Intangible Assets</link:label>
    <link:label id="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, and Capitalized Cost, Software to be Sold, Leased, or Marketed, Estimated Amortization Expense [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:to="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_EtherMember_01a015a8-8b08-7843-bfe8-dd2bca38856d_terseLabel_en-US" xlink:label="lab_gemi_EtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ether</link:label>
    <link:label id="lab_gemi_EtherMember_01a015a8-8b08-77c9-9d02-93fa6f798045_verboseLabel_en-US" xlink:label="lab_gemi_EtherMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Ether</link:label>
    <link:label id="lab_gemi_EtherMember_label_en-US" xlink:label="lab_gemi_EtherMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ether [Member]</link:label>
    <link:label id="lab_gemi_EtherMember_documentation_en-US" xlink:label="lab_gemi_EtherMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Ether</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_EtherMember" xlink:href="gemi-20260930.xsd#gemi_EtherMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_EtherMember" xlink:to="lab_gemi_EtherMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestructuringPlanAxis_01a015a8-8b8d-796a-8e87-5c56086f3db2_terseLabel_en-US" xlink:label="lab_us-gaap_RestructuringPlanAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restructuring Plan [Axis]</link:label>
    <link:label id="lab_us-gaap_RestructuringPlanAxis_label_en-US" xlink:label="lab_us-gaap_RestructuringPlanAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restructuring Plan [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestructuringPlanAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestructuringPlanAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestructuringPlanAxis" xlink:to="lab_us-gaap_RestructuringPlanAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent_01a015a8-8b8d-7f95-960c-05a37321afb1_verboseLabel_en-US" xlink:label="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accrued salaries and benefits</link:label>
    <link:label id="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Employee-related Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeRelatedLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:to="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingencyAccrualAtCarryingValue_01a015a8-8b08-7bf8-b260-fc7817aa26f8_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Estimated loss contingency accrued</link:label>
    <link:label id="lab_us-gaap_LossContingencyAccrualAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency Accrual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingencyAccrualAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:to="lab_us-gaap_LossContingencyAccrualAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_DebtCovenantCapacityThresholdTrigger_01a015a8-8b8e-716a-bc36-6722a01a7beb_terseLabel_en-US" xlink:label="lab_gemi_DebtCovenantCapacityThresholdTrigger" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt covenant, capacity threshold trigger</link:label>
    <link:label id="lab_gemi_DebtCovenantCapacityThresholdTrigger_label_en-US" xlink:label="lab_gemi_DebtCovenantCapacityThresholdTrigger" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Covenant, Capacity Threshold Trigger</link:label>
    <link:label id="lab_gemi_DebtCovenantCapacityThresholdTrigger_documentation_en-US" xlink:label="lab_gemi_DebtCovenantCapacityThresholdTrigger" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Covenant, Capacity Threshold Trigger</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_DebtCovenantCapacityThresholdTrigger" xlink:href="gemi-20260930.xsd#gemi_DebtCovenantCapacityThresholdTrigger"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_DebtCovenantCapacityThresholdTrigger" xlink:to="lab_gemi_DebtCovenantCapacityThresholdTrigger" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityExTransitionPeriod_01a015a8-8b08-773c-95f9-093459b1ac3c_terseLabel_en-US" xlink:label="lab_dei_EntityExTransitionPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Ex Transition Period</link:label>
    <link:label id="lab_dei_EntityExTransitionPeriod_label_en-US" xlink:label="lab_dei_EntityExTransitionPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Ex Transition Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityExTransitionPeriod" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityExTransitionPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityExTransitionPeriod" xlink:to="lab_dei_EntityExTransitionPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_01a015a8-8b08-7797-8cb6-bdc52b7cd8fc_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeInstrumentRiskAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:to="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardNetOfForfeitures_01a015a8-8b8d-7e8c-8398-e072b4d58da4_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardNetOfForfeitures" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common stock upon settlement of RSUs, net of shares withheld (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardNetOfForfeitures_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardNetOfForfeitures" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Restricted Stock Award, Net of Forfeitures</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardNetOfForfeitures" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardNetOfForfeitures"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardNetOfForfeitures" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardNetOfForfeitures" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoAssetsPledgedAsCollateral_01a015a8-8b08-7de3-9ce7-bc68c78be626_terseLabel_en-US" xlink:label="lab_gemi_CryptoAssetsPledgedAsCollateral" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto assets pledged as collateral not meeting the derecognition criteria</link:label>
    <link:label id="lab_gemi_CryptoAssetsPledgedAsCollateral_label_en-US" xlink:label="lab_gemi_CryptoAssetsPledgedAsCollateral" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Assets Pledged As Collateral</link:label>
    <link:label id="lab_gemi_CryptoAssetsPledgedAsCollateral_documentation_en-US" xlink:label="lab_gemi_CryptoAssetsPledgedAsCollateral" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Assets Pledged As Collateral</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoAssetsPledgedAsCollateral" xlink:href="gemi-20260930.xsd#gemi_CryptoAssetsPledgedAsCollateral"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoAssetsPledgedAsCollateral" xlink:to="lab_gemi_CryptoAssetsPledgedAsCollateral" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTextBlock_01a015a8-8a6b-7e79-8192-0c20cdb78d90_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Prepaid Expenses and Other Assets</link:label>
    <link:label id="lab_us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Costs, Capitalized, Prepaid, and Other Assets Disclosure [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTextBlock" xlink:to="lab_us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherSundryLiabilitiesCurrent_01a015a8-8b8d-7c09-af50-e3db95965955_terseLabel_en-US" xlink:label="lab_us-gaap_OtherSundryLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other current liabilities</link:label>
    <link:label id="lab_us-gaap_OtherSundryLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_OtherSundryLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Sundry Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherSundryLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherSundryLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherSundryLiabilitiesCurrent" xlink:to="lab_us-gaap_OtherSundryLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_IncreaseDecreaseInCryptoAssetDisposition_01a015a8-8b8d-7bfb-81da-74f1279f1519_terseLabel_en-US" xlink:label="lab_gemi_IncreaseDecreaseInCryptoAssetDisposition" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal of crypto assets</link:label>
    <link:label id="lab_gemi_IncreaseDecreaseInCryptoAssetDisposition_label_en-US" xlink:label="lab_gemi_IncreaseDecreaseInCryptoAssetDisposition" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) In Crypto Asset, Disposition</link:label>
    <link:label id="lab_gemi_IncreaseDecreaseInCryptoAssetDisposition_documentation_en-US" xlink:label="lab_gemi_IncreaseDecreaseInCryptoAssetDisposition" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Increase (Decrease) In Crypto Asset, Disposition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_IncreaseDecreaseInCryptoAssetDisposition" xlink:href="gemi-20260930.xsd#gemi_IncreaseDecreaseInCryptoAssetDisposition"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_IncreaseDecreaseInCryptoAssetDisposition" xlink:to="lab_gemi_IncreaseDecreaseInCryptoAssetDisposition" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_01a015a8-8b08-7737-aca3-6a076e810c35_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCommonStockSharesOutstanding" xlink:to="lab_dei_EntityCommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DevelopedTechnologyRightsMember_01a015a8-8b08-7ae4-a0d4-4e530f1b7a4f_verboseLabel_en-US" xlink:label="lab_us-gaap_DevelopedTechnologyRightsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Developed technology</link:label>
    <link:label id="lab_us-gaap_DevelopedTechnologyRightsMember_label_en-US" xlink:label="lab_us-gaap_DevelopedTechnologyRightsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Developed Technology Rights [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DevelopedTechnologyRightsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DevelopedTechnologyRightsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DevelopedTechnologyRightsMember" xlink:to="lab_us-gaap_DevelopedTechnologyRightsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentForAmortization_01a015a8-8b8d-7129-9b7d-d61980860e2b_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentForAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization expenses</link:label>
    <link:label id="lab_us-gaap_AdjustmentForAmortization_label_en-US" xlink:label="lab_us-gaap_AdjustmentForAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentForAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentForAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentForAmortization" xlink:to="lab_us-gaap_AdjustmentForAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeasesAbstract_label_en-US" xlink:label="lab_us-gaap_LeasesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leases [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeasesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LeasesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeasesAbstract" xlink:to="lab_us-gaap_LeasesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CommonUnitConversionMember_01a015a8-8b8d-74fd-a3a6-46d06dfd6e43_terseLabel_en-US" xlink:label="lab_gemi_CommonUnitConversionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion of Common Units to common stock in connection with IPO</link:label>
    <link:label id="lab_gemi_CommonUnitConversionMember_label_en-US" xlink:label="lab_gemi_CommonUnitConversionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Unit Conversion [Member]</link:label>
    <link:label id="lab_gemi_CommonUnitConversionMember_documentation_en-US" xlink:label="lab_gemi_CommonUnitConversionMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Unit Conversion</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CommonUnitConversionMember" xlink:href="gemi-20260930.xsd#gemi_CommonUnitConversionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CommonUnitConversionMember" xlink:to="lab_gemi_CommonUnitConversionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableNoncurrentPastDueTableTextBlock_01a015a8-8b8e-7688-80b1-500dfefd6ca1_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNoncurrentPastDueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Accounts Receivable, Noncurrent, Past Due</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableNoncurrentPastDueTableTextBlock_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableNoncurrentPastDueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Noncurrent, Past Due [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableNoncurrentPastDueTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableNoncurrentPastDueTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableNoncurrentPastDueTableTextBlock" xlink:to="lab_us-gaap_AccountsReceivableNoncurrentPastDueTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_01a015a8-8a6b-71b2-ae52-3323f99f241f_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transactions</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:to="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_01a015a8-8b08-7410-afd7-033408a9cb75_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Granted (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_01a015a8-8b08-7715-90a0-06b5493fc802_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesNoncurrentAbstract_01a015a8-8b08-7f1c-9696-55abcdd676a6_verboseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesNoncurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Non-current liabilities:</link:label>
    <link:label id="lab_us-gaap_LiabilitiesNoncurrentAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesNoncurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Noncurrent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesNoncurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesNoncurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesNoncurrentAbstract" xlink:to="lab_us-gaap_LiabilitiesNoncurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_01a015a8-8b08-733b-87f8-c12f88c01bab_periodStartLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Unvested beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_01a015a8-8b08-70e0-a7f2-34c0df46125e_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Unvested ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_RelatedPartyDebtIncludingAccruedInterestCurrent_01a015a8-8a6b-745a-a142-50e258097251_terseLabel_en-US" xlink:label="lab_gemi_RelatedPartyDebtIncludingAccruedInterestCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related party loans</link:label>
    <link:label id="lab_gemi_RelatedPartyDebtIncludingAccruedInterestCurrent_label_en-US" xlink:label="lab_gemi_RelatedPartyDebtIncludingAccruedInterestCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Debt, Including Accrued Interest, Current</link:label>
    <link:label id="lab_gemi_RelatedPartyDebtIncludingAccruedInterestCurrent_documentation_en-US" xlink:label="lab_gemi_RelatedPartyDebtIncludingAccruedInterestCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Debt, Including Accrued Interest, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_RelatedPartyDebtIncludingAccruedInterestCurrent" xlink:href="gemi-20260930.xsd#gemi_RelatedPartyDebtIncludingAccruedInterestCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_RelatedPartyDebtIncludingAccruedInterestCurrent" xlink:to="lab_gemi_RelatedPartyDebtIncludingAccruedInterestCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServiceAgreementsMember_01a10cbe-071b-7ff4-858c-4939e7176fbf_terseLabel_en-US" xlink:label="lab_us-gaap_ServiceAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Service Agreements</link:label>
    <link:label id="lab_us-gaap_ServiceAgreementsMember_label_en-US" xlink:label="lab_us-gaap_ServiceAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Service Agreements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServiceAgreementsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ServiceAgreementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServiceAgreementsMember" xlink:to="lab_us-gaap_ServiceAgreementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentCollateralAmount_01a015a8-8b08-7328-854f-485b307b0344_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCollateralAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit card receivables</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCollateralAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentCollateralAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Collateral Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCollateralAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentCollateralAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentCollateralAmount" xlink:to="lab_us-gaap_DebtInstrumentCollateralAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CryptoAssetRealizedAndUnrealizedGainLossOperating_01a015a8-8b08-706f-b1c7-bca0cf8af452_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetRealizedAndUnrealizedGainLossOperating" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Realized and unrealized loss (gain) on crypto assets and receivable, crypto assets pledged</link:label>
    <link:label id="lab_us-gaap_CryptoAssetRealizedAndUnrealizedGainLossOperating_label_en-US" xlink:label="lab_us-gaap_CryptoAssetRealizedAndUnrealizedGainLossOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Realized and Unrealized Gain (Loss), Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetRealizedAndUnrealizedGainLossOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetRealizedAndUnrealizedGainLossOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CryptoAssetRealizedAndUnrealizedGainLossOperating" xlink:to="lab_us-gaap_CryptoAssetRealizedAndUnrealizedGainLossOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingAggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingAggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingAggtErrCompAmt" xlink:to="lab_ecd_OutstandingAggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_01a015a8-8b08-7c4e-995d-d2a4966e55e2_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total current liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesCurrent" xlink:to="lab_us-gaap_LiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_CryptoAssetDomain_01a015a8-8a6b-7d55-9bb7-3385eed34b61_terseLabel_en-US" xlink:label="lab_srt_CryptoAssetDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto Asset [Domain]</link:label>
    <link:label id="lab_srt_CryptoAssetDomain_label_en-US" xlink:label="lab_srt_CryptoAssetDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CryptoAssetDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_CryptoAssetDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_CryptoAssetDomain" xlink:to="lab_srt_CryptoAssetDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CustomerRelationshipsMember_01a015a8-8b08-7646-9518-42c1d55637b9_verboseLabel_en-US" xlink:label="lab_us-gaap_CustomerRelationshipsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Customer relationships</link:label>
    <link:label id="lab_us-gaap_CustomerRelationshipsMember_label_en-US" xlink:label="lab_us-gaap_CustomerRelationshipsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer Relationships [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CustomerRelationshipsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CustomerRelationshipsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CustomerRelationshipsMember" xlink:to="lab_us-gaap_CustomerRelationshipsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesCurrent_01a015a8-8b08-79bf-8160-e1618f0608dc_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilitiesCurrent" xlink:to="lab_us-gaap_DerivativeLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_01a015a8-8b8d-7271-bce5-9feccd6bb0b5_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Breakdown of Crypto Asset Collateral Associated with Derivative Positions</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Instruments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDerivativeInstrumentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_A86BTCMarch112025Member_01a015a8-8a6b-7b3a-85a2-22569f28b8a9_terseLabel_en-US" xlink:label="lab_gemi_A86BTCMarch112025Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">86 BTC, March 11, 2025</link:label>
    <link:label id="lab_gemi_A86BTCMarch112025Member_label_en-US" xlink:label="lab_gemi_A86BTCMarch112025Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">86 BTC, March 11, 2025 [Member]</link:label>
    <link:label id="lab_gemi_A86BTCMarch112025Member_documentation_en-US" xlink:label="lab_gemi_A86BTCMarch112025Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">86 BTC, March 11, 2025</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_A86BTCMarch112025Member" xlink:href="gemi-20260930.xsd#gemi_A86BTCMarch112025Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_A86BTCMarch112025Member" xlink:to="lab_gemi_A86BTCMarch112025Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShortTermDebtTypeDomain_01a015a8-8b08-79e9-9a65-b67f8cec295e_terseLabel_en-US" xlink:label="lab_us-gaap_ShortTermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Short-Term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ShortTermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_ShortTermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShortTermDebtTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortTermDebtTypeDomain" xlink:to="lab_us-gaap_ShortTermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock_01a015a8-8a6b-705b-8394-d2b691f17ca8_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Assets at Fair Value</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Assets at Fair Value [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativeAssetsAtFairValueTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_01a015a8-8b08-7abe-bc43-1b2e82360f82_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CryptoAssetActivityTable_01a015a8-8b8d-7a78-88d5-6da457fb81cc_terseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetActivityTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto Asset, Activity [Table]</link:label>
    <link:label id="lab_us-gaap_CryptoAssetActivityTable_label_en-US" xlink:label="lab_us-gaap_CryptoAssetActivityTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Activity [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetActivityTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetActivityTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CryptoAssetActivityTable" xlink:to="lab_us-gaap_CryptoAssetActivityTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_01a015a8-8a6b-73a2-9243-438e28a3a637_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Granted (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CryptoAssetCumulativeRealizedGainFromDisposition_01a1a68e-893c-77a6-a226-aac8a54ef995_terseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetCumulativeRealizedGainFromDisposition" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Realized gains</link:label>
    <link:label id="lab_us-gaap_CryptoAssetCumulativeRealizedGainFromDisposition_label_en-US" xlink:label="lab_us-gaap_CryptoAssetCumulativeRealizedGainFromDisposition" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Cumulative Realized Gain from Disposition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetCumulativeRealizedGainFromDisposition" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetCumulativeRealizedGainFromDisposition"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CryptoAssetCumulativeRealizedGainFromDisposition" xlink:to="lab_us-gaap_CryptoAssetCumulativeRealizedGainFromDisposition" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_01a015a8-8b8d-78f0-a3d2-d7bc065755bd_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReceivablesAbstract_label_en-US" xlink:label="lab_us-gaap_ReceivablesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivables [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivablesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReceivablesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReceivablesAbstract" xlink:to="lab_us-gaap_ReceivablesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:to="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain_01a015a8-8b8d-789e-a2c5-26074f686de9_terseLabel_en-US" xlink:label="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title and Position [Domain]</link:label>
    <link:label id="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain_label_en-US" xlink:label="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title and Position [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_TitleOfIndividualWithRelationshipToEntityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:to="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_01a015a8-8b08-7976-a981-e6cd251fc127_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible assets, net</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_01a015a8-8b08-7f6c-bec4-d01bf91f08fd_totalLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Intangible Assets, Net</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, after Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeerGroupTotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:to="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_TemporaryEquityValueConversionOfConvertibleSecurities_01a015a8-8b08-7c35-b146-afaaafa878f6_negatedTerseLabel_en-US" xlink:label="lab_gemi_TemporaryEquityValueConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Conversion of convertible preferred units to common stock in connection with IPO</link:label>
    <link:label id="lab_gemi_TemporaryEquityValueConversionOfConvertibleSecurities_label_en-US" xlink:label="lab_gemi_TemporaryEquityValueConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Value, Conversion Of Convertible Securities</link:label>
    <link:label id="lab_gemi_TemporaryEquityValueConversionOfConvertibleSecurities_documentation_en-US" xlink:label="lab_gemi_TemporaryEquityValueConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Value, Conversion Of Convertible Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_TemporaryEquityValueConversionOfConvertibleSecurities" xlink:href="gemi-20260930.xsd#gemi_TemporaryEquityValueConversionOfConvertibleSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_TemporaryEquityValueConversionOfConvertibleSecurities" xlink:to="lab_gemi_TemporaryEquityValueConversionOfConvertibleSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_01a015a8-8a6b-7fda-a944-41e1262cc821_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 2</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel2Member" xlink:to="lab_us-gaap_FairValueInputsLevel2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpenseAbstract_01a015a8-8b8d-7b2d-92b0-42c7f09f229d_terseLabel_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income (expense):</link:label>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpenseAbstract_label_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonoperating Income (Expense) [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonoperatingIncomeExpenseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:to="lab_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TotalShareholderRtnVsPeerGroupTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:to="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonRule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:to="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember_01a015a8-8b8e-7a60-abff-08eec3bca1c1_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equal to or Greater than 90 Days</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Equal to or Greater than 90 Days Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:to="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_country_US_01a015a8-8b08-789b-bfcb-ea79752a1642_terseLabel_en-US" xlink:label="lab_country_US" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U.S.</link:label>
    <link:label id="lab_country_US_label_en-US" xlink:label="lab_country_US" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">UNITED STATES</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_US" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_US"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_US" xlink:to="lab_country_US" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_OtherFeesReceivableNettingMember_01a015a8-8a6b-76af-9432-d3a0c270a5da_verboseLabel_en-US" xlink:label="lab_gemi_OtherFeesReceivableNettingMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other fees receivable</link:label>
    <link:label id="lab_gemi_OtherFeesReceivableNettingMember_01a015a8-8a6b-7985-9b13-eaac4486a029_terseLabel_en-US" xlink:label="lab_gemi_OtherFeesReceivableNettingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other fees receivable</link:label>
    <link:label id="lab_gemi_OtherFeesReceivableNettingMember_label_en-US" xlink:label="lab_gemi_OtherFeesReceivableNettingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Fees Receivable, Netting [Member]</link:label>
    <link:label id="lab_gemi_OtherFeesReceivableNettingMember_documentation_en-US" xlink:label="lab_gemi_OtherFeesReceivableNettingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Fees Receivable, Netting</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_OtherFeesReceivableNettingMember" xlink:href="gemi-20260930.xsd#gemi_OtherFeesReceivableNettingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_OtherFeesReceivableNettingMember" xlink:to="lab_gemi_OtherFeesReceivableNettingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_01a015a8-8a6b-7358-b7a2-6aacc66c34ba_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeAxis" xlink:to="lab_us-gaap_SubsequentEventTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTable_01a015a8-8b8d-7afc-a395-935a65716457_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTable_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTable" xlink:to="lab_us-gaap_DebtInstrumentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UseOfEstimates_01a015a8-8a6b-7f65-8edf-140c96f84996_terseLabel_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Use of estimates</link:label>
    <link:label id="lab_us-gaap_UseOfEstimates_label_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Use of Estimates, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UseOfEstimates" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UseOfEstimates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UseOfEstimates" xlink:to="lab_us-gaap_UseOfEstimates" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_01a015a8-8b08-766b-9e9a-b7d0a0ffb329_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueUpwardPriceAdjustmentCumulativeAmount_01a015a8-8b08-744f-bef1-389ff979fdf7_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueUpwardPriceAdjustmentCumulativeAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cumulative upward adjustments for strategic investments</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueUpwardPriceAdjustmentCumulativeAmount_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueUpwardPriceAdjustmentCumulativeAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities without Readily Determinable Fair Value, Upward Price Adjustment, Cumulative Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueUpwardPriceAdjustmentCumulativeAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueUpwardPriceAdjustmentCumulativeAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueUpwardPriceAdjustmentCumulativeAmount" xlink:to="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueUpwardPriceAdjustmentCumulativeAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_01a015a8-8b08-7187-87fd-2d08be218ce4_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total other comprehensive income (loss)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_01a015a8-8b08-75e8-92fe-8093ed04a4c2_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income (loss)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_01a015a8-8b8d-71eb-96e6-88c88e0aea34_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Roll-Forward of Level 3 Investments Measured on Recurring Basis</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_RelatedPartyDebtReceivedInCryptoAssets_01a1cda5-a508-7a34-ae8c-a35846f3736c_terseLabel_en-US" xlink:label="lab_gemi_RelatedPartyDebtReceivedInCryptoAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related party debt, received in crypto assets</link:label>
    <link:label id="lab_gemi_RelatedPartyDebtReceivedInCryptoAssets_label_en-US" xlink:label="lab_gemi_RelatedPartyDebtReceivedInCryptoAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Debt, Received In Crypto Assets</link:label>
    <link:label id="lab_gemi_RelatedPartyDebtReceivedInCryptoAssets_documentation_en-US" xlink:label="lab_gemi_RelatedPartyDebtReceivedInCryptoAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Debt, Received In Crypto Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_RelatedPartyDebtReceivedInCryptoAssets" xlink:href="gemi-20260930.xsd#gemi_RelatedPartyDebtReceivedInCryptoAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_RelatedPartyDebtReceivedInCryptoAssets" xlink:to="lab_gemi_RelatedPartyDebtReceivedInCryptoAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_CryptoAssetOtherMember_01a015a8-8a6b-7034-b005-4264a6fed58c_terseLabel_en-US" xlink:label="lab_srt_CryptoAssetOtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other crypto assets</link:label>
    <link:label id="lab_srt_CryptoAssetOtherMember_01a015a8-8a6b-77e6-8b88-bfc3cdd2ab8f_verboseLabel_en-US" xlink:label="lab_srt_CryptoAssetOtherMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_srt_CryptoAssetOtherMember_label_en-US" xlink:label="lab_srt_CryptoAssetOtherMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Other [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CryptoAssetOtherMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_CryptoAssetOtherMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_CryptoAssetOtherMember" xlink:to="lab_srt_CryptoAssetOtherMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_01a015a8-8b08-7c63-aaec-6342cd29f69d_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Maturities of Operating Lease Liabilities</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Maturity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentPeriodEndDate_01a015a8-8b8d-75bc-8d19-c928a2699d12_terseLabel_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:label id="lab_dei_DocumentPeriodEndDate_label_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Period End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentPeriodEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentPeriodEndDate" xlink:to="lab_dei_DocumentPeriodEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_TransactionAndServiceRevenueAndInterestIncomeMember_01a015a8-8b08-744c-909d-15c1a76c24c5_terseLabel_en-US" xlink:label="lab_gemi_TransactionAndServiceRevenueAndInterestIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net revenue</link:label>
    <link:label id="lab_gemi_TransactionAndServiceRevenueAndInterestIncomeMember_label_en-US" xlink:label="lab_gemi_TransactionAndServiceRevenueAndInterestIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transaction And Service Revenue And Interest Income [Member]</link:label>
    <link:label id="lab_gemi_TransactionAndServiceRevenueAndInterestIncomeMember_documentation_en-US" xlink:label="lab_gemi_TransactionAndServiceRevenueAndInterestIncomeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Product And Service Revenue And Interest Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_TransactionAndServiceRevenueAndInterestIncomeMember" xlink:href="gemi-20260930.xsd#gemi_TransactionAndServiceRevenueAndInterestIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_TransactionAndServiceRevenueAndInterestIncomeMember" xlink:to="lab_gemi_TransactionAndServiceRevenueAndInterestIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_01a015a8-8b08-77fd-902f-e195c701dcc4_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesOutstanding" xlink:to="lab_us-gaap_PreferredStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_01a015a8-8b08-7043-b335-282902b601d1_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, face amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Face Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFaceAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentFaceAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFaceAmount" xlink:to="lab_us-gaap_DebtInstrumentFaceAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasicAbstract_01a015a8-8b08-7a65-a22a-d220bbaa0c8e_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net loss per share attributable to common stockholders:</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasicAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasicAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareBasicAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasicAbstract" xlink:to="lab_us-gaap_EarningsPerShareBasicAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_01a015a8-8b08-7e7b-bd7a-5ce67048a684_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ConvertibleDebtAndLoansPayableMember_01a015a8-8b08-7abd-aae2-4358ebe5ff68_terseLabel_en-US" xlink:label="lab_gemi_ConvertibleDebtAndLoansPayableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Convertible Debt And Loans Payable</link:label>
    <link:label id="lab_gemi_ConvertibleDebtAndLoansPayableMember_label_en-US" xlink:label="lab_gemi_ConvertibleDebtAndLoansPayableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Convertible Debt And Loans Payable [Member]</link:label>
    <link:label id="lab_gemi_ConvertibleDebtAndLoansPayableMember_documentation_en-US" xlink:label="lab_gemi_ConvertibleDebtAndLoansPayableMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Convertible Debt And Loans Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ConvertibleDebtAndLoansPayableMember" xlink:href="gemi-20260930.xsd#gemi_ConvertibleDebtAndLoansPayableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ConvertibleDebtAndLoansPayableMember" xlink:to="lab_gemi_ConvertibleDebtAndLoansPayableMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockCommonValue_01a015a8-8b08-70c6-984f-19791a718126_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonValue" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Treasury stock at cost; 1,392 and 284 shares as of September&#160;30, 2026 and December&#160;31, 2025, respectively</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonValue_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockCommonValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonValue" xlink:to="lab_us-gaap_TreasuryStockCommonValue" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoAssetPledgedAmount_01a1cd65-6f2c-7064-a673-585b0e535b2c_terseLabel_en-US" xlink:label="lab_gemi_CryptoAssetPledgedAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nominal value</link:label>
    <link:label id="lab_gemi_CryptoAssetPledgedAmount_label_en-US" xlink:label="lab_gemi_CryptoAssetPledgedAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset Pledged, Amount</link:label>
    <link:label id="lab_gemi_CryptoAssetPledgedAmount_documentation_en-US" xlink:label="lab_gemi_CryptoAssetPledgedAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Asset Pledged, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoAssetPledgedAmount" xlink:href="gemi-20260930.xsd#gemi_CryptoAssetPledgedAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoAssetPledgedAmount" xlink:to="lab_gemi_CryptoAssetPledgedAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_DerivativeInstrumentRecognitionCriteriaDomain_01a015a8-8b8d-73fa-a6d1-9a9df1ed591f_terseLabel_en-US" xlink:label="lab_gemi_DerivativeInstrumentRecognitionCriteriaDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Recognition Criteria [Domain]</link:label>
    <link:label id="lab_gemi_DerivativeInstrumentRecognitionCriteriaDomain_label_en-US" xlink:label="lab_gemi_DerivativeInstrumentRecognitionCriteriaDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Recognition Criteria [Domain]</link:label>
    <link:label id="lab_gemi_DerivativeInstrumentRecognitionCriteriaDomain_documentation_en-US" xlink:label="lab_gemi_DerivativeInstrumentRecognitionCriteriaDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Recognition Criteria [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_DerivativeInstrumentRecognitionCriteriaDomain" xlink:href="gemi-20260930.xsd#gemi_DerivativeInstrumentRecognitionCriteriaDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_DerivativeInstrumentRecognitionCriteriaDomain" xlink:to="lab_gemi_DerivativeInstrumentRecognitionCriteriaDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionLineItems_01a015a8-8b8d-7e3a-a065-529b8e65adb0_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Leased Assets [Line Items]</link:label>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionLineItems_label_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeLeaseDescriptionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeLeaseDescriptionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeLeaseDescriptionLineItems" xlink:to="lab_us-gaap_LesseeLeaseDescriptionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue_01a015a8-8a6b-7bd5-a853-3e85a9b8b912_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate fair value for awards vested</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Vested in Period, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_RelatedPartyDebtReceivedInCryptoAsset_01a015a8-8b08-715b-94dd-fb0a9853712c_terseLabel_en-US" xlink:label="lab_gemi_RelatedPartyDebtReceivedInCryptoAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related party loans received in crypto assets</link:label>
    <link:label id="lab_gemi_RelatedPartyDebtReceivedInCryptoAsset_01a015a8-8b08-7724-b730-d49582f3df41_verboseLabel_en-US" xlink:label="lab_gemi_RelatedPartyDebtReceivedInCryptoAsset" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Amount Borrowed</link:label>
    <link:label id="lab_gemi_RelatedPartyDebtReceivedInCryptoAsset_label_en-US" xlink:label="lab_gemi_RelatedPartyDebtReceivedInCryptoAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Debt, Received In Crypto Asset</link:label>
    <link:label id="lab_gemi_RelatedPartyDebtReceivedInCryptoAsset_documentation_en-US" xlink:label="lab_gemi_RelatedPartyDebtReceivedInCryptoAsset" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Debt, Received In Crypto Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_RelatedPartyDebtReceivedInCryptoAsset" xlink:href="gemi-20260930.xsd#gemi_RelatedPartyDebtReceivedInCryptoAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_RelatedPartyDebtReceivedInCryptoAsset" xlink:to="lab_gemi_RelatedPartyDebtReceivedInCryptoAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_01a015a8-8b08-76d8-967a-a0347f9c824c_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated other comprehensive income</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityShellCompany_01a015a8-8b8d-794a-a337-03fa770c58dc_terseLabel_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:label id="lab_dei_EntityShellCompany_label_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityShellCompany" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityShellCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityShellCompany" xlink:to="lab_dei_EntityShellCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonClassBMember_01a015a8-8b8d-7ec2-8016-2e325bc6582e_terseLabel_en-US" xlink:label="lab_us-gaap_CommonClassBMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Class B</link:label>
    <link:label id="lab_us-gaap_CommonClassBMember_label_en-US" xlink:label="lab_us-gaap_CommonClassBMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Class B [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassBMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassBMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonClassBMember" xlink:to="lab_us-gaap_CommonClassBMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_TransactionRevenueOverTheCounterMember_01a015a8-8b8d-7774-93ad-04cc7cdcfa81_terseLabel_en-US" xlink:label="lab_gemi_TransactionRevenueOverTheCounterMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">OTC</link:label>
    <link:label id="lab_gemi_TransactionRevenueOverTheCounterMember_label_en-US" xlink:label="lab_gemi_TransactionRevenueOverTheCounterMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transaction Revenue, Over-The-Counter [Member]</link:label>
    <link:label id="lab_gemi_TransactionRevenueOverTheCounterMember_documentation_en-US" xlink:label="lab_gemi_TransactionRevenueOverTheCounterMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Transaction Revenue, Over-The-Counter</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_TransactionRevenueOverTheCounterMember" xlink:href="gemi-20260930.xsd#gemi_TransactionRevenueOverTheCounterMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_TransactionRevenueOverTheCounterMember" xlink:to="lab_gemi_TransactionRevenueOverTheCounterMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoAssetsPostedReturnedAsCollateralForDerivatives_01a015a8-8b08-762c-9041-eb5ef9cb0bc0_terseLabel_en-US" xlink:label="lab_gemi_CryptoAssetsPostedReturnedAsCollateralForDerivatives" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto assets posted (returned) as collateral for derivatives, net</link:label>
    <link:label id="lab_gemi_CryptoAssetsPostedReturnedAsCollateralForDerivatives_label_en-US" xlink:label="lab_gemi_CryptoAssetsPostedReturnedAsCollateralForDerivatives" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Assets Posted (Returned) As Collateral For Derivatives</link:label>
    <link:label id="lab_gemi_CryptoAssetsPostedReturnedAsCollateralForDerivatives_documentation_en-US" xlink:label="lab_gemi_CryptoAssetsPostedReturnedAsCollateralForDerivatives" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Assets Posted (Returned) As Collateral For Derivatives</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoAssetsPostedReturnedAsCollateralForDerivatives" xlink:href="gemi-20260930.xsd#gemi_CryptoAssetsPostedReturnedAsCollateralForDerivatives"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoAssetsPostedReturnedAsCollateralForDerivatives" xlink:to="lab_gemi_CryptoAssetsPostedReturnedAsCollateralForDerivatives" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings_01a015a8-8a6b-774e-b63a-ef5374ebaebf_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized loss attributable to change in fair value</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Gain (Loss) Included in Earnings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityCurrent_01a015a8-8b08-7003-a37d-6d57570c0e6c_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current lease liabilities</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityCurrent_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilityCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilityCurrent" xlink:to="lab_us-gaap_OperatingLeaseLiabilityCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock_01a015a8-8b08-7fca-8001-bbb7b3c2da95_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Allowance for Transaction Losses</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock" xlink:to="lab_us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_01a015a8-8b8d-7be2-b950-6e6b7b37670d_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Loss Per Share</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareTextBlock" xlink:to="lab_us-gaap_EarningsPerShareTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_01a015a8-8b08-7915-a4aa-4cb94baac742_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net loss per share attributable to common stockholders:</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareAbstract" xlink:to="lab_us-gaap_EarningsPerShareAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_01a015a8-8b08-7bb1-9993-8500d0a8d3a1_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalPeriodFocus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalPeriodFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalPeriodFocus" xlink:to="lab_dei_DocumentFiscalPeriodFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote</link:label>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_label_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeerGroupIssuersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:to="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Liabilities_01a015a8-8b8d-77c3-ad1d-6236b63657b5_totalLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_label_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Liabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Liabilities" xlink:to="lab_us-gaap_Liabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_TradingSymbol_01a015a8-8b08-7344-9c14-fcd991e9e169_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:label id="lab_dei_TradingSymbol_label_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_TradingSymbol"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_TradingSymbol" xlink:to="lab_dei_TradingSymbol" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputDiscountRateMember_01a015a8-8b8d-7575-93ec-f3274cfcc577_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input, Discount Rate</link:label>
    <link:label id="lab_us-gaap_MeasurementInputDiscountRateMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Discount Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputDiscountRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputDiscountRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputDiscountRateMember" xlink:to="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRepurchaseAgreementCounterpartyTable_01a015a8-8b08-7adc-8b29-8a0fd39ea616_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRepurchaseAgreementCounterpartyTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase Agreement, Counterparty [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRepurchaseAgreementCounterpartyTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRepurchaseAgreementCounterpartyTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repurchase Agreement, Counterparty [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRepurchaseAgreementCounterpartyTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRepurchaseAgreementCounterpartyTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRepurchaseAgreementCounterpartyTable" xlink:to="lab_us-gaap_ScheduleOfRepurchaseAgreementCounterpartyTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_01a015a8-8b8d-7761-a752-69de4a7f8a77_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchase of software, property and equipment</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:to="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_FinancingAgreementsCryptoAssetPledgedNumberOfUnits_01a015a8-8b8d-720f-bbab-af88c0cec7f4_terseLabel_en-US" xlink:label="lab_gemi_FinancingAgreementsCryptoAssetPledgedNumberOfUnits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pledged crypto subject to a margin call (in units)</link:label>
    <link:label id="lab_gemi_FinancingAgreementsCryptoAssetPledgedNumberOfUnits_label_en-US" xlink:label="lab_gemi_FinancingAgreementsCryptoAssetPledgedNumberOfUnits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Agreements, Crypto Asset, Pledged, Number Of Units</link:label>
    <link:label id="lab_gemi_FinancingAgreementsCryptoAssetPledgedNumberOfUnits_documentation_en-US" xlink:label="lab_gemi_FinancingAgreementsCryptoAssetPledgedNumberOfUnits" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Agreements, Crypto Asset, Pledged, Number Of Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_FinancingAgreementsCryptoAssetPledgedNumberOfUnits" xlink:href="gemi-20260930.xsd#gemi_FinancingAgreementsCryptoAssetPledgedNumberOfUnits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_FinancingAgreementsCryptoAssetPledgedNumberOfUnits" xlink:to="lab_gemi_FinancingAgreementsCryptoAssetPledgedNumberOfUnits" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoAssetIssuedAsCollateralFairValue_01a015a8-8b08-76fe-81fa-5103ee737ec0_terseLabel_en-US" xlink:label="lab_gemi_CryptoAssetIssuedAsCollateralFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of crypto assets designed as collateral</link:label>
    <link:label id="lab_gemi_CryptoAssetIssuedAsCollateralFairValue_label_en-US" xlink:label="lab_gemi_CryptoAssetIssuedAsCollateralFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Issued As Collateral, Fair Value</link:label>
    <link:label id="lab_gemi_CryptoAssetIssuedAsCollateralFairValue_documentation_en-US" xlink:label="lab_gemi_CryptoAssetIssuedAsCollateralFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Asset, Issued As Collateral, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoAssetIssuedAsCollateralFairValue" xlink:href="gemi-20260930.xsd#gemi_CryptoAssetIssuedAsCollateralFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoAssetIssuedAsCollateralFairValue" xlink:to="lab_gemi_CryptoAssetIssuedAsCollateralFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureName_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureName_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CoSelectedMeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureName" xlink:to="lab_ecd_CoSelectedMeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_01a015a8-8b08-7774-b0e6-f8cbcced54db_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_label_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockNameOfTransactionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_A3400ETHMarch102025Member_01a015a8-8a6b-7d02-a5e9-f909f98592ec_terseLabel_en-US" xlink:label="lab_gemi_A3400ETHMarch102025Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">3,400 ETH March 10, 2025</link:label>
    <link:label id="lab_gemi_A3400ETHMarch102025Member_label_en-US" xlink:label="lab_gemi_A3400ETHMarch102025Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">3,400 ETH March 10, 2025 [Member]</link:label>
    <link:label id="lab_gemi_A3400ETHMarch102025Member_documentation_en-US" xlink:label="lab_gemi_A3400ETHMarch102025Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">3,400 ETH March 10, 2025</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_A3400ETHMarch102025Member" xlink:href="gemi-20260930.xsd#gemi_A3400ETHMarch102025Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_A3400ETHMarch102025Member" xlink:to="lab_gemi_A3400ETHMarch102025Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:to="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansPayableToBankCurrent_01a015a8-8b8d-7a83-be22-c04314b2a240_terseLabel_en-US" xlink:label="lab_us-gaap_LoansPayableToBankCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payable to Issuing Bank</link:label>
    <link:label id="lab_us-gaap_LoansPayableToBankCurrent_label_en-US" xlink:label="lab_us-gaap_LoansPayableToBankCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Payable to Bank, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansPayableToBankCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LoansPayableToBankCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansPayableToBankCurrent" xlink:to="lab_us-gaap_LoansPayableToBankCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasicLineItems_01a015a8-8b08-78ff-9c69-5c5c04d76694_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasicLineItems_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasicLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareBasicLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasicLineItems" xlink:to="lab_us-gaap_EarningsPerShareBasicLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CryptoAssetHoldingTable_01a015a8-8a6b-7a94-8e3f-4efb47a6096e_terseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetHoldingTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto Asset, Holding [Table]</link:label>
    <link:label id="lab_us-gaap_CryptoAssetHoldingTable_label_en-US" xlink:label="lab_us-gaap_CryptoAssetHoldingTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Holding [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetHoldingTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetHoldingTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CryptoAssetHoldingTable" xlink:to="lab_us-gaap_CryptoAssetHoldingTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityDomain_01a015a8-8b08-7dab-bf93-2dd2b4600dc4_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityDomain_label_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CreditFacilityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityDomain" xlink:to="lab_us-gaap_CreditFacilityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_01a015a8-8b08-729a-997f-08e0a4067f82_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_RepurchaseAgreementsSecuritiesTransferred_01a015a8-8b08-73ee-b06c-2a05450dd5f8_terseLabel_en-US" xlink:label="lab_gemi_RepurchaseAgreementsSecuritiesTransferred" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transferred amount (in units)</link:label>
    <link:label id="lab_gemi_RepurchaseAgreementsSecuritiesTransferred_label_en-US" xlink:label="lab_gemi_RepurchaseAgreementsSecuritiesTransferred" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repurchase Agreements, Securities Transferred</link:label>
    <link:label id="lab_gemi_RepurchaseAgreementsSecuritiesTransferred_documentation_en-US" xlink:label="lab_gemi_RepurchaseAgreementsSecuritiesTransferred" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Repurchase Agreements, Securities Transferred</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_RepurchaseAgreementsSecuritiesTransferred" xlink:href="gemi-20260930.xsd#gemi_RepurchaseAgreementsSecuritiesTransferred"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_RepurchaseAgreementsSecuritiesTransferred" xlink:to="lab_gemi_RepurchaseAgreementsSecuritiesTransferred" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_LesseeOperatingLeaseTerminationFee_01a015a8-8a6b-7024-8c42-062325a61376_terseLabel_en-US" xlink:label="lab_gemi_LesseeOperatingLeaseTerminationFee" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease termination fee</link:label>
    <link:label id="lab_gemi_LesseeOperatingLeaseTerminationFee_label_en-US" xlink:label="lab_gemi_LesseeOperatingLeaseTerminationFee" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Termination Fee</link:label>
    <link:label id="lab_gemi_LesseeOperatingLeaseTerminationFee_documentation_en-US" xlink:label="lab_gemi_LesseeOperatingLeaseTerminationFee" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Termination Fee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_LesseeOperatingLeaseTerminationFee" xlink:href="gemi-20260930.xsd#gemi_LesseeOperatingLeaseTerminationFee"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_LesseeOperatingLeaseTerminationFee" xlink:to="lab_gemi_LesseeOperatingLeaseTerminationFee" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_TotalCollateralAssociatedWithFinancingAgreements_01a015a8-8b8d-77b2-a54e-055aae0b81bd_terseLabel_en-US" xlink:label="lab_gemi_TotalCollateralAssociatedWithFinancingAgreements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral amount</link:label>
    <link:label id="lab_gemi_TotalCollateralAssociatedWithFinancingAgreements_label_en-US" xlink:label="lab_gemi_TotalCollateralAssociatedWithFinancingAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Collateral Associated With Financing Agreements</link:label>
    <link:label id="lab_gemi_TotalCollateralAssociatedWithFinancingAgreements_documentation_en-US" xlink:label="lab_gemi_TotalCollateralAssociatedWithFinancingAgreements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Total Collateral Associated With Financing Agreements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_TotalCollateralAssociatedWithFinancingAgreements" xlink:href="gemi-20260930.xsd#gemi_TotalCollateralAssociatedWithFinancingAgreements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_TotalCollateralAssociatedWithFinancingAgreements" xlink:to="lab_gemi_TotalCollateralAssociatedWithFinancingAgreements" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote</link:label>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_label_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EquityValuationAssumptionDifferenceFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:to="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonvestedForfeituresInPeriod_01a015a8-8a6b-7d59-834c-3cefd95020e9_terseLabel_en-US" xlink:label="lab_gemi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonvestedForfeituresInPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forfeitures of unvested awards</link:label>
    <link:label id="lab_gemi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonvestedForfeituresInPeriod_label_en-US" xlink:label="lab_gemi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonvestedForfeituresInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement By Share-Based Payment Award, Nonvested, Forfeitures In Period</link:label>
    <link:label id="lab_gemi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonvestedForfeituresInPeriod_documentation_en-US" xlink:label="lab_gemi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonvestedForfeituresInPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement By Share-Based Payment Award, Nonvested, Forfeitures In Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonvestedForfeituresInPeriod" xlink:href="gemi-20260930.xsd#gemi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonvestedForfeituresInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonvestedForfeituresInPeriod" xlink:to="lab_gemi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonvestedForfeituresInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ConvertiblePreferredUnitsMember_01a015a8-8b08-71be-97ca-856bdc55e855_verboseLabel_en-US" xlink:label="lab_gemi_ConvertiblePreferredUnitsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Conversion of convertible preferred units to common stock in connection with IPO</link:label>
    <link:label id="lab_gemi_ConvertiblePreferredUnitsMember_label_en-US" xlink:label="lab_gemi_ConvertiblePreferredUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Convertible Preferred Units [Member]</link:label>
    <link:label id="lab_gemi_ConvertiblePreferredUnitsMember_documentation_en-US" xlink:label="lab_gemi_ConvertiblePreferredUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Convertible Preferred Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ConvertiblePreferredUnitsMember" xlink:href="gemi-20260930.xsd#gemi_ConvertiblePreferredUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ConvertiblePreferredUnitsMember" xlink:to="lab_gemi_ConvertiblePreferredUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_FinancingAgreementsInterestPayable_01a015a8-8b8d-75ff-a54d-e34adb03a6da_terseLabel_en-US" xlink:label="lab_gemi_FinancingAgreementsInterestPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Payable</link:label>
    <link:label id="lab_gemi_FinancingAgreementsInterestPayable_label_en-US" xlink:label="lab_gemi_FinancingAgreementsInterestPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Agreements, Interest Payable</link:label>
    <link:label id="lab_gemi_FinancingAgreementsInterestPayable_documentation_en-US" xlink:label="lab_gemi_FinancingAgreementsInterestPayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Agreements, Interest Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_FinancingAgreementsInterestPayable" xlink:href="gemi-20260930.xsd#gemi_FinancingAgreementsInterestPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_FinancingAgreementsInterestPayable" xlink:to="lab_gemi_FinancingAgreementsInterestPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_01a015a8-8b8d-781d-b699-e1fe2ecb0445_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:to="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity_01a015a8-8b8d-7734-b385-f91daec2edba_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of credit facility, current borrowing capacity</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Current Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy_01a015a8-8a6b-77aa-b899-1810dabbbbe3_verboseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Customer custodial funds and custodial funds due to customers</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Restricted Cash and Cash Equivalents, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:to="lab_us-gaap_CashAndCashEquivalentsRestrictedCashAndCashEquivalentsPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ScheduleOfFinancingFacilityAgreementsTableTextBlock_01a015a8-8b8d-721f-9ef9-3d7df3060cd3_terseLabel_en-US" xlink:label="lab_gemi_ScheduleOfFinancingFacilityAgreementsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Financing Facility Agreements</link:label>
    <link:label id="lab_gemi_ScheduleOfFinancingFacilityAgreementsTableTextBlock_label_en-US" xlink:label="lab_gemi_ScheduleOfFinancingFacilityAgreementsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Financing Facility Agreements [Table Text Block]</link:label>
    <link:label id="lab_gemi_ScheduleOfFinancingFacilityAgreementsTableTextBlock_documentation_en-US" xlink:label="lab_gemi_ScheduleOfFinancingFacilityAgreementsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Financing Facility Agreements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ScheduleOfFinancingFacilityAgreementsTableTextBlock" xlink:href="gemi-20260930.xsd#gemi_ScheduleOfFinancingFacilityAgreementsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ScheduleOfFinancingFacilityAgreementsTableTextBlock" xlink:to="lab_gemi_ScheduleOfFinancingFacilityAgreementsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined</link:label>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_label_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgPredtrmndFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgPredtrmndFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgPredtrmndFlag" xlink:to="lab_ecd_AwardTmgPredtrmndFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote</link:label>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToPeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToPeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToPeoCompFnTextBlock" xlink:to="lab_ecd_AdjToPeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_01a015a8-8b8d-795a-99c0-445a5619a347_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock-based compensation</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:to="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_01a015a8-8b08-7780-ad9f-85bc1bb9b7bf_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 1</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel1Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel1Member" xlink:to="lab_us-gaap_FairValueInputsLevel1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SoftwareDevelopmentMember_01a015a8-8b8d-74c7-ae5a-6cb17507eba1_verboseLabel_en-US" xlink:label="lab_us-gaap_SoftwareDevelopmentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Software</link:label>
    <link:label id="lab_us-gaap_SoftwareDevelopmentMember_label_en-US" xlink:label="lab_us-gaap_SoftwareDevelopmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Software, Internally Developed [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SoftwareDevelopmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SoftwareDevelopmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SoftwareDevelopmentMember" xlink:to="lab_us-gaap_SoftwareDevelopmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations_01a015a8-8b8d-7444-be18-20855f358c63_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effective tax rate</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EffectiveIncomeTaxRateContinuingOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability_01a015a8-8b8d-7e81-ac6d-aa6b82e54c56_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability_01a015a8-8b8d-7f92-8de4-0623144fe35c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Lease liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Operating Lease Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOperatingLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_01a015a8-8b08-7737-9ee5-dd8b1586a4be_verboseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Depreciation_01a015a8-8b8d-758f-928a-349691482c20_terseLabel_en-US" xlink:label="lab_us-gaap_Depreciation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation expense</link:label>
    <link:label id="lab_us-gaap_Depreciation_label_en-US" xlink:label="lab_us-gaap_Depreciation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Depreciation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Depreciation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Depreciation" xlink:to="lab_us-gaap_Depreciation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_01a015a8-8a6b-73e6-8bbf-a80b59bc2ceb_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis"/>
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    <link:label id="lab_srt_ScenarioUnspecifiedDomain_01a1abfb-15ed-7937-912a-2cab2dcf35cc_terseLabel_en-US" xlink:label="lab_srt_ScenarioUnspecifiedDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario [Domain]</link:label>
    <link:label id="lab_srt_ScenarioUnspecifiedDomain_label_en-US" xlink:label="lab_srt_ScenarioUnspecifiedDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScenarioUnspecifiedDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ScenarioUnspecifiedDomain"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_01a015a8-8b08-79c5-ab8d-dc4995a22974_periodStartLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_01a015a8-8b08-733b-bc2a-9e9381c125d9_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance (in dollars per share)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingRollForward_01a015a8-8a6b-7a2b-ab1f-e78a3bd144fa_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Non-Option Equity Instruments, Outstanding [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingRollForward_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Non-Option Equity Instruments, Outstanding [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingRollForward" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueImpairmentLossAndDownwardPriceAdjustmentCumulativeAmount_01a015a8-8a6b-721d-be6a-c613a8ac5718_terseLabel_en-US" xlink:label="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueImpairmentLossAndDownwardPriceAdjustmentCumulativeAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cumulative impairments and downward adjustments</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueImpairmentLossAndDownwardPriceAdjustmentCumulativeAmount" xlink:href="gemi-20260930.xsd#gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueImpairmentLossAndDownwardPriceAdjustmentCumulativeAmount"/>
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    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_01a015a8-8a6b-7ef7-a2c6-1644a944c737_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease right-of-use assets, net</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LegalFees_01a1ac00-6c45-733a-abc0-114dc86e2a78_terseLabel_en-US" xlink:label="lab_us-gaap_LegalFees" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legal fees</link:label>
    <link:label id="lab_us-gaap_LegalFees_label_en-US" xlink:label="lab_us-gaap_LegalFees" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legal Fees</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LegalFees" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LegalFees"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LegalFees" xlink:to="lab_us-gaap_LegalFees" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_FinancingAgreementsSecuritiesTransferred_01a015a8-8b8d-76df-a0e4-92a32d6ad8d7_terseLabel_en-US" xlink:label="lab_gemi_FinancingAgreementsSecuritiesTransferred" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing agreements, securities transferred</link:label>
    <link:label id="lab_gemi_FinancingAgreementsSecuritiesTransferred_label_en-US" xlink:label="lab_gemi_FinancingAgreementsSecuritiesTransferred" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Agreements, Securities Transferred</link:label>
    <link:label id="lab_gemi_FinancingAgreementsSecuritiesTransferred_documentation_en-US" xlink:label="lab_gemi_FinancingAgreementsSecuritiesTransferred" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Agreements, Securities Transferred</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_FinancingAgreementsSecuritiesTransferred" xlink:href="gemi-20260930.xsd#gemi_FinancingAgreementsSecuritiesTransferred"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_FinancingAgreementsSecuritiesTransferred" xlink:to="lab_gemi_FinancingAgreementsSecuritiesTransferred" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CustomerCustodialFundsDueToCustomersGeminiDollar_01a015a8-8b8d-78f0-b540-3b4321d697e8_negatedTerseLabel_en-US" xlink:label="lab_gemi_CustomerCustodialFundsDueToCustomersGeminiDollar" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Customer custodial funds due to customers</link:label>
    <link:label id="lab_gemi_CustomerCustodialFundsDueToCustomersGeminiDollar_label_en-US" xlink:label="lab_gemi_CustomerCustodialFundsDueToCustomersGeminiDollar" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer Custodial Funds Due To Customers, Gemini Dollar</link:label>
    <link:label id="lab_gemi_CustomerCustodialFundsDueToCustomersGeminiDollar_documentation_en-US" xlink:label="lab_gemi_CustomerCustodialFundsDueToCustomersGeminiDollar" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Customer Custodial Funds Due To Customers, Gemini Dollar</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CustomerCustodialFundsDueToCustomersGeminiDollar" xlink:href="gemi-20260930.xsd#gemi_CustomerCustodialFundsDueToCustomersGeminiDollar"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CustomerCustodialFundsDueToCustomersGeminiDollar" xlink:to="lab_gemi_CustomerCustodialFundsDueToCustomersGeminiDollar" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_SanFranciscoOfficeLeaseMember_01a015a8-8b8d-733b-9552-6653cb2cbf98_terseLabel_en-US" xlink:label="lab_gemi_SanFranciscoOfficeLeaseMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">San Francisco Office Lease</link:label>
    <link:label id="lab_gemi_SanFranciscoOfficeLeaseMember_label_en-US" xlink:label="lab_gemi_SanFranciscoOfficeLeaseMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">San Francisco Office Lease [Member]</link:label>
    <link:label id="lab_gemi_SanFranciscoOfficeLeaseMember_documentation_en-US" xlink:label="lab_gemi_SanFranciscoOfficeLeaseMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">San Francisco Office Lease</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_SanFranciscoOfficeLeaseMember" xlink:href="gemi-20260930.xsd#gemi_SanFranciscoOfficeLeaseMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_SanFranciscoOfficeLeaseMember" xlink:to="lab_gemi_SanFranciscoOfficeLeaseMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_01a015a8-8b8d-7fcf-8ec1-9147e9690c27_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentNameDomain" xlink:to="lab_us-gaap_DebtInstrumentNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCredit_01a015a8-8b8d-7a51-98b0-26e44e3ef6b3_verboseLabel_en-US" xlink:label="lab_us-gaap_LineOfCredit" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Principal Outstanding</link:label>
    <link:label id="lab_us-gaap_LineOfCredit_label_en-US" xlink:label="lab_us-gaap_LineOfCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Line of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCredit" xlink:to="lab_us-gaap_LineOfCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrExpirationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expiration Date</link:label>
    <link:label id="lab_ecd_TrdArrExpirationDate_label_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Expiration Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrExpirationDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrExpirationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrExpirationDate" xlink:to="lab_ecd_TrdArrExpirationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CryptoAssetHoldingTableTextBlock_01a015a8-8b08-76e0-aa10-9d019d391af8_terseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetHoldingTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Crypto Assets Held at Fair Value</link:label>
    <link:label id="lab_us-gaap_CryptoAssetHoldingTableTextBlock_label_en-US" xlink:label="lab_us-gaap_CryptoAssetHoldingTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Holding [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetHoldingTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetHoldingTableTextBlock"/>
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    <link:label id="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure_01a015a8-8b08-7787-a2c9-136f679624fa_verboseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:to="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CustodialFundsDueToCustomersCurrent_01a015a8-8b08-749e-9d37-4dac52d6c13e_terseLabel_en-US" xlink:label="lab_gemi_CustodialFundsDueToCustomersCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Custodial funds due to customers</link:label>
    <link:label id="lab_gemi_CustodialFundsDueToCustomersCurrent_label_en-US" xlink:label="lab_gemi_CustodialFundsDueToCustomersCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Custodial Funds Due To Customers, Current</link:label>
    <link:label id="lab_gemi_CustodialFundsDueToCustomersCurrent_documentation_en-US" xlink:label="lab_gemi_CustodialFundsDueToCustomersCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Custodial Funds Due To Customers, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CustodialFundsDueToCustomersCurrent" xlink:href="gemi-20260930.xsd#gemi_CustodialFundsDueToCustomersCurrent"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber_01a015a8-8b8d-77d9-a072-bb600a5c245f_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of stock options exercisable (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercisable, Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber"/>
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    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtPnsnAdjsSvcCstMember"/>
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    <link:label id="lab_us-gaap_DerivativeTable_01a015a8-8a6b-7bcf-8152-c62496a715c5_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
    <link:label id="lab_us-gaap_DerivativeTable_label_en-US" xlink:label="lab_us-gaap_DerivativeTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Table]</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetPurchase" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetPurchase"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract"/>
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    <link:label id="lab_us-gaap_LitigationStatusAxis_01a015a8-8b8e-7dfc-93f8-e7f63ae26000_terseLabel_en-US" xlink:label="lab_us-gaap_LitigationStatusAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Litigation Status [Axis]</link:label>
    <link:label id="lab_us-gaap_LitigationStatusAxis_label_en-US" xlink:label="lab_us-gaap_LitigationStatusAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Litigation Status [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LitigationStatusAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LitigationStatusAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LitigationStatusAxis" xlink:to="lab_us-gaap_LitigationStatusAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAxis_01a015a8-8b08-7666-8365-9bc73d8104c8_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseRemainingLeaseTerm_01a015a8-8b08-7270-aa10-3091f4783618_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseRemainingLeaseTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining lease term</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseRemainingLeaseTerm_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseRemainingLeaseTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Remaining Lease Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseRemainingLeaseTerm" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseRemainingLeaseTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseRemainingLeaseTerm" xlink:to="lab_us-gaap_LesseeOperatingLeaseRemainingLeaseTerm" xlink:type="arc" order="1"/>
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    <link:label id="lab_gemi_IssuanceOfCommonStockInExchangeForCryptoAssets_label_en-US" xlink:label="lab_gemi_IssuanceOfCommonStockInExchangeForCryptoAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Issuance Of Common Stock In Exchange For Crypto Assets</link:label>
    <link:label id="lab_gemi_IssuanceOfCommonStockInExchangeForCryptoAssets_documentation_en-US" xlink:label="lab_gemi_IssuanceOfCommonStockInExchangeForCryptoAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Issuance Of Common Stock In Exchange For Crypto Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_IssuanceOfCommonStockInExchangeForCryptoAssets" xlink:href="gemi-20260930.xsd#gemi_IssuanceOfCommonStockInExchangeForCryptoAssets"/>
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    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_01a015a8-8b8d-7e6e-a939-eb48395d7de4_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining unrecognized expense</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized"/>
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    <link:label id="lab_us-gaap_CryptoAssetRealizedLossOperating_01a015a8-8a6b-7dcd-aa9e-f18700ce719f_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetRealizedLossOperating" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Realized loss on crypto assets</link:label>
    <link:label id="lab_us-gaap_CryptoAssetRealizedLossOperating_label_en-US" xlink:label="lab_us-gaap_CryptoAssetRealizedLossOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Realized Loss, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetRealizedLossOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetRealizedLossOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CryptoAssetRealizedLossOperating" xlink:to="lab_us-gaap_CryptoAssetRealizedLossOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CryptoAssetNumberOfUnits_01a015a8-8a6b-741c-b83a-586d14b776ed_terseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetNumberOfUnits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Units (in unit)</link:label>
    <link:label id="lab_us-gaap_CryptoAssetNumberOfUnits_01a015a8-8a6b-7053-9852-84117985f7e6_verboseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetNumberOfUnits" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Number of crypto assets held (in units)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetNumberOfUnits" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetNumberOfUnits"/>
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    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_01a015a8-8b8d-79e8-9339-ceffd2d594c7_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Loans and Convertible Notes</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_01a015a8-8b8d-75d1-9b12-5aaabc0a679c_netLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Third Party Loans</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_01a015a8-8b8d-744c-95fa-9758269724c5_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Funding Debt</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureTextBlock" xlink:to="lab_us-gaap_DebtDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StatementScenarioAxis_01a1abfb-15ed-79ca-98c0-57f8a53a09fe_terseLabel_en-US" xlink:label="lab_srt_StatementScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario [Axis]</link:label>
    <link:label id="lab_srt_StatementScenarioAxis_label_en-US" xlink:label="lab_srt_StatementScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementScenarioAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_StatementScenarioAxis"/>
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    <link:label id="lab_gemi_FinancialAssetLesserThan90DaysPastDueMember_01a015a8-8b8e-79e9-ab64-f0f8aeb83e43_terseLabel_en-US" xlink:label="lab_gemi_FinancialAssetLesserThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less than 90 Days</link:label>
    <link:label id="lab_gemi_FinancialAssetLesserThan90DaysPastDueMember_label_en-US" xlink:label="lab_gemi_FinancialAssetLesserThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Lesser than 90 Days Past Due [Member]</link:label>
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    <link:label id="lab_us-gaap_SecuredDebtMember_01a015a8-8b8d-739b-a4af-fb95172638f9_terseLabel_en-US" xlink:label="lab_us-gaap_SecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Secured Debt</link:label>
    <link:label id="lab_us-gaap_SecuredDebtMember_label_en-US" xlink:label="lab_us-gaap_SecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secured Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuredDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SecuredDebtMember"/>
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    <link:label id="lab_us-gaap_CryptoAssetUnrealizedGainLossOperating_01a015a8-8b8d-7abd-a0bd-3d61a9d02185_verboseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetUnrealizedGainLossOperating" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unrealized gain (loss) on crypto assets</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetUnrealizedGainLossOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetUnrealizedGainLossOperating"/>
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    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_01a015a8-8b8d-7aae-ac7f-753a3adcbb56_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_01a015a8-8b8d-7f3f-b267-96dc1904d2be_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Interest rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Stated Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_01a015a8-8b08-7156-955d-e106e8b339f1_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total stockholders&#8217; equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_01a015a8-8b08-71a3-a793-8dbd61882d85_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_01a015a8-8b08-7ce0-be71-6692d6941f55_periodEndLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoAssetNumberOfUnitsIssuedAsCollateral_01a015a8-8b8d-77ec-a108-e698757c8342_terseLabel_en-US" xlink:label="lab_gemi_CryptoAssetNumberOfUnitsIssuedAsCollateral" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of crypto assets designated as collateral to insurance providers (in units)</link:label>
    <link:label id="lab_gemi_CryptoAssetNumberOfUnitsIssuedAsCollateral_label_en-US" xlink:label="lab_gemi_CryptoAssetNumberOfUnitsIssuedAsCollateral" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Number Of Units Issued As Collateral</link:label>
    <link:label id="lab_gemi_CryptoAssetNumberOfUnitsIssuedAsCollateral_documentation_en-US" xlink:label="lab_gemi_CryptoAssetNumberOfUnitsIssuedAsCollateral" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Asset, Number Of Units Issued As Collateral</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoAssetNumberOfUnitsIssuedAsCollateral" xlink:href="gemi-20260930.xsd#gemi_CryptoAssetNumberOfUnitsIssuedAsCollateral"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoAssetNumberOfUnitsIssuedAsCollateral" xlink:to="lab_gemi_CryptoAssetNumberOfUnitsIssuedAsCollateral" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ServiceAdvisoryFeeMember_01a015a8-8a6b-7fbd-a4fb-ffd50ea30ca0_terseLabel_en-US" xlink:label="lab_gemi_ServiceAdvisoryFeeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Advisory fee revenue</link:label>
    <link:label id="lab_gemi_ServiceAdvisoryFeeMember_label_en-US" xlink:label="lab_gemi_ServiceAdvisoryFeeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Service, Advisory Fee [Member]</link:label>
    <link:label id="lab_gemi_ServiceAdvisoryFeeMember_documentation_en-US" xlink:label="lab_gemi_ServiceAdvisoryFeeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Service, Advisory Fee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ServiceAdvisoryFeeMember" xlink:href="gemi-20260930.xsd#gemi_ServiceAdvisoryFeeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ServiceAdvisoryFeeMember" xlink:to="lab_gemi_ServiceAdvisoryFeeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsAbstract_01a015a8-8b08-7b37-a6ef-8e89a656e35b_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="lab_us-gaap_AssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesCurrentAbstract_01a015a8-8b8d-7583-85d9-e01ecf3a8f4a_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other current liabilities:</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities, Current [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherLiabilitiesCurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesCurrentAbstract" xlink:to="lab_us-gaap_OtherLiabilitiesCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingPoliciesProcLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTradingPoliciesProcLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:to="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_01a015a8-8a6b-7610-85e9-33d9398c97ed_negatedNetLabel_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:role="http://www.xbrl.org/2009/role/negatedNetLabel" xlink:type="resource" xml:lang="en-US">Allowance for transaction losses</link:label>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_01a015a8-8a6b-79e2-ace6-5b16cde75d45_periodStartLabel_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning Balance</link:label>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_01a015a8-8a6b-7652-bfa5-047d01d93a85_periodEndLabel_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending Balance</link:label>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_label_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent"/>
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    <link:label id="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrent_01a015a8-8b8d-76d1-b550-ad5fd1ad747c_verboseLabel_en-US" xlink:label="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Prepaid expenses and other current assets</link:label>
    <link:label id="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrent_01a015a8-8b8d-7e11-b8fa-71f2b35857c3_totalLabel_en-US" xlink:label="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total prepaid expenses and other current assets</link:label>
    <link:label id="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrent_label_en-US" xlink:label="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepaid Expense and Other Assets, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrepaidExpenseAndOtherAssetsCurrent"/>
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    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward"/>
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    <link:label id="lab_us-gaap_PrivatePlacementMember_01a015a8-8b08-7c64-99d7-9ae34787dbdb_terseLabel_en-US" xlink:label="lab_us-gaap_PrivatePlacementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private Placement</link:label>
    <link:label id="lab_us-gaap_PrivatePlacementMember_label_en-US" xlink:label="lab_us-gaap_PrivatePlacementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Private Placement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrivatePlacementMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrivatePlacementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrivatePlacementMember" xlink:to="lab_us-gaap_PrivatePlacementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_SpotExchangeAndPredictionMarketsPlatformMember_01a1aecb-6822-7e77-9aad-d1fe99895357_terseLabel_en-US" xlink:label="lab_gemi_SpotExchangeAndPredictionMarketsPlatformMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Spot Exchange And Prediction Markets Platform</link:label>
    <link:label id="lab_gemi_SpotExchangeAndPredictionMarketsPlatformMember_label_en-US" xlink:label="lab_gemi_SpotExchangeAndPredictionMarketsPlatformMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Spot Exchange And Prediction Markets Platform [Member]</link:label>
    <link:label id="lab_gemi_SpotExchangeAndPredictionMarketsPlatformMember_documentation_en-US" xlink:label="lab_gemi_SpotExchangeAndPredictionMarketsPlatformMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Spot Exchange And Prediction Markets Platform</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_SpotExchangeAndPredictionMarketsPlatformMember" xlink:href="gemi-20260930.xsd#gemi_SpotExchangeAndPredictionMarketsPlatformMember"/>
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    <link:label id="lab_us-gaap_RepurchaseAgreementsInterestExpenseAmount_01a015a8-8b8d-7173-ace5-3e514b264ff4_terseLabel_en-US" xlink:label="lab_us-gaap_RepurchaseAgreementsInterestExpenseAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Expense</link:label>
    <link:label id="lab_us-gaap_RepurchaseAgreementsInterestExpenseAmount_label_en-US" xlink:label="lab_us-gaap_RepurchaseAgreementsInterestExpenseAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repurchase Agreements, Interest Expense Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepurchaseAgreementsInterestExpenseAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepurchaseAgreementsInterestExpenseAmount"/>
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    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_01a015a8-8b08-7c9f-b0e3-8787e1b0c8d8_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Potentially dilutive units not included in calculation of diluted units outstanding (in shares)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount"/>
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    <link:label id="lab_dei_EntityCentralIndexKey_01a015a8-8b08-7522-9edd-abb238fe1bb3_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
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    <link:label id="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_01a015a8-8b08-7e02-b131-6cacb9d43dc9_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accumulated amortization and depreciation</link:label>
    <link:label id="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment, Accumulated Depreciation, Depletion, and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment"/>
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    <link:label id="lab_us-gaap_EquityAbstract_label_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityAbstract"/>
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    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year</link:label>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_label_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:to="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_01a015a8-8b8d-7429-a92e-d01b10f0231f_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CryptoAssetFairValueRestricted_01a015a8-8b8d-770f-a274-18b93d67bc3c_verboseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetFairValueRestricted" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair value of restricted crypto assets held</link:label>
    <link:label id="lab_us-gaap_CryptoAssetFairValueRestricted_label_en-US" xlink:label="lab_us-gaap_CryptoAssetFairValueRestricted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Fair Value, Restricted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetFairValueRestricted" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetFairValueRestricted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CryptoAssetFairValueRestricted" xlink:to="lab_us-gaap_CryptoAssetFairValueRestricted" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock_01a015a8-8b8d-7c3b-9e32-c352a52002e9_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Payment Award, Stock Options, Valuation Assumptions</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Payment Award, Stock Options, Valuation Assumptions [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward_01a015a8-8a6b-79d3-be79-e3d386a2bfc1_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of Stock Options</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedStockMember_01a015a8-8b08-77e1-bdc8-24d67eaa7f28_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">RSAs</link:label>
    <link:label id="lab_us-gaap_RestrictedStockMember_01a015a8-8b08-713b-b954-90650fe40f39_verboseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unvested RSAs</link:label>
    <link:label id="lab_us-gaap_RestrictedStockMember_label_en-US" xlink:label="lab_us-gaap_RestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestrictedStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedStockMember" xlink:to="lab_us-gaap_RestrictedStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_01a015a8-8b8d-7dcd-9bb8-899a7c3e9d4d_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss)</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllIndividualsMember_terseLabel_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Individuals</link:label>
    <link:label id="lab_ecd_AllIndividualsMember_label_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Individuals [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllIndividualsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllIndividualsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="lab_ecd_AllIndividualsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ContractWithCustomerAssetVested_01a015a8-8b8d-7a60-b557-d93c210651a6_terseLabel_en-US" xlink:label="lab_gemi_ContractWithCustomerAssetVested" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract asset vested</link:label>
    <link:label id="lab_gemi_ContractWithCustomerAssetVested_label_en-US" xlink:label="lab_gemi_ContractWithCustomerAssetVested" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract With Customer, Asset, Vested</link:label>
    <link:label id="lab_gemi_ContractWithCustomerAssetVested_documentation_en-US" xlink:label="lab_gemi_ContractWithCustomerAssetVested" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Contract With Customer, Asset, Vested</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ContractWithCustomerAssetVested" xlink:href="gemi-20260930.xsd#gemi_ContractWithCustomerAssetVested"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ContractWithCustomerAssetVested" xlink:to="lab_gemi_ContractWithCustomerAssetVested" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock_01a015a8-8b08-7721-93a2-9807eecdc6ad_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Revenues Disaggregated by Geography</link:label>
    <link:label id="lab_us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock_label_en-US" xlink:label="lab_us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Entity-Wide Information Not Provided as Part of Reportable Segment, Geographical Area, Revenue [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock" xlink:to="lab_us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CryptoAssetRealizedGainOperating_01a015a8-8a6b-7f35-8f58-7adb763ebab3_terseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetRealizedGainOperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Realized gain on crypto assets</link:label>
    <link:label id="lab_us-gaap_CryptoAssetRealizedGainOperating_label_en-US" xlink:label="lab_us-gaap_CryptoAssetRealizedGainOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Realized Gain, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetRealizedGainOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetRealizedGainOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CryptoAssetRealizedGainOperating" xlink:to="lab_us-gaap_CryptoAssetRealizedGainOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_01a015a8-8a6b-7327-94a9-1ec99796216b_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average recognition period for unrecognized compensation expense</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:to="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CryptoAssetFairValueCurrent_01a015a8-8b08-79f4-9efe-fc37b51845ef_terseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetFairValueCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto assets held</link:label>
    <link:label id="lab_us-gaap_CryptoAssetFairValueCurrent_label_en-US" xlink:label="lab_us-gaap_CryptoAssetFairValueCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Fair Value, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetFairValueCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetFairValueCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CryptoAssetFairValueCurrent" xlink:to="lab_us-gaap_CryptoAssetFairValueCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_TimeBasedStockOptionsMember_01a015a8-8b08-7d52-ba8a-66eae5b2d068_terseLabel_en-US" xlink:label="lab_gemi_TimeBasedStockOptionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Time-Based Stock Options</link:label>
    <link:label id="lab_gemi_TimeBasedStockOptionsMember_label_en-US" xlink:label="lab_gemi_TimeBasedStockOptionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Time Based Stock Options [Member]</link:label>
    <link:label id="lab_gemi_TimeBasedStockOptionsMember_documentation_en-US" xlink:label="lab_gemi_TimeBasedStockOptionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Time Based Stock Options</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_TimeBasedStockOptionsMember" xlink:href="gemi-20260930.xsd#gemi_TimeBasedStockOptionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_TimeBasedStockOptionsMember" xlink:to="lab_gemi_TimeBasedStockOptionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMeasurementInput_01a015a8-8b08-73bb-8ea1-1e5ddd3a5228_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Significant input utilized in analysis</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMeasurementInput_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMeasurementInput" xlink:to="lab_us-gaap_LongTermDebtMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IntangibleAssetsDisclosureTextBlock_01a015a8-8b8d-7039-81cf-04d142798bbe_terseLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Assets, Net</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IntangibleAssetsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:to="lab_us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLeaseNotYetCommencedTermOfContract1_01a1c83b-8337-72de-ae4c-ff130de14a76_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLeaseNotYetCommencedTermOfContract1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, lease not yet commenced, term of contract</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLeaseNotYetCommencedTermOfContract1_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLeaseNotYetCommencedTermOfContract1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Lease Not yet Commenced, Term of Contract</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLeaseNotYetCommencedTermOfContract1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLeaseNotYetCommencedTermOfContract1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLeaseNotYetCommencedTermOfContract1" xlink:to="lab_us-gaap_LesseeOperatingLeaseLeaseNotYetCommencedTermOfContract1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementLineItems_01a015a8-8a6b-7b17-b841-b3e28f348c65_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_01a015a8-8a6b-7e44-b3e5-3964d5b8ac70_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_01a015a8-8b8d-7808-a6e6-56793e9f5c7a_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share available for future issuance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_label_en-US" xlink:label="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Capital Shares Reserved for Future Issuance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockCapitalSharesReservedForFutureIssuance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:to="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConvertibleDebtMember_01a015a8-8b08-7a02-afd1-60f3150d90bc_terseLabel_en-US" xlink:label="lab_us-gaap_ConvertibleDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Convertible Debt</link:label>
    <link:label id="lab_us-gaap_ConvertibleDebtMember_label_en-US" xlink:label="lab_us-gaap_ConvertibleDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Convertible Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConvertibleDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConvertibleDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConvertibleDebtMember" xlink:to="lab_us-gaap_ConvertibleDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParentAbstract_01a015a8-8b8d-7143-be42-d5f6bd81bf01_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income (loss):</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParentAbstract_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), before Tax, Portion Attributable to Parent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParentAbstract" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_A5000BTCDecember292022Member_01a015a8-8b08-704b-88e3-5a36db4f158c_terseLabel_en-US" xlink:label="lab_gemi_A5000BTCDecember292022Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">5,000 BTC December 29, 2022</link:label>
    <link:label id="lab_gemi_A5000BTCDecember292022Member_label_en-US" xlink:label="lab_gemi_A5000BTCDecember292022Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">5,000 BTC December 29, 2022 [Member]</link:label>
    <link:label id="lab_gemi_A5000BTCDecember292022Member_documentation_en-US" xlink:label="lab_gemi_A5000BTCDecember292022Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">5,000 BTC December 29, 2022</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_A5000BTCDecember292022Member" xlink:href="gemi-20260930.xsd#gemi_A5000BTCDecember292022Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_A5000BTCDecember292022Member" xlink:to="lab_gemi_A5000BTCDecember292022Member" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoAssetOptionsAssetMember_01a015a8-8b8d-7f88-b6e1-7b5ed0cf36db_terseLabel_en-US" xlink:label="lab_gemi_CryptoAssetOptionsAssetMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto asset options</link:label>
    <link:label id="lab_gemi_CryptoAssetOptionsAssetMember_label_en-US" xlink:label="lab_gemi_CryptoAssetOptionsAssetMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset Options, Asset [Member]</link:label>
    <link:label id="lab_gemi_CryptoAssetOptionsAssetMember_documentation_en-US" xlink:label="lab_gemi_CryptoAssetOptionsAssetMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Asset Options, Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoAssetOptionsAssetMember" xlink:href="gemi-20260930.xsd#gemi_CryptoAssetOptionsAssetMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoAssetOptionsAssetMember" xlink:to="lab_gemi_CryptoAssetOptionsAssetMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueAmount_01a015a8-8b08-7743-ab97-e890a42b15be_verboseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Strategic investments</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueAmount_01a015a8-8b08-7430-a6c7-9da519b6589d_periodStartLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueAmount" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Carrying amount, beginning balance</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueAmount_01a015a8-8b08-7078-921c-c266e49c86a8_periodEndLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueAmount" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Carrying amount, ending balance</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueAmount_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities without Readily Determinable Fair Value, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueAmount" xlink:to="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_01a015a8-8a6b-7a5b-b64d-87fe71f49543_terseLabel_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock-Based Compensation</link:label>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:to="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoMember_terseLabel_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO</link:label>
    <link:label id="lab_ecd_PeoMember_label_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoMember" xlink:to="lab_ecd_PeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoLoansPayableRealizedAndUnrealizedGainLossNonoperating_01a015a8-8b08-75ea-a477-ddfe20525957_terseLabel_en-US" xlink:label="lab_gemi_CryptoLoansPayableRealizedAndUnrealizedGainLossNonoperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Realized and unrealized gain (loss) on related party crypto loans</link:label>
    <link:label id="lab_gemi_CryptoLoansPayableRealizedAndUnrealizedGainLossNonoperating_01a015a8-8b08-7347-afd0-b46336e077f1_negatedTerseLabel_en-US" xlink:label="lab_gemi_CryptoLoansPayableRealizedAndUnrealizedGainLossNonoperating" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Realized and unrealized loss (gain) on related party crypto loans</link:label>
    <link:label id="lab_gemi_CryptoLoansPayableRealizedAndUnrealizedGainLossNonoperating_label_en-US" xlink:label="lab_gemi_CryptoLoansPayableRealizedAndUnrealizedGainLossNonoperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Loans Payable, Realized And Unrealized Gain (Loss), Nonoperating</link:label>
    <link:label id="lab_gemi_CryptoLoansPayableRealizedAndUnrealizedGainLossNonoperating_documentation_en-US" xlink:label="lab_gemi_CryptoLoansPayableRealizedAndUnrealizedGainLossNonoperating" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Loans Payable, Realized And Unrealized Gain (Loss), Nonoperating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoLoansPayableRealizedAndUnrealizedGainLossNonoperating" xlink:href="gemi-20260930.xsd#gemi_CryptoLoansPayableRealizedAndUnrealizedGainLossNonoperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoLoansPayableRealizedAndUnrealizedGainLossNonoperating" xlink:to="lab_gemi_CryptoLoansPayableRealizedAndUnrealizedGainLossNonoperating" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ShareBasedPaymentArrangementOptionAndRestrictedStockUnitsRSUsMember_01a015a8-8a6b-7315-9a2a-19647335f155_terseLabel_en-US" xlink:label="lab_gemi_ShareBasedPaymentArrangementOptionAndRestrictedStockUnitsRSUsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">RSUs and Options</link:label>
    <link:label id="lab_gemi_ShareBasedPaymentArrangementOptionAndRestrictedStockUnitsRSUsMember_label_en-US" xlink:label="lab_gemi_ShareBasedPaymentArrangementOptionAndRestrictedStockUnitsRSUsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option And Restricted Stock Units (RSUs) [Member]</link:label>
    <link:label id="lab_gemi_ShareBasedPaymentArrangementOptionAndRestrictedStockUnitsRSUsMember_documentation_en-US" xlink:label="lab_gemi_ShareBasedPaymentArrangementOptionAndRestrictedStockUnitsRSUsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option And Restricted Stock Units (RSUs)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ShareBasedPaymentArrangementOptionAndRestrictedStockUnitsRSUsMember" xlink:href="gemi-20260930.xsd#gemi_ShareBasedPaymentArrangementOptionAndRestrictedStockUnitsRSUsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ShareBasedPaymentArrangementOptionAndRestrictedStockUnitsRSUsMember" xlink:to="lab_gemi_ShareBasedPaymentArrangementOptionAndRestrictedStockUnitsRSUsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExpirationsInPeriodWeightedAverageExercisePrice_01a015a8-8b08-7932-ab4c-41894fe70422_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExpirationsInPeriodWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expirations (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExpirationsInPeriodWeightedAverageExercisePrice_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExpirationsInPeriodWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Expirations in Period, Weighted Average Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExpirationsInPeriodWeightedAverageExercisePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExpirationsInPeriodWeightedAverageExercisePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExpirationsInPeriodWeightedAverageExercisePrice" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExpirationsInPeriodWeightedAverageExercisePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_TransactionRevenueExchangeMember_01a015a8-8b08-71a9-9400-6714d6547df2_terseLabel_en-US" xlink:label="lab_gemi_TransactionRevenueExchangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exchange</link:label>
    <link:label id="lab_gemi_TransactionRevenueExchangeMember_label_en-US" xlink:label="lab_gemi_TransactionRevenueExchangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transaction Revenue, Exchange [Member]</link:label>
    <link:label id="lab_gemi_TransactionRevenueExchangeMember_documentation_en-US" xlink:label="lab_gemi_TransactionRevenueExchangeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Transaction Revenue, Exchange</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_TransactionRevenueExchangeMember" xlink:href="gemi-20260930.xsd#gemi_TransactionRevenueExchangeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_TransactionRevenueExchangeMember" xlink:to="lab_gemi_TransactionRevenueExchangeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ReceivableForCryptoAssetsPledgedAsCollateralForThirdPartyLoansNet_01a1c302-33ca-74a1-8f53-672aff32cbdb_terseLabel_en-US" xlink:label="lab_gemi_ReceivableForCryptoAssetsPledgedAsCollateralForThirdPartyLoansNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivable for crypto assets pledged as collateral for third-party loans, net</link:label>
    <link:label id="lab_gemi_ReceivableForCryptoAssetsPledgedAsCollateralForThirdPartyLoansNet_label_en-US" xlink:label="lab_gemi_ReceivableForCryptoAssetsPledgedAsCollateralForThirdPartyLoansNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivable For Crypto Assets Pledged As Collateral For Third-Party Loans, Net</link:label>
    <link:label id="lab_gemi_ReceivableForCryptoAssetsPledgedAsCollateralForThirdPartyLoansNet_documentation_en-US" xlink:label="lab_gemi_ReceivableForCryptoAssetsPledgedAsCollateralForThirdPartyLoansNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Receivable For Crypto Assets Pledged As Collateral For Third-Party Loans, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ReceivableForCryptoAssetsPledgedAsCollateralForThirdPartyLoansNet" xlink:href="gemi-20260930.xsd#gemi_ReceivableForCryptoAssetsPledgedAsCollateralForThirdPartyLoansNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ReceivableForCryptoAssetsPledgedAsCollateralForThirdPartyLoansNet" xlink:to="lab_gemi_ReceivableForCryptoAssetsPledgedAsCollateralForThirdPartyLoansNet" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_DeferredOfferingCostsIncurredButNotYetPaid_01a015a8-8b8d-78d0-9b86-4adfcc6cc9e3_terseLabel_en-US" xlink:label="lab_gemi_DeferredOfferingCostsIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred offering costs not yet paid</link:label>
    <link:label id="lab_gemi_DeferredOfferingCostsIncurredButNotYetPaid_label_en-US" xlink:label="lab_gemi_DeferredOfferingCostsIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Offering Costs, Incurred But Not Yet Paid</link:label>
    <link:label id="lab_gemi_DeferredOfferingCostsIncurredButNotYetPaid_documentation_en-US" xlink:label="lab_gemi_DeferredOfferingCostsIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Offering Costs, Incurred But Not Yet Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_DeferredOfferingCostsIncurredButNotYetPaid" xlink:href="gemi-20260930.xsd#gemi_DeferredOfferingCostsIncurredButNotYetPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_DeferredOfferingCostsIncurredButNotYetPaid" xlink:to="lab_gemi_DeferredOfferingCostsIncurredButNotYetPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsMember_01a015a8-8a6b-7124-ab86-897faf00655a_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Deficit</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsMember_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsMember" xlink:to="lab_us-gaap_RetainedEarningsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityNoncurrent_01a015a8-8b08-7c0c-bfaf-0b230a858fd4_verboseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Lease liabilities</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityNoncurrent_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilityNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:to="lab_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_FinancingAgreementsCollateralRate_01a015a8-8b8d-7aa7-b16b-fe5bc2f45bb5_terseLabel_en-US" xlink:label="lab_gemi_FinancingAgreementsCollateralRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing agreements, collateral rate</link:label>
    <link:label id="lab_gemi_FinancingAgreementsCollateralRate_01a015a8-8b8d-7256-af50-0edaecc7a624_verboseLabel_en-US" xlink:label="lab_gemi_FinancingAgreementsCollateralRate" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Collateral Rate</link:label>
    <link:label id="lab_gemi_FinancingAgreementsCollateralRate_label_en-US" xlink:label="lab_gemi_FinancingAgreementsCollateralRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Agreements, Collateral Rate</link:label>
    <link:label id="lab_gemi_FinancingAgreementsCollateralRate_documentation_en-US" xlink:label="lab_gemi_FinancingAgreementsCollateralRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Agreements, Collateral Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_FinancingAgreementsCollateralRate" xlink:href="gemi-20260930.xsd#gemi_FinancingAgreementsCollateralRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_FinancingAgreementsCollateralRate" xlink:to="lab_gemi_FinancingAgreementsCollateralRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpenses_01a015a8-8a6b-75a0-a3ee-5ebf76ccc090_totalLabel_en-US" xlink:label="lab_us-gaap_OperatingExpenses" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total operating expenses</link:label>
    <link:label id="lab_us-gaap_OperatingExpenses_label_en-US" xlink:label="lab_us-gaap_OperatingExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpenses" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpenses" xlink:to="lab_us-gaap_OperatingExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseImpairmentLoss_01a015a8-8b08-7df8-ae81-6dcac5fb5e8a_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Impairment charges</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseImpairmentLoss_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Impairment Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseImpairmentLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseImpairmentLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseImpairmentLoss" xlink:to="lab_us-gaap_OperatingLeaseImpairmentLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_01a015a8-8b08-7f0f-9d30-a2ae7e7fcac4_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_01a015a8-8b8d-78b2-bbcd-ab66d93faa1e_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_01a015a8-8b8d-71d0-910d-dd10398dc6c1_periodStartLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning common balance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_01a015a8-8b8d-7321-ac03-5e349a5127fa_periodEndLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending common balance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgDiscLineItems_label_en-US" xlink:label="lab_ecd_AwardTmgDiscLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Disclosures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgDiscLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgDiscLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgDiscLineItems" xlink:to="lab_ecd_AwardTmgDiscLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_01a015a8-8b8d-758e-94e4-06a44d956f43_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareDiluted" xlink:to="lab_us-gaap_EarningsPerShareDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_RelatedPartyDebtFairValueDisclosure_01a015a8-8b08-7be0-bef2-63a46f94e122_terseLabel_en-US" xlink:label="lab_gemi_RelatedPartyDebtFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related party loans:</link:label>
    <link:label id="lab_gemi_RelatedPartyDebtFairValueDisclosure_01a015a8-8b08-77fb-b5b1-7515657a55a2_verboseLabel_en-US" xlink:label="lab_gemi_RelatedPartyDebtFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Related party loans</link:label>
    <link:label id="lab_gemi_RelatedPartyDebtFairValueDisclosure_label_en-US" xlink:label="lab_gemi_RelatedPartyDebtFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Debt, Fair Value Disclosure</link:label>
    <link:label id="lab_gemi_RelatedPartyDebtFairValueDisclosure_documentation_en-US" xlink:label="lab_gemi_RelatedPartyDebtFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Debt, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_RelatedPartyDebtFairValueDisclosure" xlink:href="gemi-20260930.xsd#gemi_RelatedPartyDebtFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_RelatedPartyDebtFairValueDisclosure" xlink:to="lab_gemi_RelatedPartyDebtFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_LitigationCaseTypeDomain_01a015a8-8b8e-7071-a492-9dd68d5d8334_terseLabel_en-US" xlink:label="lab_srt_LitigationCaseTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Litigation Case [Domain]</link:label>
    <link:label id="lab_srt_LitigationCaseTypeDomain_label_en-US" xlink:label="lab_srt_LitigationCaseTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Litigation Case [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_LitigationCaseTypeDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_LitigationCaseTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_LitigationCaseTypeDomain" xlink:to="lab_srt_LitigationCaseTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_01a015a8-8a6b-714a-ac81-073b65747a29_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization expense of intangible assets</link:label>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_label_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Amortization Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfIntangibleAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:to="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems_01a015a8-8b8d-72e3-acaa-7656633d095d_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived [Line Items]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_RepurchaseAgreementsInterestRate_01a015a8-8b08-7c65-8b25-88f179bae977_terseLabel_en-US" xlink:label="lab_gemi_RepurchaseAgreementsInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase Agreements, Interest Rate</link:label>
    <link:label id="lab_gemi_RepurchaseAgreementsInterestRate_01a015a8-8b08-73b3-aee4-13e4ff93f59e_verboseLabel_en-US" xlink:label="lab_gemi_RepurchaseAgreementsInterestRate" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate</link:label>
    <link:label id="lab_gemi_RepurchaseAgreementsInterestRate_label_en-US" xlink:label="lab_gemi_RepurchaseAgreementsInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repurchase Agreements, Interest Rate</link:label>
    <link:label id="lab_gemi_RepurchaseAgreementsInterestRate_documentation_en-US" xlink:label="lab_gemi_RepurchaseAgreementsInterestRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Repurchase Agreements, Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_RepurchaseAgreementsInterestRate" xlink:href="gemi-20260930.xsd#gemi_RepurchaseAgreementsInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_RepurchaseAgreementsInterestRate" xlink:to="lab_gemi_RepurchaseAgreementsInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromLongTermLinesOfCredit_01a015a8-8b08-7d50-9a5b-d5b3f441438e_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromLongTermLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from funding debt</link:label>
    <link:label id="lab_us-gaap_ProceedsFromLongTermLinesOfCredit_label_en-US" xlink:label="lab_us-gaap_ProceedsFromLongTermLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Long-Term Lines of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromLongTermLinesOfCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromLongTermLinesOfCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromLongTermLinesOfCredit" xlink:to="lab_us-gaap_ProceedsFromLongTermLinesOfCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseContractualTermDomain_01a015a8-8b08-795f-843c-99964c959e06_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseContractualTermDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease Contractual Term [Domain]</link:label>
    <link:label id="lab_us-gaap_LeaseContractualTermDomain_label_en-US" xlink:label="lab_us-gaap_LeaseContractualTermDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease Contractual Term [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseContractualTermDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LeaseContractualTermDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseContractualTermDomain" xlink:to="lab_us-gaap_LeaseContractualTermDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_NonCashInstrumentSpecificCreditRiskGainLoss_01a015a8-8b08-72e7-b149-1773d787cec0_terseLabel_en-US" xlink:label="lab_gemi_NonCashInstrumentSpecificCreditRiskGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value attributable to instrument-specific credit risk</link:label>
    <link:label id="lab_gemi_NonCashInstrumentSpecificCreditRiskGainLoss_label_en-US" xlink:label="lab_gemi_NonCashInstrumentSpecificCreditRiskGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Cash Instrument-Specific Credit Risk, Gain (Loss)</link:label>
    <link:label id="lab_gemi_NonCashInstrumentSpecificCreditRiskGainLoss_documentation_en-US" xlink:label="lab_gemi_NonCashInstrumentSpecificCreditRiskGainLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Non-Cash Instrument-Specific Credit Risk, Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_NonCashInstrumentSpecificCreditRiskGainLoss" xlink:href="gemi-20260930.xsd#gemi_NonCashInstrumentSpecificCreditRiskGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_NonCashInstrumentSpecificCreditRiskGainLoss" xlink:to="lab_gemi_NonCashInstrumentSpecificCreditRiskGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IPOMember_01a015a8-8b08-73b4-b7e7-aa49f605d889_terseLabel_en-US" xlink:label="lab_us-gaap_IPOMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">IPO</link:label>
    <link:label id="lab_us-gaap_IPOMember_label_en-US" xlink:label="lab_us-gaap_IPOMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">IPO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IPOMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IPOMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IPOMember" xlink:to="lab_us-gaap_IPOMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:to="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_01a015a8-8b08-7b04-8d8e-88f324316d6f_verboseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net revenue</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_01a015a8-8b08-74eb-a114-dd2658e9161b_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total net revenue from contracts with customers</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_01a015a8-8b08-7c81-bd34-cb6cc799df12_netLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Revenue</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer, Excluding Assessed Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_01a015a8-8b08-7b86-be0d-f84b1194fb49_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unused, available borrowing capacity</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Remaining Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServiceOtherMember_01a015a8-8a6b-76a3-8ac8-d44c2c5a0ac8_terseLabel_en-US" xlink:label="lab_us-gaap_ServiceOtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other services revenue</link:label>
    <link:label id="lab_us-gaap_ServiceOtherMember_label_en-US" xlink:label="lab_us-gaap_ServiceOtherMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Service, Other [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServiceOtherMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ServiceOtherMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServiceOtherMember" xlink:to="lab_us-gaap_ServiceOtherMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_DerivativeInstrumentRecognitionCriteriaAxis_01a015a8-8b8d-7ce9-9c9e-a94ddbac918b_terseLabel_en-US" xlink:label="lab_gemi_DerivativeInstrumentRecognitionCriteriaAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Recognition Criteria [Axis]</link:label>
    <link:label id="lab_gemi_DerivativeInstrumentRecognitionCriteriaAxis_label_en-US" xlink:label="lab_gemi_DerivativeInstrumentRecognitionCriteriaAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Recognition Criteria [Axis]</link:label>
    <link:label id="lab_gemi_DerivativeInstrumentRecognitionCriteriaAxis_documentation_en-US" xlink:label="lab_gemi_DerivativeInstrumentRecognitionCriteriaAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Recognition Criteria</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_DerivativeInstrumentRecognitionCriteriaAxis" xlink:href="gemi-20260930.xsd#gemi_DerivativeInstrumentRecognitionCriteriaAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_DerivativeInstrumentRecognitionCriteriaAxis" xlink:to="lab_gemi_DerivativeInstrumentRecognitionCriteriaAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfOtherLongTermDebt_01a015a8-8a6b-7909-bb4f-a17f640f1cdf_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfOtherLongTermDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repayment of third party loans</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfOtherLongTermDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfOtherLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Other Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfOtherLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfOtherLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfOtherLongTermDebt" xlink:to="lab_us-gaap_RepaymentsOfOtherLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeLiabilitiesAtFairValueTableTextBlock_01a015a8-8b08-7cee-a46e-f39c1d8bc4a5_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeLiabilitiesAtFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Liabilities at Fair Value</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeLiabilitiesAtFairValueTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeLiabilitiesAtFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Liabilities at Fair Value [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativeLiabilitiesAtFairValueTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDerivativeLiabilitiesAtFairValueTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativeLiabilitiesAtFairValueTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativeLiabilitiesAtFairValueTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRestructuringReserveByTypeOfCostTextBlock_01a015a8-8b8d-7502-a638-667eca9d3567_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRestructuringReserveByTypeOfCostTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Changes in the Severance and Other Personnel Obligations</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRestructuringReserveByTypeOfCostTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRestructuringReserveByTypeOfCostTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Restructuring Reserve by Type of Cost [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRestructuringReserveByTypeOfCostTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRestructuringReserveByTypeOfCostTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRestructuringReserveByTypeOfCostTextBlock" xlink:to="lab_us-gaap_ScheduleOfRestructuringReserveByTypeOfCostTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_TransactionRevenuePredictionMarketRevenueMember_01a015a8-8a6b-7d93-8693-fcd8d7c35c9c_terseLabel_en-US" xlink:label="lab_gemi_TransactionRevenuePredictionMarketRevenueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prediction markets revenue</link:label>
    <link:label id="lab_gemi_TransactionRevenuePredictionMarketRevenueMember_label_en-US" xlink:label="lab_gemi_TransactionRevenuePredictionMarketRevenueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transaction Revenue, Prediction Market Revenue [Member]</link:label>
    <link:label id="lab_gemi_TransactionRevenuePredictionMarketRevenueMember_documentation_en-US" xlink:label="lab_gemi_TransactionRevenuePredictionMarketRevenueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Transaction Revenue, Prediction Market Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_TransactionRevenuePredictionMarketRevenueMember" xlink:href="gemi-20260930.xsd#gemi_TransactionRevenuePredictionMarketRevenueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_TransactionRevenuePredictionMarketRevenueMember" xlink:to="lab_gemi_TransactionRevenuePredictionMarketRevenueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:to="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_RepurchaseAgreementsInterestPayable_01a015a8-8a6b-74a6-ae2f-0d14d04bc94c_terseLabel_en-US" xlink:label="lab_gemi_RepurchaseAgreementsInterestPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Payable</link:label>
    <link:label id="lab_gemi_RepurchaseAgreementsInterestPayable_label_en-US" xlink:label="lab_gemi_RepurchaseAgreementsInterestPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repurchase Agreements, Interest Payable</link:label>
    <link:label id="lab_gemi_RepurchaseAgreementsInterestPayable_documentation_en-US" xlink:label="lab_gemi_RepurchaseAgreementsInterestPayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Repurchase Agreements, Interest Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_RepurchaseAgreementsInterestPayable" xlink:href="gemi-20260930.xsd#gemi_RepurchaseAgreementsInterestPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_RepurchaseAgreementsInterestPayable" xlink:to="lab_gemi_RepurchaseAgreementsInterestPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_IncreaseDecreaseInDueToFundingDebt_01a015a8-8a6b-78dc-912b-474bd08765c7_terseLabel_en-US" xlink:label="lab_gemi_IncreaseDecreaseInDueToFundingDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payables due for funding debt</link:label>
    <link:label id="lab_gemi_IncreaseDecreaseInDueToFundingDebt_label_en-US" xlink:label="lab_gemi_IncreaseDecreaseInDueToFundingDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) In Due To Funding Debt</link:label>
    <link:label id="lab_gemi_IncreaseDecreaseInDueToFundingDebt_documentation_en-US" xlink:label="lab_gemi_IncreaseDecreaseInDueToFundingDebt" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Increase (Decrease) In Due To Funding Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_IncreaseDecreaseInDueToFundingDebt" xlink:href="gemi-20260930.xsd#gemi_IncreaseDecreaseInDueToFundingDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_IncreaseDecreaseInDueToFundingDebt" xlink:to="lab_gemi_IncreaseDecreaseInDueToFundingDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_PrefundedClearingAdvancesCurrent_01a015a8-8b08-7f5b-b9cd-acf1c8368dac_terseLabel_en-US" xlink:label="lab_gemi_PrefundedClearingAdvancesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prefunded clearing advance</link:label>
    <link:label id="lab_gemi_PrefundedClearingAdvancesCurrent_label_en-US" xlink:label="lab_gemi_PrefundedClearingAdvancesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prefunded Clearing Advances, Current</link:label>
    <link:label id="lab_gemi_PrefundedClearingAdvancesCurrent_documentation_en-US" xlink:label="lab_gemi_PrefundedClearingAdvancesCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Prefunded Clearing Advances, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_PrefundedClearingAdvancesCurrent" xlink:href="gemi-20260930.xsd#gemi_PrefundedClearingAdvancesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_PrefundedClearingAdvancesCurrent" xlink:to="lab_gemi_PrefundedClearingAdvancesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_TitleOfIndividualAxis_01a015a8-8a6b-7072-9a99-8562e6e2312d_terseLabel_en-US" xlink:label="lab_srt_TitleOfIndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title and Position [Axis]</link:label>
    <link:label id="lab_srt_TitleOfIndividualAxis_label_en-US" xlink:label="lab_srt_TitleOfIndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title and Position [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_TitleOfIndividualAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_TitleOfIndividualAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_TitleOfIndividualAxis" xlink:to="lab_srt_TitleOfIndividualAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_01a015a8-8a6b-75a6-bf05-401a36cdd14a_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_label_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsidiarySaleOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:to="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableAccruedLiabilitiesAndOtherLiabilitiesDisclosureCurrentTextBlock_01a015a8-8b08-7799-b72f-d008b0677e4e_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableAccruedLiabilitiesAndOtherLiabilitiesDisclosureCurrentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued Expenses and Other Current Liabilities</link:label>
    <link:label id="lab_us-gaap_AccountsPayableAccruedLiabilitiesAndOtherLiabilitiesDisclosureCurrentTextBlock_label_en-US" xlink:label="lab_us-gaap_AccountsPayableAccruedLiabilitiesAndOtherLiabilitiesDisclosureCurrentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable, Accrued Liabilities, and Other Liabilities Disclosure, Current [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableAccruedLiabilitiesAndOtherLiabilitiesDisclosureCurrentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsPayableAccruedLiabilitiesAndOtherLiabilitiesDisclosureCurrentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableAccruedLiabilitiesAndOtherLiabilitiesDisclosureCurrentTextBlock" xlink:to="lab_us-gaap_AccountsPayableAccruedLiabilitiesAndOtherLiabilitiesDisclosureCurrentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeGainLossOnDerivativeNet_01a015a8-8b08-7457-9346-0b77d601db97_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Gain (loss) on changes in fair value of derivatives</link:label>
    <link:label id="lab_us-gaap_DerivativeGainLossOnDerivativeNet_label_en-US" xlink:label="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Gain (Loss) on Derivative, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeGainLossOnDerivativeNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:to="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_01a015a8-8b08-71db-b374-aac7966307ba_totalLabel_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Operating loss</link:label>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_label_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Income (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingIncomeLoss" xlink:to="lab_us-gaap_OperatingIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServiceMember_01a015a8-8b08-7bc1-8da3-0e4f613f48d8_terseLabel_en-US" xlink:label="lab_us-gaap_ServiceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Services revenue</link:label>
    <link:label id="lab_us-gaap_ServiceMember_label_en-US" xlink:label="lab_us-gaap_ServiceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Service [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServiceMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ServiceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServiceMember" xlink:to="lab_us-gaap_ServiceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_FinancingAgreementsInterestRate_01a015a8-8b8d-775e-9059-e0ca859f521e_verboseLabel_en-US" xlink:label="lab_gemi_FinancingAgreementsInterestRate" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Financing agreements, interest rate</link:label>
    <link:label id="lab_gemi_FinancingAgreementsInterestRate_01a015a8-8b8d-7646-9f1b-5e93fa77934d_terseLabel_en-US" xlink:label="lab_gemi_FinancingAgreementsInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate</link:label>
    <link:label id="lab_gemi_FinancingAgreementsInterestRate_label_en-US" xlink:label="lab_gemi_FinancingAgreementsInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Agreements, Interest Rate</link:label>
    <link:label id="lab_gemi_FinancingAgreementsInterestRate_documentation_en-US" xlink:label="lab_gemi_FinancingAgreementsInterestRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Agreements, Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_FinancingAgreementsInterestRate" xlink:href="gemi-20260930.xsd#gemi_FinancingAgreementsInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_FinancingAgreementsInterestRate" xlink:to="lab_gemi_FinancingAgreementsInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfDebt_01a1cd61-faec-74fa-b9f4-40e498c15938_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from issuance of debt</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromIssuanceOfDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfDebt" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_PaymentForOperatingLeaseTerminationFee_01a015a8-8b8e-77f5-9f5e-e06fdf3d96e2_terseLabel_en-US" xlink:label="lab_gemi_PaymentForOperatingLeaseTerminationFee" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee, operating lease, termination fee amount paid</link:label>
    <link:label id="lab_gemi_PaymentForOperatingLeaseTerminationFee_label_en-US" xlink:label="lab_gemi_PaymentForOperatingLeaseTerminationFee" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment For Operating Lease Termination Fee</link:label>
    <link:label id="lab_gemi_PaymentForOperatingLeaseTerminationFee_documentation_en-US" xlink:label="lab_gemi_PaymentForOperatingLeaseTerminationFee" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payment For Operating Lease Termination Fee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_PaymentForOperatingLeaseTerminationFee" xlink:href="gemi-20260930.xsd#gemi_PaymentForOperatingLeaseTerminationFee"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_PaymentForOperatingLeaseTerminationFee" xlink:to="lab_gemi_PaymentForOperatingLeaseTerminationFee" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_RelatedPartyTransactionWaivedTransactionExpenseThreshold_01a015a8-8b8d-7419-8280-96077f7bcbc2_terseLabel_en-US" xlink:label="lab_gemi_RelatedPartyTransactionWaivedTransactionExpenseThreshold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Threshold for fees, costs or expenses to be waived</link:label>
    <link:label id="lab_gemi_RelatedPartyTransactionWaivedTransactionExpenseThreshold_label_en-US" xlink:label="lab_gemi_RelatedPartyTransactionWaivedTransactionExpenseThreshold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Waived Transaction Expense Threshold</link:label>
    <link:label id="lab_gemi_RelatedPartyTransactionWaivedTransactionExpenseThreshold_documentation_en-US" xlink:label="lab_gemi_RelatedPartyTransactionWaivedTransactionExpenseThreshold" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Waived Transaction Expense Threshold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_RelatedPartyTransactionWaivedTransactionExpenseThreshold" xlink:href="gemi-20260930.xsd#gemi_RelatedPartyTransactionWaivedTransactionExpenseThreshold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_RelatedPartyTransactionWaivedTransactionExpenseThreshold" xlink:to="lab_gemi_RelatedPartyTransactionWaivedTransactionExpenseThreshold" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoAssetLoansMember_01a015a8-8a6b-7a62-a9dd-94efd4bdc165_terseLabel_en-US" xlink:label="lab_gemi_CryptoAssetLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto Asset Loans</link:label>
    <link:label id="lab_gemi_CryptoAssetLoansMember_label_en-US" xlink:label="lab_gemi_CryptoAssetLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset Loans [Member]</link:label>
    <link:label id="lab_gemi_CryptoAssetLoansMember_documentation_en-US" xlink:label="lab_gemi_CryptoAssetLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Asset Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoAssetLoansMember" xlink:href="gemi-20260930.xsd#gemi_CryptoAssetLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoAssetLoansMember" xlink:to="lab_gemi_CryptoAssetLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_01a015a8-8b8e-786f-889e-2986c0c8a85f_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionDomain" xlink:to="lab_us-gaap_RelatedPartyTransactionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CreditCardReceivablesDisputedMember_01a015a8-8b8e-767e-83cd-a167dba23b38_terseLabel_en-US" xlink:label="lab_gemi_CreditCardReceivablesDisputedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Card Receivables, Disputed</link:label>
    <link:label id="lab_gemi_CreditCardReceivablesDisputedMember_label_en-US" xlink:label="lab_gemi_CreditCardReceivablesDisputedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Card Receivables, Disputed [Member]</link:label>
    <link:label id="lab_gemi_CreditCardReceivablesDisputedMember_documentation_en-US" xlink:label="lab_gemi_CreditCardReceivablesDisputedMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Credit Card Receivables, Disputed</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CreditCardReceivablesDisputedMember" xlink:href="gemi-20260930.xsd#gemi_CreditCardReceivablesDisputedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CreditCardReceivablesDisputedMember" xlink:to="lab_gemi_CreditCardReceivablesDisputedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Rule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:to="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesPurchasedForAward_01a015a8-8a6b-7892-bca4-3834f6720cc2_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesPurchasedForAward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares purchased (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesPurchasedForAward_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesPurchasedForAward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Shares Purchased for Award</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesPurchasedForAward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesPurchasedForAward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesPurchasedForAward" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesPurchasedForAward" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_RetailReceivableMember_01a015a8-8b8d-7e0e-9328-01b53ddb3b6e_verboseLabel_en-US" xlink:label="lab_gemi_RetailReceivableMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Retail receivables</link:label>
    <link:label id="lab_gemi_RetailReceivableMember_01a015a8-8b8d-7c0a-9ff7-197340fb133d_terseLabel_en-US" xlink:label="lab_gemi_RetailReceivableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retail receivables</link:label>
    <link:label id="lab_gemi_RetailReceivableMember_label_en-US" xlink:label="lab_gemi_RetailReceivableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retail Receivable [Member]</link:label>
    <link:label id="lab_gemi_RetailReceivableMember_documentation_en-US" xlink:label="lab_gemi_RetailReceivableMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Retail Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_RetailReceivableMember" xlink:href="gemi-20260930.xsd#gemi_RetailReceivableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_RetailReceivableMember" xlink:to="lab_gemi_RetailReceivableMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_01a015a8-8a6b-7bd6-98fb-4d8ef2e9c4ff_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList_01a015a8-8b08-763c-b29b-18236142d5e4_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_01a015a8-8b08-70d7-94f6-6fe16b81f727_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesIssued" xlink:to="lab_us-gaap_CommonStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsReceivable_01a015a8-8b08-72e8-b959-eb4e7f9ec2c3_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsReceivable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accounts Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccountsReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:to="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductsAndServicesDomain_01a015a8-8b8d-7b30-b222-2268794440ac_terseLabel_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:label id="lab_srt_ProductsAndServicesDomain_label_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductsAndServicesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductsAndServicesDomain" xlink:to="lab_srt_ProductsAndServicesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTable_01a015a8-8b8d-7c95-a633-2dc6f320582e_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Table]</link:label>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTable_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisaggregationOfRevenueTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueTable" xlink:to="lab_us-gaap_DisaggregationOfRevenueTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestructuringReserveCurrent_01a015a8-8b8d-7e00-841f-236f955f216b_periodStartLabel_en-US" xlink:label="lab_us-gaap_RestructuringReserveCurrent" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balance as of January 1, 2026</link:label>
    <link:label id="lab_us-gaap_RestructuringReserveCurrent_01a015a8-8b8d-7cd4-acce-db306b2a7b2f_periodEndLabel_en-US" xlink:label="lab_us-gaap_RestructuringReserveCurrent" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Balance as of September 30, 2026</link:label>
    <link:label id="lab_us-gaap_RestructuringReserveCurrent_label_en-US" xlink:label="lab_us-gaap_RestructuringReserveCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restructuring Reserve, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestructuringReserveCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestructuringReserveCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestructuringReserveCurrent" xlink:to="lab_us-gaap_RestructuringReserveCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Costs, Capitalized, Prepaid, and Other Assets Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureAbstract" xlink:to="lab_us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_WarrantsReceivedAsRevenue_01a015a8-8b08-7209-a694-dee2220fa8c5_negatedTerseLabel_en-US" xlink:label="lab_gemi_WarrantsReceivedAsRevenue" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Warrants received as revenue</link:label>
    <link:label id="lab_gemi_WarrantsReceivedAsRevenue_label_en-US" xlink:label="lab_gemi_WarrantsReceivedAsRevenue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrants Received As Revenue</link:label>
    <link:label id="lab_gemi_WarrantsReceivedAsRevenue_documentation_en-US" xlink:label="lab_gemi_WarrantsReceivedAsRevenue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Warrants Received As Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_WarrantsReceivedAsRevenue" xlink:href="gemi-20260930.xsd#gemi_WarrantsReceivedAsRevenue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_WarrantsReceivedAsRevenue" xlink:to="lab_gemi_WarrantsReceivedAsRevenue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsOtherMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoAssetReceivedAsRevenue_01a015a8-8b8d-762f-9281-845ae4b3c13d_negatedTerseLabel_en-US" xlink:label="lab_gemi_CryptoAssetReceivedAsRevenue" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Crypto assets received as revenue</link:label>
    <link:label id="lab_gemi_CryptoAssetReceivedAsRevenue_label_en-US" xlink:label="lab_gemi_CryptoAssetReceivedAsRevenue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset Received As Revenue</link:label>
    <link:label id="lab_gemi_CryptoAssetReceivedAsRevenue_documentation_en-US" xlink:label="lab_gemi_CryptoAssetReceivedAsRevenue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Asset Received As Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoAssetReceivedAsRevenue" xlink:href="gemi-20260930.xsd#gemi_CryptoAssetReceivedAsRevenue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoAssetReceivedAsRevenue" xlink:to="lab_gemi_CryptoAssetReceivedAsRevenue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditCardMember_01a015a8-8a6b-747d-be40-3cf0dad67743_terseLabel_en-US" xlink:label="lab_us-gaap_CreditCardMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit card revenue</link:label>
    <link:label id="lab_us-gaap_CreditCardMember_label_en-US" xlink:label="lab_us-gaap_CreditCardMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Card [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditCardMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CreditCardMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditCardMember" xlink:to="lab_us-gaap_CreditCardMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_RepurchaseAgreementsSecuritiesTransferredNominalValue_01a015a8-8b8d-719c-b686-9a907b390381_terseLabel_en-US" xlink:label="lab_gemi_RepurchaseAgreementsSecuritiesTransferredNominalValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nominal value</link:label>
    <link:label id="lab_gemi_RepurchaseAgreementsSecuritiesTransferredNominalValue_label_en-US" xlink:label="lab_gemi_RepurchaseAgreementsSecuritiesTransferredNominalValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repurchase Agreements, Securities Transferred, Nominal Value</link:label>
    <link:label id="lab_gemi_RepurchaseAgreementsSecuritiesTransferredNominalValue_documentation_en-US" xlink:label="lab_gemi_RepurchaseAgreementsSecuritiesTransferredNominalValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Repurchase Agreements, Securities Transferred, Nominal Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_RepurchaseAgreementsSecuritiesTransferredNominalValue" xlink:href="gemi-20260930.xsd#gemi_RepurchaseAgreementsSecuritiesTransferredNominalValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_RepurchaseAgreementsSecuritiesTransferredNominalValue" xlink:to="lab_gemi_RepurchaseAgreementsSecuritiesTransferredNominalValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_01a015a8-8b8d-7713-a2c1-a158100cd697_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrTerminationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Termination Date</link:label>
    <link:label id="lab_ecd_TrdArrTerminationDate_label_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Termination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrTerminationDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrTerminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrTerminationDate" xlink:to="lab_ecd_TrdArrTerminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_RelatedPartyAgreementFixedMonthlyRatePayable_01a015a8-8b08-7cbd-92b4-fe9f16634c21_terseLabel_en-US" xlink:label="lab_gemi_RelatedPartyAgreementFixedMonthlyRatePayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed monthly rate</link:label>
    <link:label id="lab_gemi_RelatedPartyAgreementFixedMonthlyRatePayable_label_en-US" xlink:label="lab_gemi_RelatedPartyAgreementFixedMonthlyRatePayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Agreement, Fixed Monthly Rate Payable</link:label>
    <link:label id="lab_gemi_RelatedPartyAgreementFixedMonthlyRatePayable_documentation_en-US" xlink:label="lab_gemi_RelatedPartyAgreementFixedMonthlyRatePayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Agreement, Fixed Monthly Rate Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_RelatedPartyAgreementFixedMonthlyRatePayable" xlink:href="gemi-20260930.xsd#gemi_RelatedPartyAgreementFixedMonthlyRatePayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_RelatedPartyAgreementFixedMonthlyRatePayable" xlink:to="lab_gemi_RelatedPartyAgreementFixedMonthlyRatePayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventsAbstract_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Events [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsAbstract" xlink:to="lab_us-gaap_SubsequentEventsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_01a015a8-8b08-7e7f-a891-9a651b0793c9_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_AssetsNettingFairValueDisclosure_01a015a8-8b08-702a-8dc3-fcf42223f19b_totalLabel_en-US" xlink:label="lab_gemi_AssetsNettingFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_gemi_AssetsNettingFairValueDisclosure_label_en-US" xlink:label="lab_gemi_AssetsNettingFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Netting, Fair Value Disclosure</link:label>
    <link:label id="lab_gemi_AssetsNettingFairValueDisclosure_documentation_en-US" xlink:label="lab_gemi_AssetsNettingFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Assets, Netting, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_AssetsNettingFairValueDisclosure" xlink:href="gemi-20260930.xsd#gemi_AssetsNettingFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_AssetsNettingFairValueDisclosure" xlink:to="lab_gemi_AssetsNettingFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_LineOfCreditFacilityRequiredCollateralPledgePercentageOfAmountOutstanding_01a015a8-8a6b-711d-8ad7-556b7b2c4df2_terseLabel_en-US" xlink:label="lab_gemi_LineOfCreditFacilityRequiredCollateralPledgePercentageOfAmountOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percent of outstanding loan amount required to be pledged as collateral</link:label>
    <link:label id="lab_gemi_LineOfCreditFacilityRequiredCollateralPledgePercentageOfAmountOutstanding_label_en-US" xlink:label="lab_gemi_LineOfCreditFacilityRequiredCollateralPledgePercentageOfAmountOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line Of Credit Facility, Required Collateral Pledge, Percentage Of Amount Outstanding</link:label>
    <link:label id="lab_gemi_LineOfCreditFacilityRequiredCollateralPledgePercentageOfAmountOutstanding_documentation_en-US" xlink:label="lab_gemi_LineOfCreditFacilityRequiredCollateralPledgePercentageOfAmountOutstanding" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line Of Credit Facility, Required Collateral Pledge, Percentage Of Amount Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_LineOfCreditFacilityRequiredCollateralPledgePercentageOfAmountOutstanding" xlink:href="gemi-20260930.xsd#gemi_LineOfCreditFacilityRequiredCollateralPledgePercentageOfAmountOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_LineOfCreditFacilityRequiredCollateralPledgePercentageOfAmountOutstanding" xlink:to="lab_gemi_LineOfCreditFacilityRequiredCollateralPledgePercentageOfAmountOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_01a015a8-8b08-7e89-8c12-b2aea436578e_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other current liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_01a015a8-8b08-7f36-83a9-0b95e9ce1500_totalLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total other current liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesCurrent" xlink:to="lab_us-gaap_OtherLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetsCurrent_01a015a8-8a6b-7157-a438-b9614519156e_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative assets</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetsCurrent_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssetsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetsCurrent" xlink:to="lab_us-gaap_DerivativeAssetsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrent_01a015a8-8b08-7c0b-9bbc-b731eda62fd6_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses</link:label>
    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrent_01a015a8-8b08-7403-a794-b4ae7d0da093_totalLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total accrued expenses</link:label>
    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedLiabilitiesCurrent" xlink:to="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardGrantDateFairValue_terseLabel_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value as of Grant Date</link:label>
    <link:label id="lab_ecd_AwardGrantDateFairValue_label_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardGrantDateFairValue" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardGrantDateFairValue" xlink:to="lab_ecd_AwardGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable_01a015a8-8b08-73f8-99fa-d69203505410_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic, by Common Class, Including Two-Class Method [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic, by Common Class, Including Two-Class Method [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable" xlink:to="lab_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward_01a015a8-8a6b-7dcc-ac46-cff46e9798a8_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Temporary Equity [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Temporary Equity [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInTemporaryEquityRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:to="lab_us-gaap_IncreaseDecreaseInTemporaryEquityRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure, Table</link:label>
    <link:label id="lab_ecd_PvpTableTextBlock_label_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PvpTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTableTextBlock" xlink:to="lab_ecd_PvpTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrDuration_terseLabel_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arrangement Duration</link:label>
    <link:label id="lab_ecd_TrdArrDuration_label_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Duration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrDuration" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrDuration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrDuration" xlink:to="lab_ecd_TrdArrDuration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableExcludingAccruedInterestAfterAllowanceForCreditLossNoncurrent_01a015a8-8b8e-7327-9176-c87c71a6bb74_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableExcludingAccruedInterestAfterAllowanceForCreditLossNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total credit card receivables</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableExcludingAccruedInterestAfterAllowanceForCreditLossNoncurrent_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableExcludingAccruedInterestAfterAllowanceForCreditLossNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Excluding Accrued Interest, after Allowance for Credit Loss, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableExcludingAccruedInterestAfterAllowanceForCreditLossNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableExcludingAccruedInterestAfterAllowanceForCreditLossNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableExcludingAccruedInterestAfterAllowanceForCreditLossNoncurrent" xlink:to="lab_us-gaap_AccountsReceivableExcludingAccruedInterestAfterAllowanceForCreditLossNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_RepurchaseAgreementsCryptoAssetPledgedAndSubjectToMarginCallNumberOfUnits_01a015a8-8b8d-7d74-8311-284b0a978cbd_terseLabel_en-US" xlink:label="lab_gemi_RepurchaseAgreementsCryptoAssetPledgedAndSubjectToMarginCallNumberOfUnits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pledged crypto subject to a margin call (in units)</link:label>
    <link:label id="lab_gemi_RepurchaseAgreementsCryptoAssetPledgedAndSubjectToMarginCallNumberOfUnits_label_en-US" xlink:label="lab_gemi_RepurchaseAgreementsCryptoAssetPledgedAndSubjectToMarginCallNumberOfUnits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repurchase Agreements, Crypto Asset, Pledged And Subject To Margin Call, Number Of Units</link:label>
    <link:label id="lab_gemi_RepurchaseAgreementsCryptoAssetPledgedAndSubjectToMarginCallNumberOfUnits_documentation_en-US" xlink:label="lab_gemi_RepurchaseAgreementsCryptoAssetPledgedAndSubjectToMarginCallNumberOfUnits" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Repurchase Agreements, Crypto Asset, Pledged And Subject To Margin Call, Number Of Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_RepurchaseAgreementsCryptoAssetPledgedAndSubjectToMarginCallNumberOfUnits" xlink:href="gemi-20260930.xsd#gemi_RepurchaseAgreementsCryptoAssetPledgedAndSubjectToMarginCallNumberOfUnits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_RepurchaseAgreementsCryptoAssetPledgedAndSubjectToMarginCallNumberOfUnits" xlink:to="lab_gemi_RepurchaseAgreementsCryptoAssetPledgedAndSubjectToMarginCallNumberOfUnits" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressPostalZipCode_01a015a8-8b08-7eae-b105-17ae8a0ae378_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressPostalZipCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressPostalZipCode" xlink:to="lab_dei_EntityAddressPostalZipCode" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_01a015a8-8b8d-7ade-8538-74cb8d75452f_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_GalaxyDigitalLLCGalaxyMember_01a015a8-8b8d-7b9a-97d6-b6143f1ad70b_terseLabel_en-US" xlink:label="lab_gemi_GalaxyDigitalLLCGalaxyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Galaxy</link:label>
    <link:label id="lab_gemi_GalaxyDigitalLLCGalaxyMember_label_en-US" xlink:label="lab_gemi_GalaxyDigitalLLCGalaxyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Galaxy Digital LLC ("Galaxy") [Member]</link:label>
    <link:label id="lab_gemi_GalaxyDigitalLLCGalaxyMember_documentation_en-US" xlink:label="lab_gemi_GalaxyDigitalLLCGalaxyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Galaxy Digital LLC ("Galaxy")</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_GalaxyDigitalLLCGalaxyMember" xlink:href="gemi-20260930.xsd#gemi_GalaxyDigitalLLCGalaxyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_GalaxyDigitalLLCGalaxyMember" xlink:to="lab_gemi_GalaxyDigitalLLCGalaxyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:to="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTableTextBlock_01a015a8-8b08-756e-992b-eab508204a33_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Estimated Fair Values of our Financial Assets and Financial Liabilities Measured at Amortized Cost</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTableTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosure of Asset and Liability Not Measured at Fair Value [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTableTextBlock" xlink:to="lab_us-gaap_FairValueDisclosureOfAssetAndLiabilityNotMeasuredAtFairValueTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseOther_01a015a8-8b8d-7ce4-8188-0c88f969a41c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseOther" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Interest expense on funding debt</link:label>
    <link:label id="lab_us-gaap_InterestExpenseOther_label_en-US" xlink:label="lab_us-gaap_InterestExpenseOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Other</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseOther" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseOther" xlink:to="lab_us-gaap_InterestExpenseOther" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsGross_01a015a8-8a6b-7099-8d28-e9e4f36b5797_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Carrying Amount</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsGross_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, before Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Revenues_01a015a8-8b08-7b7c-9e86-10b8036c9fce_terseLabel_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total revenue</link:label>
    <link:label id="lab_us-gaap_Revenues_01a015a8-8b08-7fe2-a07a-0a239f66e75d_totalLabel_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total revenue</link:label>
    <link:label id="lab_us-gaap_Revenues_label_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Revenues" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Revenues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Revenues" xlink:to="lab_us-gaap_Revenues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities_01a015a8-8b08-7195-9ced-eed57a67f63d_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable and accrued expenses</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accounts Payable and Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ThirdPartyDebtIncludingAccruedInterestCurrent_01a015a8-8b8d-74e5-953f-b4c2733b4433_terseLabel_en-US" xlink:label="lab_gemi_ThirdPartyDebtIncludingAccruedInterestCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Third party loans</link:label>
    <link:label id="lab_gemi_ThirdPartyDebtIncludingAccruedInterestCurrent_label_en-US" xlink:label="lab_gemi_ThirdPartyDebtIncludingAccruedInterestCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Third Party Debt, Including Accrued Interest, Current</link:label>
    <link:label id="lab_gemi_ThirdPartyDebtIncludingAccruedInterestCurrent_documentation_en-US" xlink:label="lab_gemi_ThirdPartyDebtIncludingAccruedInterestCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Third Party Debt, Including Accrued Interest, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ThirdPartyDebtIncludingAccruedInterestCurrent" xlink:href="gemi-20260930.xsd#gemi_ThirdPartyDebtIncludingAccruedInterestCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ThirdPartyDebtIncludingAccruedInterestCurrent" xlink:to="lab_gemi_ThirdPartyDebtIncludingAccruedInterestCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_FinancingAgreementsDecreaseInCollateralRate_01a015a8-8b8d-77af-9587-66cf97ef7e4e_terseLabel_en-US" xlink:label="lab_gemi_FinancingAgreementsDecreaseInCollateralRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Decrease in collateral rate</link:label>
    <link:label id="lab_gemi_FinancingAgreementsDecreaseInCollateralRate_label_en-US" xlink:label="lab_gemi_FinancingAgreementsDecreaseInCollateralRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Agreements, Decrease in Collateral Rate</link:label>
    <link:label id="lab_gemi_FinancingAgreementsDecreaseInCollateralRate_documentation_en-US" xlink:label="lab_gemi_FinancingAgreementsDecreaseInCollateralRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Agreements, Decrease in Collateral Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_FinancingAgreementsDecreaseInCollateralRate" xlink:href="gemi-20260930.xsd#gemi_FinancingAgreementsDecreaseInCollateralRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_FinancingAgreementsDecreaseInCollateralRate" xlink:to="lab_gemi_FinancingAgreementsDecreaseInCollateralRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExpirationsInPeriod_01a015a8-8b08-7321-b89c-63f92f9dcaaf_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExpirationsInPeriod" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Expired (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExpirationsInPeriod_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExpirationsInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Expirations in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExpirationsInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExpirationsInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExpirationsInPeriod" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExpirationsInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FurnitureAndFixturesMember_01a015a8-8b08-763d-8d6d-c62a11b8bbcc_terseLabel_en-US" xlink:label="lab_us-gaap_FurnitureAndFixturesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Furniture and fixtures</link:label>
    <link:label id="lab_us-gaap_FurnitureAndFixturesMember_label_en-US" xlink:label="lab_us-gaap_FurnitureAndFixturesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Furniture and Fixtures [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FurnitureAndFixturesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FurnitureAndFixturesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FurnitureAndFixturesMember" xlink:to="lab_us-gaap_FurnitureAndFixturesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_01a015a8-8b08-79f1-840f-43a2dec012c5_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Class [Domain]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_NonCashLeaseExpense_01a015a8-8b8d-7e99-acfe-6076c01fc423_terseLabel_en-US" xlink:label="lab_gemi_NonCashLeaseExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-cash lease expense</link:label>
    <link:label id="lab_gemi_NonCashLeaseExpense_label_en-US" xlink:label="lab_gemi_NonCashLeaseExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Cash Lease Expense</link:label>
    <link:label id="lab_gemi_NonCashLeaseExpense_documentation_en-US" xlink:label="lab_gemi_NonCashLeaseExpense" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Non-Cash Lease Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_NonCashLeaseExpense" xlink:href="gemi-20260930.xsd#gemi_NonCashLeaseExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_NonCashLeaseExpense" xlink:to="lab_gemi_NonCashLeaseExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_01a015a8-8b08-7ea8-ac54-9740ed23f174_periodStartLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_01a015a8-8b08-7282-9c06-b758170d397b_periodEndLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Carrying Amount, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TemporaryEquityCarryingAmountAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:to="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_01a015a8-8b8d-7c92-a064-ddcd1c0a8d23_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_01a015a8-8b08-7418-85f1-52ffd32945f2_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_01a015a8-8b08-70f0-8250-e9c64f9ddf12_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining 2026</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoAssetSaleNumberOfUnits_01a015a8-8b08-7d7b-bb88-d735fb34aed5_terseLabel_en-US" xlink:label="lab_gemi_CryptoAssetSaleNumberOfUnits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of crypto assets disposed (in units)</link:label>
    <link:label id="lab_gemi_CryptoAssetSaleNumberOfUnits_label_en-US" xlink:label="lab_gemi_CryptoAssetSaleNumberOfUnits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Sale, Number Of Units</link:label>
    <link:label id="lab_gemi_CryptoAssetSaleNumberOfUnits_documentation_en-US" xlink:label="lab_gemi_CryptoAssetSaleNumberOfUnits" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Asset, Disposition, Number Of Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoAssetSaleNumberOfUnits" xlink:href="gemi-20260930.xsd#gemi_CryptoAssetSaleNumberOfUnits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoAssetSaleNumberOfUnits" xlink:to="lab_gemi_CryptoAssetSaleNumberOfUnits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueOptionQuantitativeDisclosuresTable_01a015a8-8b08-710f-a418-25f0268c2a19_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOptionQuantitativeDisclosuresTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Option, Disclosures [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueOptionQuantitativeDisclosuresTable_label_en-US" xlink:label="lab_us-gaap_FairValueOptionQuantitativeDisclosuresTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Option, Disclosures [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueOptionQuantitativeDisclosuresTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueOptionQuantitativeDisclosuresTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueOptionQuantitativeDisclosuresTable" xlink:to="lab_us-gaap_FairValueOptionQuantitativeDisclosuresTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_01a015a8-8a6b-7f9e-823e-0ee48e8dc4e9_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurements</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:to="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_01a015a8-8a6b-7c3c-abf1-52edb20d9393_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 3</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 3 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel3Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel3Member" xlink:to="lab_us-gaap_FairValueInputsLevel3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_01a015a8-8b8d-7219-af59-acfc9bfda336_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expected term in years</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1" xlink:to="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_01a015a8-8b08-758c-bcf9-e87fc31e3733_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharePrice_01a015a8-8b8d-7847-a3d5-bd07996157b8_terseLabel_en-US" xlink:label="lab_us-gaap_SharePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Price per share of shares issued and sold (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_SharePrice_label_en-US" xlink:label="lab_us-gaap_SharePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharePrice" xlink:to="lab_us-gaap_SharePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StatementGeographicalAxis_01a015a8-8b8d-764b-a962-01650d386864_terseLabel_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:label id="lab_srt_StatementGeographicalAxis_label_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementGeographicalAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_StatementGeographicalAxis"/>
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    <link:label id="lab_us-gaap_PreferredUnitsLineItems_01a015a8-8b8d-7aa5-a9d5-6c7ef4a8a85d_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredUnitsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Units [Line Items]</link:label>
    <link:label id="lab_us-gaap_PreferredUnitsLineItems_label_en-US" xlink:label="lab_us-gaap_PreferredUnitsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Units [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredUnitsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredUnitsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredUnitsLineItems" xlink:to="lab_us-gaap_PreferredUnitsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfShortTermDebtTable_01a015a8-8b8d-789d-bbde-09149d25005c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShortTermDebtTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Short-Term Debt [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShortTermDebtTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShortTermDebtTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Debt [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShortTermDebtTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfShortTermDebtTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfShortTermDebtTable" xlink:to="lab_us-gaap_ScheduleOfShortTermDebtTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskCreditRisk_01a015a8-8b8d-7fce-9e8d-442773191a96_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskCreditRisk" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration of credit risk</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskCreditRisk_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskCreditRisk" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk, Credit Risk, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskCreditRisk" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskCreditRisk"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskCreditRisk" xlink:to="lab_us-gaap_ConcentrationRiskCreditRisk" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LegalEntityAxis_01a015a8-8b8e-78a0-b294-f08c864ef26e_terseLabel_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:label id="lab_dei_LegalEntityAxis_label_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LegalEntityAxis" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LegalEntityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LegalEntityAxis" xlink:to="lab_dei_LegalEntityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseDebt_01a015a8-8b8d-7d1a-81fb-b2ece51e5908_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseDebt_label_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseDebt" xlink:to="lab_us-gaap_InterestExpenseDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByLiabilityClassAxis_01a015a8-8a6b-7444-b133-c593b7f6595b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liability Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByLiabilityClassAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByLiabilityClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByLiabilityClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByLiabilityClassAxis" xlink:to="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionTable_01a015a8-8b08-7a93-924e-ac9efe12cfa4_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Operating Leased Assets [Table]</link:label>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionTable_label_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeLeaseDescriptionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeLeaseDescriptionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeLeaseDescriptionTable" xlink:to="lab_us-gaap_LesseeLeaseDescriptionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForRestructuring_01a015a8-8a6b-7485-a775-37838b2874fc_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForRestructuring" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Cash payments during the period</link:label>
    <link:label id="lab_us-gaap_PaymentsForRestructuring_label_en-US" xlink:label="lab_us-gaap_PaymentsForRestructuring" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for Restructuring</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForRestructuring" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsForRestructuring"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForRestructuring" xlink:to="lab_us-gaap_PaymentsForRestructuring" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_01a015a8-8b08-724a-82dc-b52e02d4ab28_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash, cash equivalents, restricted cash and cash equivalents, beginning of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_01a015a8-8b08-770e-99fa-7fd2c6d38c49_periodEndLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Cash, cash equivalents, restricted cash and cash equivalents, end of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_01a015a8-8b08-795c-92ee-c543d956e147_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total cash, cash equivalents, restricted cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_01a015a8-8b8d-71fd-b4f6-52ef46a1d534_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:to="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonNeosMember_terseLabel_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-NEOs</link:label>
    <link:label id="lab_ecd_NonNeosMember_label_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-NEOs [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonNeosMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonNeosMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonNeosMember" xlink:to="lab_ecd_NonNeosMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ShortTermDebtAbstractRollForward_01a015a8-8a6b-7af2-aca0-1b75584ba6d1_terseLabel_en-US" xlink:label="lab_gemi_ShortTermDebtAbstractRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Short Term Debt Abstract [Roll Forward]</link:label>
    <link:label id="lab_gemi_ShortTermDebtAbstractRollForward_label_en-US" xlink:label="lab_gemi_ShortTermDebtAbstractRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short Term Debt Abstract [Roll Forward]</link:label>
    <link:label id="lab_gemi_ShortTermDebtAbstractRollForward_documentation_en-US" xlink:label="lab_gemi_ShortTermDebtAbstractRollForward" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Short Term Debt Abstract</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ShortTermDebtAbstractRollForward" xlink:href="gemi-20260930.xsd#gemi_ShortTermDebtAbstractRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ShortTermDebtAbstractRollForward" xlink:to="lab_gemi_ShortTermDebtAbstractRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoLoansPayableUnrealizedGainLossNonoperating_01a015a8-8b8d-7072-a11f-191089c9da5d_terseLabel_en-US" xlink:label="lab_gemi_CryptoLoansPayableUnrealizedGainLossNonoperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss)</link:label>
    <link:label id="lab_gemi_CryptoLoansPayableUnrealizedGainLossNonoperating_label_en-US" xlink:label="lab_gemi_CryptoLoansPayableUnrealizedGainLossNonoperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Loans Payable, Unrealized Gain (Loss), Nonoperating</link:label>
    <link:label id="lab_gemi_CryptoLoansPayableUnrealizedGainLossNonoperating_documentation_en-US" xlink:label="lab_gemi_CryptoLoansPayableUnrealizedGainLossNonoperating" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Loans Payable, Unrealized Gain (Loss), Nonoperating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoLoansPayableUnrealizedGainLossNonoperating" xlink:href="gemi-20260930.xsd#gemi_CryptoLoansPayableUnrealizedGainLossNonoperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoLoansPayableUnrealizedGainLossNonoperating" xlink:to="lab_gemi_CryptoLoansPayableUnrealizedGainLossNonoperating" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_01a015a8-8b8d-7304-8ff7-811680b25010_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_RepurchaseAgreementsDiscount_01a015a8-8b08-7543-a047-4cefdd0f3570_negatedTerseLabel_en-US" xlink:label="lab_gemi_RepurchaseAgreementsDiscount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Discount</link:label>
    <link:label id="lab_gemi_RepurchaseAgreementsDiscount_label_en-US" xlink:label="lab_gemi_RepurchaseAgreementsDiscount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repurchase Agreements, Discount</link:label>
    <link:label id="lab_gemi_RepurchaseAgreementsDiscount_documentation_en-US" xlink:label="lab_gemi_RepurchaseAgreementsDiscount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Repurchase Agreements, Discount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_RepurchaseAgreementsDiscount" xlink:href="gemi-20260930.xsd#gemi_RepurchaseAgreementsDiscount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_RepurchaseAgreementsDiscount" xlink:to="lab_gemi_RepurchaseAgreementsDiscount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeasesTextBlock_01a015a8-8a6b-733a-b0fb-f35314f8d637_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeasesTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Leases [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeasesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeasesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeasesTextBlock" xlink:to="lab_us-gaap_LesseeOperatingLeasesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_01a015a8-8b08-751a-87aa-e89dbd418ba7_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeDomain" xlink:to="lab_us-gaap_LongtermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityCurrent_01a015a8-8b8d-7e6c-b7bd-dfd74b77a3f8_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unearned advisory fee revenue</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityCurrent_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractWithCustomerLiabilityCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:to="lab_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_01a015a8-8b08-72f7-9c1c-9e0fd6005453_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock_01a015a8-8b8d-722c-8bee-d38c420be50c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Gain (Loss) on Changes in the Fair Value</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativeInstrumentsGainLossInStatementOfFinancialPerformanceTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_A500BTCMay112023Member_01a015a8-8b8d-7825-bf83-dacb58e68964_terseLabel_en-US" xlink:label="lab_gemi_A500BTCMay112023Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">500 BTC May 11, 2023</link:label>
    <link:label id="lab_gemi_A500BTCMay112023Member_label_en-US" xlink:label="lab_gemi_A500BTCMay112023Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">500 BTC May 11, 2023 [Member]</link:label>
    <link:label id="lab_gemi_A500BTCMay112023Member_documentation_en-US" xlink:label="lab_gemi_A500BTCMay112023Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">500 BTC May 11, 2023</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_A500BTCMay112023Member" xlink:href="gemi-20260930.xsd#gemi_A500BTCMay112023Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_A500BTCMay112023Member" xlink:to="lab_gemi_A500BTCMay112023Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AwardTypeAxis_01a015a8-8a6b-70a8-9c9b-d2f12f90a29d_terseLabel_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:label id="lab_us-gaap_AwardTypeAxis_label_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AwardTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AwardTypeAxis" xlink:to="lab_us-gaap_AwardTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote</link:label>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_label_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NamedExecutiveOfficersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:to="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_FinancingAgreementsLoanTerm_01a015a8-8b8e-7228-a3ae-0850cc5c3da9_terseLabel_en-US" xlink:label="lab_gemi_FinancingAgreementsLoanTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing agreements loan, term</link:label>
    <link:label id="lab_gemi_FinancingAgreementsLoanTerm_label_en-US" xlink:label="lab_gemi_FinancingAgreementsLoanTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Agreements Loan, Term</link:label>
    <link:label id="lab_gemi_FinancingAgreementsLoanTerm_documentation_en-US" xlink:label="lab_gemi_FinancingAgreementsLoanTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Agreements Loan, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_FinancingAgreementsLoanTerm" xlink:href="gemi-20260930.xsd#gemi_FinancingAgreementsLoanTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_FinancingAgreementsLoanTerm" xlink:to="lab_gemi_FinancingAgreementsLoanTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_01a015a8-8b8d-7b9f-9983-b33b9d8a5f5e_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated deficit</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestructuringAndRelatedActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_RestructuringAndRelatedActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restructuring and Related Activities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestructuringAndRelatedActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestructuringAndRelatedActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestructuringAndRelatedActivitiesAbstract" xlink:to="lab_us-gaap_RestructuringAndRelatedActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductOrServiceAxis_01a015a8-8b08-7207-9652-7b818cb82053_terseLabel_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:label id="lab_srt_ProductOrServiceAxis_label_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductOrServiceAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductOrServiceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductOrServiceAxis" xlink:to="lab_srt_ProductOrServiceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ConvertibleNotesAndRelatedPartyTermLoansMember_01a015a8-8b08-73af-a5a5-8309c9efcbc1_terseLabel_en-US" xlink:label="lab_gemi_ConvertibleNotesAndRelatedPartyTermLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion of convertible notes and related party term loans to common stock in connection with IPO</link:label>
    <link:label id="lab_gemi_ConvertibleNotesAndRelatedPartyTermLoansMember_label_en-US" xlink:label="lab_gemi_ConvertibleNotesAndRelatedPartyTermLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Convertible Notes And Related Party Term Loans [Member]</link:label>
    <link:label id="lab_gemi_ConvertibleNotesAndRelatedPartyTermLoansMember_documentation_en-US" xlink:label="lab_gemi_ConvertibleNotesAndRelatedPartyTermLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Convertible Notes And Related Party Term Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ConvertibleNotesAndRelatedPartyTermLoansMember" xlink:href="gemi-20260930.xsd#gemi_ConvertibleNotesAndRelatedPartyTermLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ConvertibleNotesAndRelatedPartyTermLoansMember" xlink:to="lab_gemi_ConvertibleNotesAndRelatedPartyTermLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShortTermDebtLineItems_01a015a8-8a6b-7e38-b812-d7144443caa7_terseLabel_en-US" xlink:label="lab_us-gaap_ShortTermDebtLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Short-Term Debt [Line Items]</link:label>
    <link:label id="lab_us-gaap_ShortTermDebtLineItems_label_en-US" xlink:label="lab_us-gaap_ShortTermDebtLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Debt [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermDebtLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShortTermDebtLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortTermDebtLineItems" xlink:to="lab_us-gaap_ShortTermDebtLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockMember_01a015a8-8a6b-7efd-8d21-4d08b9c55bce_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockMember" xlink:to="lab_us-gaap_CommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseCost_01a015a8-8a6b-7e37-afa6-7130b116d09a_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease expense</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseCost_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseCost" xlink:to="lab_us-gaap_OperatingLeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeSeveranceMember_01a015a8-8b08-71fe-9ae5-ad4b4170bc6f_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeSeveranceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Severance and Other Personnel Costs</link:label>
    <link:label id="lab_us-gaap_EmployeeSeveranceMember_label_en-US" xlink:label="lab_us-gaap_EmployeeSeveranceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Employee Severance [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeSeveranceMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeSeveranceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeSeveranceMember" xlink:to="lab_us-gaap_EmployeeSeveranceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_DebtInstrumentInterestRateUponMaximumBorrowingCapacityTrigger_01a015a8-8b08-70c5-8892-1579e9171d62_terseLabel_en-US" xlink:label="lab_gemi_DebtInstrumentInterestRateUponMaximumBorrowingCapacityTrigger" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate increase upon outstanding balance threshold</link:label>
    <link:label id="lab_gemi_DebtInstrumentInterestRateUponMaximumBorrowingCapacityTrigger_label_en-US" xlink:label="lab_gemi_DebtInstrumentInterestRateUponMaximumBorrowingCapacityTrigger" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate Upon Maximum Borrowing Capacity Trigger</link:label>
    <link:label id="lab_gemi_DebtInstrumentInterestRateUponMaximumBorrowingCapacityTrigger_documentation_en-US" xlink:label="lab_gemi_DebtInstrumentInterestRateUponMaximumBorrowingCapacityTrigger" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate Upon Maximum Borrowing Capacity Trigger</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_DebtInstrumentInterestRateUponMaximumBorrowingCapacityTrigger" xlink:href="gemi-20260930.xsd#gemi_DebtInstrumentInterestRateUponMaximumBorrowingCapacityTrigger"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_DebtInstrumentInterestRateUponMaximumBorrowingCapacityTrigger" xlink:to="lab_gemi_DebtInstrumentInterestRateUponMaximumBorrowingCapacityTrigger" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate_01a015a8-8b08-7bdd-a026-0a456d7e7b8f_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividend Yield</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Dividend Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonUsMember_01a015a8-8b08-7f5c-84ce-a348611bbd68_terseLabel_en-US" xlink:label="lab_us-gaap_NonUsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">International</link:label>
    <link:label id="lab_us-gaap_NonUsMember_label_en-US" xlink:label="lab_us-gaap_NonUsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-US [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonUsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonUsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonUsMember" xlink:to="lab_us-gaap_NonUsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_01a015a8-8a6b-7f63-be2f-6697f4b5e4d8_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_label_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeContractTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeContractTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeContractTypeDomain" xlink:to="lab_us-gaap_DerivativeContractTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReceivablesPolicyTextBlock_01a015a8-8b08-75a0-9891-5b3b070ee00b_terseLabel_en-US" xlink:label="lab_us-gaap_ReceivablesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan receivables</link:label>
    <link:label id="lab_us-gaap_ReceivablesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ReceivablesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivable [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivablesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReceivablesPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReceivablesPolicyTextBlock" xlink:to="lab_us-gaap_ReceivablesPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialAssetPastDueMember_01a015a8-8b8e-79b5-8775-60b27dda5858_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialAssetPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total past due receivables</link:label>
    <link:label id="lab_us-gaap_FinancialAssetPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancialAssetPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialAssetPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancialAssetPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialAssetPastDueMember" xlink:to="lab_us-gaap_FinancialAssetPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_01a015a8-8b8d-7e6a-bd99-78f128758681_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities and stockholders&#8217; equity</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAcceleratedCompensationCost_01a015a8-8b8d-718b-a13a-bf10d2b91fbb_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAcceleratedCompensationCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Incremental expense from acceleration of vesting of certain awards</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAcceleratedCompensationCost_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAcceleratedCompensationCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Accelerated Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAcceleratedCompensationCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAcceleratedCompensationCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAcceleratedCompensationCost" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAcceleratedCompensationCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_01a015a8-8b8d-7ba5-98d8-78c1640783b5_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding stock options</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure</link:label>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_label_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Additional402vDisclosureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Additional402vDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Additional402vDisclosureTextBlock" xlink:to="lab_ecd_Additional402vDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestructuringCharges_01a015a8-8b8d-7158-822c-950a34a47688_terseLabel_en-US" xlink:label="lab_us-gaap_RestructuringCharges" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restructuring charges</link:label>
    <link:label id="lab_us-gaap_RestructuringCharges_01a015a8-8b8d-794d-96a6-a07cd09d22cc_verboseLabel_en-US" xlink:label="lab_us-gaap_RestructuringCharges" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Severance and other personnel costs</link:label>
    <link:label id="lab_us-gaap_RestructuringCharges_label_en-US" xlink:label="lab_us-gaap_RestructuringCharges" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restructuring Charges</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestructuringCharges" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestructuringCharges"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestructuringCharges" xlink:to="lab_us-gaap_RestructuringCharges" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ExitAndWindDownMember_01a015a8-8b08-7b1d-9a70-846b41040737_terseLabel_en-US" xlink:label="lab_gemi_ExitAndWindDownMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exit And Wind-Down</link:label>
    <link:label id="lab_gemi_ExitAndWindDownMember_label_en-US" xlink:label="lab_gemi_ExitAndWindDownMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Exit And Wind-Down [Member]</link:label>
    <link:label id="lab_gemi_ExitAndWindDownMember_documentation_en-US" xlink:label="lab_gemi_ExitAndWindDownMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Exit And Wind-Down Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ExitAndWindDownMember" xlink:href="gemi-20260930.xsd#gemi_ExitAndWindDownMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ExitAndWindDownMember" xlink:to="lab_gemi_ExitAndWindDownMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyDomain_01a015a8-8b8d-70c8-830f-ef205ded30b3_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyDomain" xlink:to="lab_us-gaap_RelatedPartyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuredDebtRepurchaseAgreements_01a015a8-8b08-7690-bc6b-9ce099f2a9c2_terseLabel_en-US" xlink:label="lab_us-gaap_SecuredDebtRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreement</link:label>
    <link:label id="lab_us-gaap_SecuredDebtRepurchaseAgreements_01a015a8-8b08-70bb-8607-685e33a5311c_verboseLabel_en-US" xlink:label="lab_us-gaap_SecuredDebtRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Principal Outstanding</link:label>
    <link:label id="lab_us-gaap_SecuredDebtRepurchaseAgreements_label_en-US" xlink:label="lab_us-gaap_SecuredDebtRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secured Debt, Repurchase Agreements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuredDebtRepurchaseAgreements" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SecuredDebtRepurchaseAgreements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuredDebtRepurchaseAgreements" xlink:to="lab_us-gaap_SecuredDebtRepurchaseAgreements" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TabularListTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tabular List, Table</link:label>
    <link:label id="lab_ecd_TabularListTableTextBlock_label_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tabular List [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TabularListTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TabularListTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TabularListTableTextBlock" xlink:to="lab_ecd_TabularListTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_01a015a8-8b8d-7885-9adb-336aca2c1ee2_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid in Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapital" xlink:to="lab_us-gaap_AdditionalPaidInCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_AccountsReceivableCreditLossExpenseReversalIncludingPledgedAmounts_01a015a8-8b8d-79f8-a675-b9d9253eca57_verboseLabel_en-US" xlink:label="lab_gemi_AccountsReceivableCreditLossExpenseReversalIncludingPledgedAmounts" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Transaction losses</link:label>
    <link:label id="lab_gemi_AccountsReceivableCreditLossExpenseReversalIncludingPledgedAmounts_01a015a8-8b8d-7e48-8b11-9a992597a1e8_netLabel_en-US" xlink:label="lab_gemi_AccountsReceivableCreditLossExpenseReversalIncludingPledgedAmounts" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Provision for transaction losses</link:label>
    <link:label id="lab_gemi_AccountsReceivableCreditLossExpenseReversalIncludingPledgedAmounts_label_en-US" xlink:label="lab_gemi_AccountsReceivableCreditLossExpenseReversalIncludingPledgedAmounts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Credit Loss Expense (Reversal), Including Pledged Amounts</link:label>
    <link:label id="lab_gemi_AccountsReceivableCreditLossExpenseReversalIncludingPledgedAmounts_documentation_en-US" xlink:label="lab_gemi_AccountsReceivableCreditLossExpenseReversalIncludingPledgedAmounts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Credit Loss Expense (Reversal), Including Pledged Amounts</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_AccountsReceivableCreditLossExpenseReversalIncludingPledgedAmounts" xlink:href="gemi-20260930.xsd#gemi_AccountsReceivableCreditLossExpenseReversalIncludingPledgedAmounts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_AccountsReceivableCreditLossExpenseReversalIncludingPledgedAmounts" xlink:to="lab_gemi_AccountsReceivableCreditLossExpenseReversalIncludingPledgedAmounts" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_BitcoinRestrictedForRegulatoryCapitalRequirementsMember_01a015a8-8b08-7508-8a81-68af19b1fba0_terseLabel_en-US" xlink:label="lab_gemi_BitcoinRestrictedForRegulatoryCapitalRequirementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted For Regulatory Capital Requirements</link:label>
    <link:label id="lab_gemi_BitcoinRestrictedForRegulatoryCapitalRequirementsMember_label_en-US" xlink:label="lab_gemi_BitcoinRestrictedForRegulatoryCapitalRequirementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Bitcoin, Restricted For Regulatory Capital Requirements [Member]</link:label>
    <link:label id="lab_gemi_BitcoinRestrictedForRegulatoryCapitalRequirementsMember_documentation_en-US" xlink:label="lab_gemi_BitcoinRestrictedForRegulatoryCapitalRequirementsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Bitcoin, Restricted Under Related Party Crypto Asset Loan Agreements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_BitcoinRestrictedForRegulatoryCapitalRequirementsMember" xlink:href="gemi-20260930.xsd#gemi_BitcoinRestrictedForRegulatoryCapitalRequirementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_BitcoinRestrictedForRegulatoryCapitalRequirementsMember" xlink:to="lab_gemi_BitcoinRestrictedForRegulatoryCapitalRequirementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_01a015a8-8b8d-784f-9893-09b7dd521727_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CommonUnitNumberOfClasses_01a015a8-8b8d-7dd9-bf6b-75b5daad7a9b_terseLabel_en-US" xlink:label="lab_gemi_CommonUnitNumberOfClasses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of classes of common units</link:label>
    <link:label id="lab_gemi_CommonUnitNumberOfClasses_label_en-US" xlink:label="lab_gemi_CommonUnitNumberOfClasses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Unit, Number Of Classes</link:label>
    <link:label id="lab_gemi_CommonUnitNumberOfClasses_documentation_en-US" xlink:label="lab_gemi_CommonUnitNumberOfClasses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Units, Number Of Classes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CommonUnitNumberOfClasses" xlink:href="gemi-20260930.xsd#gemi_CommonUnitNumberOfClasses"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear_01a015a8-8a6b-7c81-9bcd-7181f1c555cd_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining 2026</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear"/>
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    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscIndName"/>
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    <link:label id="lab_us-gaap_LineOfCreditFacilityAverageOutstandingAmount_01a1bdf5-5ef9-7e2b-9aef-006a1ec1b94a_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityAverageOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Average principal outstanding balance</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityAverageOutstandingAmount_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityAverageOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Average Outstanding Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityAverageOutstandingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityAverageOutstandingAmount"/>
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    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_terseLabel_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_label_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:to="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_01a015a8-8b08-7711-9529-9b966ea8860c_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate intrinsic value of options outstanding</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Intrinsic Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_01a015a8-8a6b-74d5-92ec-09cf848d84de_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Lived Asset, Class [Domain]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Asset, Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain_01a015a8-8b08-7c23-8be8-5626d2eda2fc_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value by Liability Class [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value by Liability Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_CryptoAssetAxis_01a015a8-8a6b-74dc-82c6-89f80ce5cc90_terseLabel_en-US" xlink:label="lab_srt_CryptoAssetAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto Asset [Axis]</link:label>
    <link:label id="lab_srt_CryptoAssetAxis_label_en-US" xlink:label="lab_srt_CryptoAssetAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CryptoAssetAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_CryptoAssetAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_CryptoAssetAxis" xlink:to="lab_srt_CryptoAssetAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_BitcoinBitcoinRestrictedForCollateralRequirementsMember_01a015a8-8b08-7f06-8e81-d5daaf7de7df_terseLabel_en-US" xlink:label="lab_gemi_BitcoinBitcoinRestrictedForCollateralRequirementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted For Collateral Requirements</link:label>
    <link:label id="lab_gemi_BitcoinBitcoinRestrictedForCollateralRequirementsMember_label_en-US" xlink:label="lab_gemi_BitcoinBitcoinRestrictedForCollateralRequirementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Bitcoin, Bitcoin, Restricted For Collateral Requirements [Member]</link:label>
    <link:label id="lab_gemi_BitcoinBitcoinRestrictedForCollateralRequirementsMember_documentation_en-US" xlink:label="lab_gemi_BitcoinBitcoinRestrictedForCollateralRequirementsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Bitcoin, Bitcoin, Restricted For Collateral Requirements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_BitcoinBitcoinRestrictedForCollateralRequirementsMember" xlink:href="gemi-20260930.xsd#gemi_BitcoinBitcoinRestrictedForCollateralRequirementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_BitcoinBitcoinRestrictedForCollateralRequirementsMember" xlink:to="lab_gemi_BitcoinBitcoinRestrictedForCollateralRequirementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PortionAtOtherThanFairValueFairValueDisclosureMember_01a015a8-8b08-708d-82d5-18be7d6fbd93_terseLabel_en-US" xlink:label="lab_us-gaap_PortionAtOtherThanFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portion at Other than Fair Value Measurement</link:label>
    <link:label id="lab_us-gaap_PortionAtOtherThanFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_PortionAtOtherThanFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Portion at Other than Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtOtherThanFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PortionAtOtherThanFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PortionAtOtherThanFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_PortionAtOtherThanFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_LesseeOperatingLeaseLeaseNotYetCommencedTermOfRentAbatement_01a1cd97-3d31-7024-8aec-71259016419a_terseLabel_en-US" xlink:label="lab_gemi_LesseeOperatingLeaseLeaseNotYetCommencedTermOfRentAbatement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, lease not yet commenced, monthly rent term</link:label>
    <link:label id="lab_gemi_LesseeOperatingLeaseLeaseNotYetCommencedTermOfRentAbatement_label_en-US" xlink:label="lab_gemi_LesseeOperatingLeaseLeaseNotYetCommencedTermOfRentAbatement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Lease Not Yet Commenced, Term Of Rent Abatement</link:label>
    <link:label id="lab_gemi_LesseeOperatingLeaseLeaseNotYetCommencedTermOfRentAbatement_documentation_en-US" xlink:label="lab_gemi_LesseeOperatingLeaseLeaseNotYetCommencedTermOfRentAbatement" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Lease Not Yet Commenced, Term Of Rent Abatement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_LesseeOperatingLeaseLeaseNotYetCommencedTermOfRentAbatement" xlink:href="gemi-20260930.xsd#gemi_LesseeOperatingLeaseLeaseNotYetCommencedTermOfRentAbatement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_LesseeOperatingLeaseLeaseNotYetCommencedTermOfRentAbatement" xlink:to="lab_gemi_LesseeOperatingLeaseLeaseNotYetCommencedTermOfRentAbatement" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_01a015a8-8b8d-7287-a875-5d08282b155f_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfPropertyPlantAndEquipmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:to="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockValue_01a015a8-8a6b-7412-a1e9-225dc2ac67e2_verboseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, par value $0.001 per share; 20,000 shares authorized, no shares issued and outstanding as of September&#160;30, 2026 and December&#160;31, 2025</link:label>
    <link:label id="lab_us-gaap_PreferredStockValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockValue" xlink:to="lab_us-gaap_PreferredStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAxis_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation:</link:label>
    <link:label id="lab_ecd_AdjToCompAxis_label_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToCompAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAxis" xlink:to="lab_ecd_AdjToCompAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ChicagoOfficeLeaseMember_01a015a8-8b8d-7dc0-bbe5-07192b31580d_terseLabel_en-US" xlink:label="lab_gemi_ChicagoOfficeLeaseMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Chicago Office Lease</link:label>
    <link:label id="lab_gemi_ChicagoOfficeLeaseMember_label_en-US" xlink:label="lab_gemi_ChicagoOfficeLeaseMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Chicago Office Lease [Member]</link:label>
    <link:label id="lab_gemi_ChicagoOfficeLeaseMember_documentation_en-US" xlink:label="lab_gemi_ChicagoOfficeLeaseMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Chicago Office Lease</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ChicagoOfficeLeaseMember" xlink:href="gemi-20260930.xsd#gemi_ChicagoOfficeLeaseMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ChicagoOfficeLeaseMember" xlink:to="lab_gemi_ChicagoOfficeLeaseMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_EmperyDigitalInc.WarrantsMember_01a015a8-8a6b-779b-9683-51ea56665651_terseLabel_en-US" xlink:label="lab_gemi_EmperyDigitalInc.WarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Empery Common Stock</link:label>
    <link:label id="lab_gemi_EmperyDigitalInc.WarrantsMember_label_en-US" xlink:label="lab_gemi_EmperyDigitalInc.WarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Empery Digital Inc. Warrants [Member]</link:label>
    <link:label id="lab_gemi_EmperyDigitalInc.WarrantsMember_documentation_en-US" xlink:label="lab_gemi_EmperyDigitalInc.WarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Empery Digital Inc. Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_EmperyDigitalInc.WarrantsMember" xlink:href="gemi-20260930.xsd#gemi_EmperyDigitalInc.WarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_EmperyDigitalInc.WarrantsMember" xlink:to="lab_gemi_EmperyDigitalInc.WarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestructuringCostAndReserveLineItems_01a015a8-8b08-7094-beec-0a519b4e5320_terseLabel_en-US" xlink:label="lab_us-gaap_RestructuringCostAndReserveLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restructuring Cost and Reserve [Line Items]</link:label>
    <link:label id="lab_us-gaap_RestructuringCostAndReserveLineItems_label_en-US" xlink:label="lab_us-gaap_RestructuringCostAndReserveLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restructuring Cost and Reserve [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestructuringCostAndReserveLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestructuringCostAndReserveLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestructuringCostAndReserveLineItems" xlink:to="lab_us-gaap_RestructuringCostAndReserveLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Rule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:to="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_AggtErrCompAmt_label_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompAmt" xlink:to="lab_ecd_AggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPaidNet_01a015a8-8b8d-74dc-8a53-d188b60c0003_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash paid during the period for interest</link:label>
    <link:label id="lab_us-gaap_InterestPaidNet_label_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Paid, Excluding Capitalized Interest, Operating Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPaidNet" xlink:to="lab_us-gaap_InterestPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_July22026MarkerMember_01a015a8-8b08-73ac-bb8f-84e9ca60d17b_terseLabel_en-US" xlink:label="lab_gemi_July22026MarkerMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">July 2, 2026 Marker</link:label>
    <link:label id="lab_gemi_July22026MarkerMember_label_en-US" xlink:label="lab_gemi_July22026MarkerMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">July 2, 2026 Marker [Member]</link:label>
    <link:label id="lab_gemi_July22026MarkerMember_documentation_en-US" xlink:label="lab_gemi_July22026MarkerMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">July 2, 2026 Marker</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_July22026MarkerMember" xlink:href="gemi-20260930.xsd#gemi_July22026MarkerMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_July22026MarkerMember" xlink:to="lab_gemi_July22026MarkerMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_TotalCollateralAssociatedWithRepurchaseAgreements_01a015a8-8b08-7653-ab44-34ec7eaa216b_terseLabel_en-US" xlink:label="lab_gemi_TotalCollateralAssociatedWithRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral amount</link:label>
    <link:label id="lab_gemi_TotalCollateralAssociatedWithRepurchaseAgreements_label_en-US" xlink:label="lab_gemi_TotalCollateralAssociatedWithRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Collateral Associated With Repurchase Agreements</link:label>
    <link:label id="lab_gemi_TotalCollateralAssociatedWithRepurchaseAgreements_documentation_en-US" xlink:label="lab_gemi_TotalCollateralAssociatedWithRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Total Collateral Associated With Repurchase Agreements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_TotalCollateralAssociatedWithRepurchaseAgreements" xlink:href="gemi-20260930.xsd#gemi_TotalCollateralAssociatedWithRepurchaseAgreements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_TotalCollateralAssociatedWithRepurchaseAgreements" xlink:to="lab_gemi_TotalCollateralAssociatedWithRepurchaseAgreements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityAxis_01a015a8-8b08-7d97-996c-a7f2a6280c48_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityAxis_label_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CreditFacilityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityAxis" xlink:to="lab_us-gaap_CreditFacilityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestructuringAndRelatedActivitiesDisclosureTextBlock_01a015a8-8b8d-7640-b1de-af52e906d497_terseLabel_en-US" xlink:label="lab_us-gaap_RestructuringAndRelatedActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restructuring Activities</link:label>
    <link:label id="lab_us-gaap_RestructuringAndRelatedActivitiesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_RestructuringAndRelatedActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restructuring and Related Activities Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestructuringAndRelatedActivitiesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestructuringAndRelatedActivitiesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestructuringAndRelatedActivitiesDisclosureTextBlock" xlink:to="lab_us-gaap_RestructuringAndRelatedActivitiesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRepurchaseAgreements_01a015a8-8b8d-7411-b82b-5afc6fbb2f21_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Repurchase Agreements</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRepurchaseAgreements_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Repurchase Agreements [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRepurchaseAgreements" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRepurchaseAgreements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRepurchaseAgreements" xlink:to="lab_us-gaap_ScheduleOfRepurchaseAgreements" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureName_terseLabel_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_MeasureName_label_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureName" xlink:to="lab_ecd_MeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PayVsPerformanceDisclosureLineItems_label_en-US" xlink:label="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PayVsPerformanceDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:to="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_01a015a8-8b08-765f-9f34-2e3e57136c56_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_01a015a8-8b08-71fd-95f3-7d321ceb5773_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_WarrantNoncurrent_01a015a8-8b8d-7364-8e08-eb432b81709a_terseLabel_en-US" xlink:label="lab_gemi_WarrantNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrant derivative</link:label>
    <link:label id="lab_gemi_WarrantNoncurrent_label_en-US" xlink:label="lab_gemi_WarrantNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrant, Noncurrent</link:label>
    <link:label id="lab_gemi_WarrantNoncurrent_documentation_en-US" xlink:label="lab_gemi_WarrantNoncurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Warrant Derivative, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_WarrantNoncurrent" xlink:href="gemi-20260930.xsd#gemi_WarrantNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_WarrantNoncurrent" xlink:to="lab_gemi_WarrantNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_01a015a8-8a6b-765d-afa6-a387c567855e_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional Paid-In Capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:to="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_GeminiTrustCompanyLLCMember_01a015a8-8b08-79dc-9b14-fcbc99722428_terseLabel_en-US" xlink:label="lab_gemi_GeminiTrustCompanyLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">GTC</link:label>
    <link:label id="lab_gemi_GeminiTrustCompanyLLCMember_label_en-US" xlink:label="lab_gemi_GeminiTrustCompanyLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gemini Trust Company, LLC [Member]</link:label>
    <link:label id="lab_gemi_GeminiTrustCompanyLLCMember_documentation_en-US" xlink:label="lab_gemi_GeminiTrustCompanyLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gemini Trust Company, LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_GeminiTrustCompanyLLCMember" xlink:href="gemi-20260930.xsd#gemi_GeminiTrustCompanyLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_GeminiTrustCompanyLLCMember" xlink:to="lab_gemi_GeminiTrustCompanyLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_RepurchaseAgreementsCryptoAssetPledgedNumberOfUnits_01a015a8-8b08-74c1-99ca-e7ab872ead4a_terseLabel_en-US" xlink:label="lab_gemi_RepurchaseAgreementsCryptoAssetPledgedNumberOfUnits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pledged crypto (in units)</link:label>
    <link:label id="lab_gemi_RepurchaseAgreementsCryptoAssetPledgedNumberOfUnits_label_en-US" xlink:label="lab_gemi_RepurchaseAgreementsCryptoAssetPledgedNumberOfUnits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repurchase Agreements, Crypto Asset, Pledged, Number Of Units</link:label>
    <link:label id="lab_gemi_RepurchaseAgreementsCryptoAssetPledgedNumberOfUnits_documentation_en-US" xlink:label="lab_gemi_RepurchaseAgreementsCryptoAssetPledgedNumberOfUnits" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Repurchase Agreements, Crypto Asset, Pledged, Number Of Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_RepurchaseAgreementsCryptoAssetPledgedNumberOfUnits" xlink:href="gemi-20260930.xsd#gemi_RepurchaseAgreementsCryptoAssetPledgedNumberOfUnits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_RepurchaseAgreementsCryptoAssetPledgedNumberOfUnits" xlink:to="lab_gemi_RepurchaseAgreementsCryptoAssetPledgedNumberOfUnits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardForfeitures_01a015a8-8b08-73e0-9a7e-85c86d890e9e_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardForfeitures" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Forfeiture of unvested restricted shares</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardForfeitures_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardForfeitures" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Restricted Stock Award, Forfeitures</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardForfeitures" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardForfeitures"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardForfeitures" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardForfeitures" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueNotFromContractWithCustomer_01a015a8-8b08-73e0-ac7c-4007f6a34bd0_totalLabel_en-US" xlink:label="lab_us-gaap_RevenueNotFromContractWithCustomer" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total revenue not from contracts with customers</link:label>
    <link:label id="lab_us-gaap_RevenueNotFromContractWithCustomer_01a015a8-8b08-7a49-a946-6fb172db8aa3_verboseLabel_en-US" xlink:label="lab_us-gaap_RevenueNotFromContractWithCustomer" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total revenue not from contracts with customers</link:label>
    <link:label id="lab_us-gaap_RevenueNotFromContractWithCustomer_label_en-US" xlink:label="lab_us-gaap_RevenueNotFromContractWithCustomer" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue Not from Contract with Customer</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueNotFromContractWithCustomer" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueNotFromContractWithCustomer"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueNotFromContractWithCustomer" xlink:to="lab_us-gaap_RevenueNotFromContractWithCustomer" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestReceivable_01a015a8-8b08-74cb-b0dc-6a804fe7bbb8_terseLabel_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest receivable</link:label>
    <link:label id="lab_us-gaap_InterestReceivable_label_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestReceivable" xlink:to="lab_us-gaap_InterestReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndName_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_TrdArrIndName_label_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndName" xlink:to="lab_ecd_TrdArrIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_01a015a8-8b8d-7b88-aa36-dd3e1945fe2d_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_01a015a8-8b8d-7577-a434-f8f6a0e15642_verboseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffectContinuingOperations_01a015a8-8b8d-70a1-82c6-25971b9d8329_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffectContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net increase (decrease) in cash, cash equivalents, restricted cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffectContinuingOperations_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffectContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Including Exchange Rate Effect, Continuing Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffectContinuingOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffectContinuingOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffectContinuingOperations" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffectContinuingOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForSoftware_01a015a8-8b08-70dd-a483-8bc3d5830f2a_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForSoftware" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additions to software</link:label>
    <link:label id="lab_us-gaap_PaymentsForSoftware_label_en-US" xlink:label="lab_us-gaap_PaymentsForSoftware" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for Software</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForSoftware" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsForSoftware"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForSoftware" xlink:to="lab_us-gaap_PaymentsForSoftware" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CoSelectedMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureAmt" xlink:to="lab_ecd_CoSelectedMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_01a015a8-8b8d-7da5-bca5-435804449113_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization</link:label>
    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_label_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation, Depletion and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationDepletionAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DepreciationDepletionAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DepreciationDepletionAndAmortization" xlink:to="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoAssetOptionsMember_01a015a8-8a6b-77b8-8abc-b2e67be2528a_terseLabel_en-US" xlink:label="lab_gemi_CryptoAssetOptionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto asset options</link:label>
    <link:label id="lab_gemi_CryptoAssetOptionsMember_label_en-US" xlink:label="lab_gemi_CryptoAssetOptionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset Options [Member]</link:label>
    <link:label id="lab_gemi_CryptoAssetOptionsMember_documentation_en-US" xlink:label="lab_gemi_CryptoAssetOptionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Asset Options</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoAssetOptionsMember" xlink:href="gemi-20260930.xsd#gemi_CryptoAssetOptionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoAssetOptionsMember" xlink:to="lab_gemi_CryptoAssetOptionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_01a015a8-8b08-78da-86c6-ccb0e43b15d2_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common stock upon settlement of stock awards, net of shares withheld (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Issued, Shares, Share-Based Payment Arrangement, after Forfeiture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoLoansPayableRealizedGainLossNonoperating_01a015a8-8b08-7ac1-b269-347ba7268e21_terseLabel_en-US" xlink:label="lab_gemi_CryptoLoansPayableRealizedGainLossNonoperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Realized Gain (Loss)</link:label>
    <link:label id="lab_gemi_CryptoLoansPayableRealizedGainLossNonoperating_label_en-US" xlink:label="lab_gemi_CryptoLoansPayableRealizedGainLossNonoperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Loans Payable, Realized Gain (Loss), Nonoperating</link:label>
    <link:label id="lab_gemi_CryptoLoansPayableRealizedGainLossNonoperating_documentation_en-US" xlink:label="lab_gemi_CryptoLoansPayableRealizedGainLossNonoperating" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Loans Payable, Realized Gain (Loss), Nonoperating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoLoansPayableRealizedGainLossNonoperating" xlink:href="gemi-20260930.xsd#gemi_CryptoLoansPayableRealizedGainLossNonoperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoLoansPayableRealizedGainLossNonoperating" xlink:to="lab_gemi_CryptoLoansPayableRealizedGainLossNonoperating" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable_01a015a8-8a6b-7203-9e26-fb2064ba7f96_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts and Financing Receivables [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts and Financing Receivables [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:to="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ClassOfWarrantOrRightVestedPercentage_01a015a8-8b08-7a21-b2fc-53b19814da92_terseLabel_en-US" xlink:label="lab_gemi_ClassOfWarrantOrRightVestedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage of warrant vesting conditions met</link:label>
    <link:label id="lab_gemi_ClassOfWarrantOrRightVestedPercentage_label_en-US" xlink:label="lab_gemi_ClassOfWarrantOrRightVestedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Vested, Percentage</link:label>
    <link:label id="lab_gemi_ClassOfWarrantOrRightVestedPercentage_documentation_en-US" xlink:label="lab_gemi_ClassOfWarrantOrRightVestedPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Vested, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ClassOfWarrantOrRightVestedPercentage" xlink:href="gemi-20260930.xsd#gemi_ClassOfWarrantOrRightVestedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ClassOfWarrantOrRightVestedPercentage" xlink:to="lab_gemi_ClassOfWarrantOrRightVestedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_01a015a8-8b08-78ba-be7e-3d6f24cd8738_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average remaining lease term (in years)</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Weighted Average Remaining Lease Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:to="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepurchaseAgreementCounterpartyLineItems_01a015a8-8a6b-75aa-88a3-c6c438aed8be_terseLabel_en-US" xlink:label="lab_us-gaap_RepurchaseAgreementCounterpartyLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase Agreement Counterparty [Line Items]</link:label>
    <link:label id="lab_us-gaap_RepurchaseAgreementCounterpartyLineItems_label_en-US" xlink:label="lab_us-gaap_RepurchaseAgreementCounterpartyLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repurchase Agreement Counterparty [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepurchaseAgreementCounterpartyLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepurchaseAgreementCounterpartyLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepurchaseAgreementCounterpartyLineItems" xlink:to="lab_us-gaap_RepurchaseAgreementCounterpartyLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoMember_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO</link:label>
    <link:label id="lab_ecd_NonPeoNeoMember_label_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoMember" xlink:to="lab_ecd_NonPeoNeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardForfeited_01a015a8-8b08-7132-aa6a-d2cc948cd389_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardForfeited" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Forfeiture of unvested restricted shares (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardForfeited_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardForfeited" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Restricted Stock Award, Forfeited</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardForfeited" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardForfeited"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardForfeited" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardForfeited" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PurchaseObligation_01a015a8-8b08-732b-87d4-d48b617a07c0_terseLabel_en-US" xlink:label="lab_us-gaap_PurchaseObligation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding purchase commitments</link:label>
    <link:label id="lab_us-gaap_PurchaseObligation_label_en-US" xlink:label="lab_us-gaap_PurchaseObligation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Purchase Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PurchaseObligation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PurchaseObligation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PurchaseObligation" xlink:to="lab_us-gaap_PurchaseObligation" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_NumberOfVotesPerShareOfCommonStockHeld_01a015a8-8a6b-798f-ba84-3fb00617d430_terseLabel_en-US" xlink:label="lab_gemi_NumberOfVotesPerShareOfCommonStockHeld" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of votes for each share of common stock held</link:label>
    <link:label id="lab_gemi_NumberOfVotesPerShareOfCommonStockHeld_label_en-US" xlink:label="lab_gemi_NumberOfVotesPerShareOfCommonStockHeld" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Votes Per Share Of Common Stock Held</link:label>
    <link:label id="lab_gemi_NumberOfVotesPerShareOfCommonStockHeld_documentation_en-US" xlink:label="lab_gemi_NumberOfVotesPerShareOfCommonStockHeld" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number Of Votes Per Share Of Common Stock Held</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_NumberOfVotesPerShareOfCommonStockHeld" xlink:href="gemi-20260930.xsd#gemi_NumberOfVotesPerShareOfCommonStockHeld"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_NumberOfVotesPerShareOfCommonStockHeld" xlink:to="lab_gemi_NumberOfVotesPerShareOfCommonStockHeld" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Method</link:label>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMethodTextBlock" xlink:to="lab_ecd_AwardTmgMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScenarioForecastMember_01a1abfb-706e-7cbe-8188-7d1731bee067_terseLabel_en-US" xlink:label="lab_srt_ScenarioForecastMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forecast</link:label>
    <link:label id="lab_srt_ScenarioForecastMember_label_en-US" xlink:label="lab_srt_ScenarioForecastMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forecast [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScenarioForecastMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ScenarioForecastMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScenarioForecastMember" xlink:to="lab_srt_ScenarioForecastMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:to="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_01a015a8-8a6b-76f1-b079-6a96ee404973_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net loss</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_01a015a8-8a6b-70fd-93d3-07c6ead2e0db_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net loss</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_01a015a8-8a6b-7cf2-b104-2b2e87c828a6_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net loss</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_01a015a8-8a6b-7bfb-a2cc-f4838885f0a4_netLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Net loss</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_01a015a8-8b08-7b25-991b-49df3d5be32a_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis</link:label>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_label_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompAnalysisTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ErrCompAnalysisTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompAnalysisTextBlock" xlink:to="lab_ecd_ErrCompAnalysisTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDateAxis_terseLabel_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date:</link:label>
    <link:label id="lab_ecd_RestatementDateAxis_label_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDateAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDateAxis" xlink:to="lab_ecd_RestatementDateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice_01a015a8-8b08-76cb-861a-96f73ad9f733_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average exercise price exercisable (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercisable, Weighted Average Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueNetReductions_01a015a8-8b08-79fd-86fb-d3ea1d629b12_negatedTerseLabel_en-US" xlink:label="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueNetReductions" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net reductions</link:label>
    <link:label id="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueNetReductions_label_en-US" xlink:label="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueNetReductions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities Without Readily Determinable Fair Value, Net Reductions</link:label>
    <link:label id="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueNetReductions_documentation_en-US" xlink:label="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueNetReductions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Securities Without Readily Determinable Fair Value, Net Reductions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueNetReductions" xlink:href="gemi-20260930.xsd#gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueNetReductions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueNetReductions" xlink:to="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueNetReductions" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityConversions_01a015a8-8b08-7cc1-b1df-7c93d91c6541_terseLabel_en-US" xlink:label="lab_gemi_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityConversions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion of convertible notes to common stock in connection with IPO</link:label>
    <link:label id="lab_gemi_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityConversions_label_en-US" xlink:label="lab_gemi_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityConversions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement With Unobservable Inputs Reconciliation, Recurring Basis, Liability, Conversions</link:label>
    <link:label id="lab_gemi_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityConversions_documentation_en-US" xlink:label="lab_gemi_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityConversions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement With Unobservable Inputs Reconciliation, Recurring Basis, Liability, Conversions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityConversions" xlink:href="gemi-20260930.xsd#gemi_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityConversions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityConversions" xlink:to="lab_gemi_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityConversions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInOtherComprehensiveIncome_01a015a8-8b08-79b7-af8e-462a4de947c3_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInOtherComprehensiveIncome" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">OCI - Change in fair value attributable to instrument-specific credit risk</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInOtherComprehensiveIncome_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInOtherComprehensiveIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Gain (Loss) Included in Other Comprehensive Income (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInOtherComprehensiveIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInOtherComprehensiveIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInOtherComprehensiveIncome" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInOtherComprehensiveIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_U.S.DistrictCourtForTheSouthernDistrictOfNewYorkMember_01a015a8-8b8e-782e-8767-cd68c6944b82_terseLabel_en-US" xlink:label="lab_gemi_U.S.DistrictCourtForTheSouthernDistrictOfNewYorkMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U.S. District Court for the Southern District of New York</link:label>
    <link:label id="lab_gemi_U.S.DistrictCourtForTheSouthernDistrictOfNewYorkMember_label_en-US" xlink:label="lab_gemi_U.S.DistrictCourtForTheSouthernDistrictOfNewYorkMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">U.S. District Court for the Southern District of New York [Member]</link:label>
    <link:label id="lab_gemi_U.S.DistrictCourtForTheSouthernDistrictOfNewYorkMember_documentation_en-US" xlink:label="lab_gemi_U.S.DistrictCourtForTheSouthernDistrictOfNewYorkMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">U.S. District Court for the Southern District of New York</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_U.S.DistrictCourtForTheSouthernDistrictOfNewYorkMember" xlink:href="gemi-20260930.xsd#gemi_U.S.DistrictCourtForTheSouthernDistrictOfNewYorkMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_U.S.DistrictCourtForTheSouthernDistrictOfNewYorkMember" xlink:to="lab_gemi_U.S.DistrictCourtForTheSouthernDistrictOfNewYorkMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenuesAbstract_01a015a8-8b8d-730b-809b-fd051bcbd153_terseLabel_en-US" xlink:label="lab_us-gaap_RevenuesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue:</link:label>
    <link:label id="lab_us-gaap_RevenuesAbstract_label_en-US" xlink:label="lab_us-gaap_RevenuesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenuesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenuesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenuesAbstract" xlink:to="lab_us-gaap_RevenuesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnBnftsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:to="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeMember_01a015a8-8a6b-7ffc-965e-1da22de274f0_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeMember" xlink:to="lab_srt_RangeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_01a015a8-8a6b-72e0-8f17-df40ee41b6f9_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalYearFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalYearFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalYearFocus" xlink:to="lab_dei_DocumentFiscalYearFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockValue_01a015a8-8a6b-7221-95e2-6d4419897351_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockValue" xlink:to="lab_us-gaap_CommonStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_01a015a8-8b08-79cf-a3b4-5bac4d7ed6a2_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_01a015a8-8a6b-759e-b4f7-edca589f42a1_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payment of withholding taxes</link:label>
    <link:label id="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment, Tax Withholding, Share-Based Payment Arrangement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:to="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock_01a015a8-8b08-75ef-91be-97cfe75cf139_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Funding Debt</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDebtInstrumentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssetsMiscellaneousNoncurrent_01a015a8-8b8d-7afb-a089-f665fb31fad4_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsMiscellaneousNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_OtherAssetsMiscellaneousNoncurrent_label_en-US" xlink:label="lab_us-gaap_OtherAssetsMiscellaneousNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets, Miscellaneous, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsMiscellaneousNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAssetsMiscellaneousNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsMiscellaneousNoncurrent" xlink:to="lab_us-gaap_OtherAssetsMiscellaneousNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditMember_01a015a8-8b8d-7ef9-97ab-9523aef79caa_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit</link:label>
    <link:label id="lab_us-gaap_LineOfCreditMember_label_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditMember" xlink:to="lab_us-gaap_LineOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDeterminationDate_terseLabel_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:label id="lab_ecd_RestatementDeterminationDate_label_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDeterminationDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDeterminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDeterminationDate" xlink:to="lab_ecd_RestatementDeterminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightDomain_01a015a8-8b08-72bc-aea7-cfd219a2da0b_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfWarrantOrRightDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightDomain" xlink:to="lab_us-gaap_ClassOfWarrantOrRightDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_FundingDebtFairValueDisclosure_01a015a8-8a6b-765e-bdf6-91d16cc81355_terseLabel_en-US" xlink:label="lab_gemi_FundingDebtFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Funding debt</link:label>
    <link:label id="lab_gemi_FundingDebtFairValueDisclosure_label_en-US" xlink:label="lab_gemi_FundingDebtFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Funding Debt, Fair Value Disclosure</link:label>
    <link:label id="lab_gemi_FundingDebtFairValueDisclosure_documentation_en-US" xlink:label="lab_gemi_FundingDebtFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Funding Debt, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_FundingDebtFairValueDisclosure" xlink:href="gemi-20260930.xsd#gemi_FundingDebtFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_FundingDebtFairValueDisclosure" xlink:to="lab_gemi_FundingDebtFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_RelatedPartyAgreementTerm_01a015a8-8b08-761a-a3b2-5ecb11d4e46a_terseLabel_en-US" xlink:label="lab_gemi_RelatedPartyAgreementTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Initial agreement term</link:label>
    <link:label id="lab_gemi_RelatedPartyAgreementTerm_label_en-US" xlink:label="lab_gemi_RelatedPartyAgreementTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Agreement, Term</link:label>
    <link:label id="lab_gemi_RelatedPartyAgreementTerm_documentation_en-US" xlink:label="lab_gemi_RelatedPartyAgreementTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Agreement, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_RelatedPartyAgreementTerm" xlink:href="gemi-20260930.xsd#gemi_RelatedPartyAgreementTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_RelatedPartyAgreementTerm" xlink:to="lab_gemi_RelatedPartyAgreementTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ThirdPartyDebtFairValueDisclosure_01a015a8-8b8d-78e5-8be1-52f6800869c2_terseLabel_en-US" xlink:label="lab_gemi_ThirdPartyDebtFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Third party loans</link:label>
    <link:label id="lab_gemi_ThirdPartyDebtFairValueDisclosure_label_en-US" xlink:label="lab_gemi_ThirdPartyDebtFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Third Party Debt, Fair Value Disclosure</link:label>
    <link:label id="lab_gemi_ThirdPartyDebtFairValueDisclosure_documentation_en-US" xlink:label="lab_gemi_ThirdPartyDebtFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Third Party Debt, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ThirdPartyDebtFairValueDisclosure" xlink:href="gemi-20260930.xsd#gemi_ThirdPartyDebtFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ThirdPartyDebtFairValueDisclosure" xlink:to="lab_gemi_ThirdPartyDebtFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoAssetAdditionNumberOfUnits_01a015a8-8b8d-72a0-ae39-600dbc761a9d_terseLabel_en-US" xlink:label="lab_gemi_CryptoAssetAdditionNumberOfUnits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto assets received (in units)</link:label>
    <link:label id="lab_gemi_CryptoAssetAdditionNumberOfUnits_label_en-US" xlink:label="lab_gemi_CryptoAssetAdditionNumberOfUnits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Addition, Number Of Units</link:label>
    <link:label id="lab_gemi_CryptoAssetAdditionNumberOfUnits_documentation_en-US" xlink:label="lab_gemi_CryptoAssetAdditionNumberOfUnits" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Asset, Addition, Number Of Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoAssetAdditionNumberOfUnits" xlink:href="gemi-20260930.xsd#gemi_CryptoAssetAdditionNumberOfUnits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoAssetAdditionNumberOfUnits" xlink:to="lab_gemi_CryptoAssetAdditionNumberOfUnits" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_RecognitionCriteriaNotMetMember_01a015a8-8a6b-7011-945b-af1104f8c207_terseLabel_en-US" xlink:label="lab_gemi_RecognitionCriteriaNotMetMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recognition Criteria, Not Met</link:label>
    <link:label id="lab_gemi_RecognitionCriteriaNotMetMember_label_en-US" xlink:label="lab_gemi_RecognitionCriteriaNotMetMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recognition Criteria, Not Met [Member]</link:label>
    <link:label id="lab_gemi_RecognitionCriteriaNotMetMember_documentation_en-US" xlink:label="lab_gemi_RecognitionCriteriaNotMetMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Recognition Criteria, Not Met</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_RecognitionCriteriaNotMetMember" xlink:href="gemi-20260930.xsd#gemi_RecognitionCriteriaNotMetMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_RecognitionCriteriaNotMetMember" xlink:to="lab_gemi_RecognitionCriteriaNotMetMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoAssetsHeldAsCollateral_01a015a8-8b08-78da-b4ee-6229d6fe6a03_terseLabel_en-US" xlink:label="lab_gemi_CryptoAssetsHeldAsCollateral" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto assets held as collateral</link:label>
    <link:label id="lab_gemi_CryptoAssetsHeldAsCollateral_label_en-US" xlink:label="lab_gemi_CryptoAssetsHeldAsCollateral" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Assets Held As Collateral</link:label>
    <link:label id="lab_gemi_CryptoAssetsHeldAsCollateral_documentation_en-US" xlink:label="lab_gemi_CryptoAssetsHeldAsCollateral" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Assets Held As Collateral</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoAssetsHeldAsCollateral" xlink:href="gemi-20260930.xsd#gemi_CryptoAssetsHeldAsCollateral"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoAssetsHeldAsCollateral" xlink:to="lab_gemi_CryptoAssetsHeldAsCollateral" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AmendmentFlag_01a015a8-8b8d-7c0d-ba70-7e479dd04877_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:label id="lab_dei_AmendmentFlag_label_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_AmendmentFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AmendmentFlag" xlink:to="lab_dei_AmendmentFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CryptoAssetActivityTableTextBlock_01a015a8-8a6b-75b8-8501-73b434822a88_terseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Roll-forward of Crypto Assets Measured at Fair Value</link:label>
    <link:label id="lab_us-gaap_CryptoAssetActivityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_CryptoAssetActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Activity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetActivityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetActivityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CryptoAssetActivityTableTextBlock" xlink:to="lab_us-gaap_CryptoAssetActivityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesCurrentAbstract_01a015a8-8b08-7c59-86c8-6edae0f4ffb0_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current liabilities:</link:label>
    <link:label id="lab_us-gaap_LiabilitiesCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Current [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesCurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesCurrentAbstract" xlink:to="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProvisionForDoubtfulAccounts_01a015a8-8a6b-7761-958a-71e5653e3246_terseLabel_en-US" xlink:label="lab_us-gaap_ProvisionForDoubtfulAccounts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision for credit losses</link:label>
    <link:label id="lab_us-gaap_ProvisionForDoubtfulAccounts_label_en-US" xlink:label="lab_us-gaap_ProvisionForDoubtfulAccounts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Credit Loss Expense (Reversal)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProvisionForDoubtfulAccounts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProvisionForDoubtfulAccounts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProvisionForDoubtfulAccounts" xlink:to="lab_us-gaap_ProvisionForDoubtfulAccounts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CryptoAssetRealizedAndUnrealizedGainLossNonoperating_01a015a8-8b08-7476-95d5-4e6727bc73e3_terseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetRealizedAndUnrealizedGainLossNonoperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Realized and unrealized gain (loss) on crypto assets and receivable, crypto assets pledged</link:label>
    <link:label id="lab_us-gaap_CryptoAssetRealizedAndUnrealizedGainLossNonoperating_label_en-US" xlink:label="lab_us-gaap_CryptoAssetRealizedAndUnrealizedGainLossNonoperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Realized and Unrealized Gain (Loss), Nonoperating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetRealizedAndUnrealizedGainLossNonoperating" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetRealizedAndUnrealizedGainLossNonoperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CryptoAssetRealizedAndUnrealizedGainLossNonoperating" xlink:to="lab_us-gaap_CryptoAssetRealizedAndUnrealizedGainLossNonoperating" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CustomerCustodialFundsGeminiDollar_01a015a8-8a6b-7158-ae6f-f7a4a426e38f_terseLabel_en-US" xlink:label="lab_gemi_CustomerCustodialFundsGeminiDollar" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer custodial funds</link:label>
    <link:label id="lab_gemi_CustomerCustodialFundsGeminiDollar_label_en-US" xlink:label="lab_gemi_CustomerCustodialFundsGeminiDollar" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer Custodial Funds, Gemini Dollar</link:label>
    <link:label id="lab_gemi_CustomerCustodialFundsGeminiDollar_documentation_en-US" xlink:label="lab_gemi_CustomerCustodialFundsGeminiDollar" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Customer Custodial Funds, Gemini Dollar</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CustomerCustodialFundsGeminiDollar" xlink:href="gemi-20260930.xsd#gemi_CustomerCustodialFundsGeminiDollar"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CustomerCustodialFundsGeminiDollar" xlink:to="lab_gemi_CustomerCustodialFundsGeminiDollar" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_GainLossOnChangeInFairValueOfRelatedPartyConvertibleDebt_01a015a8-8b08-7a52-8208-e1c5cf311dcd_terseLabel_en-US" xlink:label="lab_gemi_GainLossOnChangeInFairValueOfRelatedPartyConvertibleDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value on related party convertible notes</link:label>
    <link:label id="lab_gemi_GainLossOnChangeInFairValueOfRelatedPartyConvertibleDebt_01a015a8-8b08-7aaf-893b-167cab51d120_negatedTerseLabel_en-US" xlink:label="lab_gemi_GainLossOnChangeInFairValueOfRelatedPartyConvertibleDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value on related party convertible notes</link:label>
    <link:label id="lab_gemi_GainLossOnChangeInFairValueOfRelatedPartyConvertibleDebt_label_en-US" xlink:label="lab_gemi_GainLossOnChangeInFairValueOfRelatedPartyConvertibleDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) On Change In Fair Value Of Related Party Convertible Debt</link:label>
    <link:label id="lab_gemi_GainLossOnChangeInFairValueOfRelatedPartyConvertibleDebt_documentation_en-US" xlink:label="lab_gemi_GainLossOnChangeInFairValueOfRelatedPartyConvertibleDebt" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gain (Loss) On Change In Fair Value Of Related Party Convertible Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_GainLossOnChangeInFairValueOfRelatedPartyConvertibleDebt" xlink:href="gemi-20260930.xsd#gemi_GainLossOnChangeInFairValueOfRelatedPartyConvertibleDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_GainLossOnChangeInFairValueOfRelatedPartyConvertibleDebt" xlink:to="lab_gemi_GainLossOnChangeInFairValueOfRelatedPartyConvertibleDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingenciesTable_01a015a8-8a6b-760a-b679-c6b8d6b25977_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingenciesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Table]</link:label>
    <link:label id="lab_us-gaap_LossContingenciesTable_label_en-US" xlink:label="lab_us-gaap_LossContingenciesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingenciesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingenciesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingenciesTable" xlink:to="lab_us-gaap_LossContingenciesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesNoncurrent_01a015a8-8a6b-7b6f-bea3-0af7d68fac9b_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total non-current liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesNoncurrent_label_en-US" xlink:label="lab_us-gaap_LiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesNoncurrent" xlink:to="lab_us-gaap_LiabilitiesNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote</link:label>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToNonPeoNeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:to="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAbstract_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_01a015a8-8a6b-76af-ac7d-747368a6db71_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressStateOrProvince"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent_01a015a8-8b08-77e6-8c34-70a8c5ac5e04_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign currency translation, net of tax</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax, Portion Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent" xlink:to="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoTotalCompAmt_label_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoTotalCompAmt" xlink:to="lab_ecd_PeoTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_01a015a8-8b08-7b9f-abc6-6d96c226b672_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_01a015a8-8b08-7273-a324-7dd286b72609_verboseLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Financial Assets:</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsFairValueDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosureAbstract" xlink:to="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_01a015a8-8a6b-7f73-b91e-f898f8e4d9cb_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Notional</link:label>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_label_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Notional Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeNotionalAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeNotionalAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeNotionalAmount" xlink:to="lab_us-gaap_DerivativeNotionalAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_01a015a8-8b08-7f60-81a8-1f7678635099_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average shares outstanding - basic (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_01a015a8-8b08-7f6e-8128-b7d217af3153_verboseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Weighted average common stock outstanding, basic (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTable_01a015a8-8b8d-73bd-b912-778740021d35_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTable_label_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByBalanceSheetGroupingTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:to="lab_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingenciesLineItems_01a015a8-8a6b-7f78-b126-2513f6b69bb2_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingenciesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Line Items]</link:label>
    <link:label id="lab_us-gaap_LossContingenciesLineItems_label_en-US" xlink:label="lab_us-gaap_LossContingenciesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingenciesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingenciesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingenciesLineItems" xlink:to="lab_us-gaap_LossContingenciesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_01a015a8-8b08-72a3-9fe0-942010c1dfaf_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_FinancingAgreementsSecuritiesDesignatedForFutureRequirement_01a015a8-8b8e-7f65-adf5-10b510e4f609_terseLabel_en-US" xlink:label="lab_gemi_FinancingAgreementsSecuritiesDesignatedForFutureRequirement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing agreements, securities designated for future requirement</link:label>
    <link:label id="lab_gemi_FinancingAgreementsSecuritiesDesignatedForFutureRequirement_label_en-US" xlink:label="lab_gemi_FinancingAgreementsSecuritiesDesignatedForFutureRequirement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Agreements, Securities Designated For Future Requirement</link:label>
    <link:label id="lab_gemi_FinancingAgreementsSecuritiesDesignatedForFutureRequirement_documentation_en-US" xlink:label="lab_gemi_FinancingAgreementsSecuritiesDesignatedForFutureRequirement" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Agreements, Securities Designated For Future Requirement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_FinancingAgreementsSecuritiesDesignatedForFutureRequirement" xlink:href="gemi-20260930.xsd#gemi_FinancingAgreementsSecuritiesDesignatedForFutureRequirement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_FinancingAgreementsSecuritiesDesignatedForFutureRequirement" xlink:to="lab_gemi_FinancingAgreementsSecuritiesDesignatedForFutureRequirement" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PendingLitigationMember_01a015a8-8b8e-7688-b5a9-354b8ff822c5_terseLabel_en-US" xlink:label="lab_us-gaap_PendingLitigationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pending Litigation</link:label>
    <link:label id="lab_us-gaap_PendingLitigationMember_label_en-US" xlink:label="lab_us-gaap_PendingLitigationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pending Litigation [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PendingLitigationMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PendingLitigationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PendingLitigationMember" xlink:to="lab_us-gaap_PendingLitigationMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock_01a015a8-8b8d-7eae-9750-05db1db2c07a_terseLabel_en-US" xlink:label="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Net</link:label>
    <link:label id="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans, Notes, Trade and Other Receivables Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:to="lab_us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentInformationLineItems_01a015a8-8b8d-70a7-9edd-214bded8df73_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Line Items]</link:label>
    <link:label id="lab_dei_DocumentInformationLineItems_label_en-US" xlink:label="lab_dei_DocumentInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationLineItems" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentInformationLineItems" xlink:to="lab_dei_DocumentInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMnpiDiscTextBlock"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_01a015a8-8b08-77ab-9ce4-88c6bf4d5d87_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Vested (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Vested in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod"/>
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    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_01a015a8-8b08-7b6c-bbc7-a28d3cb9afce_terseLabel_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basis of presentation</link:label>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Basis of Accounting, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BasisOfAccountingPolicyPolicyTextBlock"/>
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    <link:label id="lab_us-gaap_StatementClassOfStockAxis_01a015a8-8b08-7919-a5be-845a345ffd33_terseLabel_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_label_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementClassOfStockAxis"/>
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    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_01a015a8-8a6b-749c-8531-f6d081211e0d_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net loss attributable to common stockholders, basic</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
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    <link:label id="lab_gemi_NewYorkDigitalInvestmentGroupFundingLLCNYDIGMember_01a015a8-8b08-773c-a8b5-15d278443944_terseLabel_en-US" xlink:label="lab_gemi_NewYorkDigitalInvestmentGroupFundingLLCNYDIGMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NYDIG</link:label>
    <link:label id="lab_gemi_NewYorkDigitalInvestmentGroupFundingLLCNYDIGMember_label_en-US" xlink:label="lab_gemi_NewYorkDigitalInvestmentGroupFundingLLCNYDIGMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New York Digital Investment Group Funding LLC ("NYDIG") [Member]</link:label>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_01a015a8-8b08-75a5-a051-82b3ec602bd7_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Amortization</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Accumulated Amortization</link:label>
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    <link:label id="lab_us-gaap_ReceivableTypeDomain_01a015a8-8b8d-7ff2-bf4d-f25bfbfb1dd3_terseLabel_en-US" xlink:label="lab_us-gaap_ReceivableTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivable [Domain]</link:label>
    <link:label id="lab_us-gaap_ReceivableTypeDomain_label_en-US" xlink:label="lab_us-gaap_ReceivableTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivable [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivableTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReceivableTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReceivableTypeDomain" xlink:to="lab_us-gaap_ReceivableTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_01a015a8-8a6b-70ca-a892-3515cc013015_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of credit facility, maximum borrowing capacity</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoAssetPledged_01a1cd66-47e8-7404-b69a-df2f283310e4_terseLabel_en-US" xlink:label="lab_gemi_CryptoAssetPledged" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto asset pledged (in units)</link:label>
    <link:label id="lab_gemi_CryptoAssetPledged_label_en-US" xlink:label="lab_gemi_CryptoAssetPledged" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset Pledged</link:label>
    <link:label id="lab_gemi_CryptoAssetPledged_documentation_en-US" xlink:label="lab_gemi_CryptoAssetPledged" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Asset Pledged</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoAssetPledged" xlink:href="gemi-20260930.xsd#gemi_CryptoAssetPledged"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoAssetPledged" xlink:to="lab_gemi_CryptoAssetPledged" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_01a015a8-8b08-7e79-bafd-bff023948a5b_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recent accounting pronouncements</link:label>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_LitigationCaseAxis_01a015a8-8b8e-7ace-973f-5aaceb1ea6a7_terseLabel_en-US" xlink:label="lab_srt_LitigationCaseAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Litigation Case [Axis]</link:label>
    <link:label id="lab_srt_LitigationCaseAxis_label_en-US" xlink:label="lab_srt_LitigationCaseAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Litigation Case [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_LitigationCaseAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_LitigationCaseAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_LitigationCaseAxis" xlink:to="lab_srt_LitigationCaseAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfPreferredUnitsTable_01a015a8-8a6b-75f8-a095-cdf32688561f_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfPreferredUnitsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Partners' Capital, Master Limited Partnership, Preferred Unit [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfPreferredUnitsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfPreferredUnitsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Partners' Capital, Master Limited Partnership, Preferred Unit [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfPreferredUnitsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfPreferredUnitsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfPreferredUnitsTable" xlink:to="lab_us-gaap_ScheduleOfPreferredUnitsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LitigationReserveCurrent_01a015a8-8a6b-7039-8cc3-4d8df965eab1_terseLabel_en-US" xlink:label="lab_us-gaap_LitigationReserveCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued loss contingencies</link:label>
    <link:label id="lab_us-gaap_LitigationReserveCurrent_label_en-US" xlink:label="lab_us-gaap_LitigationReserveCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Estimated Litigation Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LitigationReserveCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LitigationReserveCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LitigationReserveCurrent" xlink:to="lab_us-gaap_LitigationReserveCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromRelatedPartyDebt_01a015a8-8b08-70be-9df9-3419e9dbb50e_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromRelatedPartyDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from related party loans</link:label>
    <link:label id="lab_us-gaap_ProceedsFromRelatedPartyDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromRelatedPartyDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Related Party Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromRelatedPartyDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromRelatedPartyDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromRelatedPartyDebt" xlink:to="lab_us-gaap_ProceedsFromRelatedPartyDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock_01a015a8-8b08-7649-8449-35c99a32ade9_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Software, Property and Equipment, Net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueRollForward_01a015a8-8b08-7555-ac8c-d88116b21c0f_terseLabel_en-US" xlink:label="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Securities Without Readily Determinable Fair Value [Roll Forward]</link:label>
    <link:label id="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueRollForward_label_en-US" xlink:label="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities Without Readily Determinable Fair Value [Roll Forward]</link:label>
    <link:label id="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueRollForward_documentation_en-US" xlink:label="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueRollForward" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Securities Without Readily Determinable Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueRollForward" xlink:href="gemi-20260930.xsd#gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueRollForward" xlink:to="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_01a015a8-8a6b-7eaf-8378-2654520e530d_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in operating assets and liabilities:</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Increase (Decrease) in Operating Capital [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOperatingCapitalAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_01a015a8-8a6b-7beb-89b4-5356cdf7bb8b_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by investing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in the Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:to="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoAssetOptionsLiabilityMember_01a015a8-8b08-7a56-acc0-e3ebfd08a2d2_terseLabel_en-US" xlink:label="lab_gemi_CryptoAssetOptionsLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto asset options</link:label>
    <link:label id="lab_gemi_CryptoAssetOptionsLiabilityMember_label_en-US" xlink:label="lab_gemi_CryptoAssetOptionsLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset Options, Liability [Member]</link:label>
    <link:label id="lab_gemi_CryptoAssetOptionsLiabilityMember_documentation_en-US" xlink:label="lab_gemi_CryptoAssetOptionsLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Asset Options, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoAssetOptionsLiabilityMember" xlink:href="gemi-20260930.xsd#gemi_CryptoAssetOptionsLiabilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoAssetOptionsLiabilityMember" xlink:to="lab_gemi_CryptoAssetOptionsLiabilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_01a015a8-8a6b-7252-b08c-5aee3081291b_verboseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Stockholders' Equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConversionOfStockNameDomain_01a015a8-8b8d-72a1-83ec-1bb0a4379320_terseLabel_en-US" xlink:label="lab_us-gaap_ConversionOfStockNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion of Stock, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_ConversionOfStockNameDomain_label_en-US" xlink:label="lab_us-gaap_ConversionOfStockNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Conversion of Stock, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConversionOfStockNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConversionOfStockNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConversionOfStockNameDomain" xlink:to="lab_us-gaap_ConversionOfStockNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquitySharesOutstanding_01a015a8-8b08-795e-bdf6-00e1dfc6ed6d_periodStartLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesOutstanding_01a015a8-8b08-7d5d-b81c-134a4d00ecf8_periodEndLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesOutstanding_label_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquitySharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TemporaryEquitySharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquitySharesOutstanding" xlink:to="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_01a015a8-8b08-7109-a076-c9c322b502f6_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_SecurityExchangeName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_SecurityExchangeName" xlink:to="lab_dei_SecurityExchangeName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_01a015a8-8b8d-7315-a803-a706ed063fa0_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Granted (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Grants in Period, Weighted Average Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_A2000BTCMarch12023Member_01a015a8-8a6b-7b09-a027-77b685c54799_terseLabel_en-US" xlink:label="lab_gemi_A2000BTCMarch12023Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2,000 BTC March 1, 2023</link:label>
    <link:label id="lab_gemi_A2000BTCMarch12023Member_label_en-US" xlink:label="lab_gemi_A2000BTCMarch12023Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2,000 BTC March 1, 2023 [Member]</link:label>
    <link:label id="lab_gemi_A2000BTCMarch12023Member_documentation_en-US" xlink:label="lab_gemi_A2000BTCMarch12023Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2,000 BTC March 1, 2023</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_A2000BTCMarch12023Member" xlink:href="gemi-20260930.xsd#gemi_A2000BTCMarch12023Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_A2000BTCMarch12023Member" xlink:to="lab_gemi_A2000BTCMarch12023Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosure_01a015a8-8b08-724f-9038-bcbd32bd48a7_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesFairValueDisclosure" xlink:to="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPayableCurrent_01a015a8-8a6b-7a1a-9641-ac8acea6f680_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Payable</link:label>
    <link:label id="lab_us-gaap_InterestPayableCurrent_label_en-US" xlink:label="lab_us-gaap_InterestPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPayableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestPayableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPayableCurrent" xlink:to="lab_us-gaap_InterestPayableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsShareBasedLiabilities_01a015a8-8b08-7664-8568-95594f0cb33b_terseLabel_en-US" xlink:label="lab_gemi_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsShareBasedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liability recognized as service conditions were considered probable</link:label>
    <link:label id="lab_gemi_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsShareBasedLiabilities_label_en-US" xlink:label="lab_gemi_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsShareBasedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement By Share-Based Payment Award, Equity Instruments Other Than Options, Share-Based Liabilities</link:label>
    <link:label id="lab_gemi_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsShareBasedLiabilities_documentation_en-US" xlink:label="lab_gemi_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsShareBasedLiabilities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement By Share-Based Payment Award, Equity Instruments Other Than Options, Share-Based Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsShareBasedLiabilities" xlink:href="gemi-20260930.xsd#gemi_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsShareBasedLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsShareBasedLiabilities" xlink:to="lab_gemi_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsShareBasedLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTextBlock_01a015a8-8b08-75be-ba1e-0f1c3d04adf0_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Software, Property and Equipment, Net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTextBlock_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryIndName" xlink:to="lab_ecd_OutstandingRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgHowMnpiCnsdrdTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:to="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_SegmentGeographicalDomain_01a015a8-8b08-7f9d-9b75-322b284af0c6_terseLabel_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:label id="lab_srt_SegmentGeographicalDomain_label_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_SegmentGeographicalDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_SegmentGeographicalDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_SegmentGeographicalDomain" xlink:to="lab_srt_SegmentGeographicalDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year</link:label>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_label_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:to="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnAdjsPrrSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:to="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract_01a015a8-8a6b-77cc-a8cb-397702719ca7_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Denominator:</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_SecurityServicesMember_01a1c881-5d93-79a2-b715-a4778fc45b60_terseLabel_en-US" xlink:label="lab_gemi_SecurityServicesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Services</link:label>
    <link:label id="lab_gemi_SecurityServicesMember_label_en-US" xlink:label="lab_gemi_SecurityServicesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Services [Member]</link:label>
    <link:label id="lab_gemi_SecurityServicesMember_documentation_en-US" xlink:label="lab_gemi_SecurityServicesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Security Services</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_SecurityServicesMember" xlink:href="gemi-20260930.xsd#gemi_SecurityServicesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_SecurityServicesMember" xlink:to="lab_gemi_SecurityServicesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract_01a015a8-8a6b-7102-8440-8d6657915dfe_terseLabel_en-US" xlink:label="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental schedule of non-cash investing and financing activities</link:label>
    <link:label id="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract_label_en-US" xlink:label="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncash Investing and Financing Items [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoncashInvestingAndFinancingItemsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:to="lab_us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CryptoAssetSale_01a015a8-8a6b-7292-b751-ce9aa122d7fb_terseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposition</link:label>
    <link:label id="lab_us-gaap_CryptoAssetSale_label_en-US" xlink:label="lab_us-gaap_CryptoAssetSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetSale" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CryptoAssetSale" xlink:to="lab_us-gaap_CryptoAssetSale" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_A2825BTCJune302026Member_01a015a8-8b8d-7d84-8e4c-7fa56961c689_terseLabel_en-US" xlink:label="lab_gemi_A2825BTCJune302026Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2825 BTC, June 30, 2026</link:label>
    <link:label id="lab_gemi_A2825BTCJune302026Member_label_en-US" xlink:label="lab_gemi_A2825BTCJune302026Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2825 BTC, June 30, 2026 [Member]</link:label>
    <link:label id="lab_gemi_A2825BTCJune302026Member_documentation_en-US" xlink:label="lab_gemi_A2825BTCJune302026Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2825 BTC, June 30, 2026</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_A2825BTCJune302026Member" xlink:href="gemi-20260930.xsd#gemi_A2825BTCJune302026Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_A2825BTCJune302026Member" xlink:to="lab_gemi_A2825BTCJune302026Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:to="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CustodialFeesReceivableMember_01a015a8-8b8d-72d6-b4d5-c92ecac2184a_terseLabel_en-US" xlink:label="lab_gemi_CustodialFeesReceivableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Custodial fees receivable</link:label>
    <link:label id="lab_gemi_CustodialFeesReceivableMember_01a015a8-8b8d-717d-ac14-b6ac4c55a51c_verboseLabel_en-US" xlink:label="lab_gemi_CustodialFeesReceivableMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Custody fees receivable</link:label>
    <link:label id="lab_gemi_CustodialFeesReceivableMember_label_en-US" xlink:label="lab_gemi_CustodialFeesReceivableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Custodial Fees Receivable [Member]</link:label>
    <link:label id="lab_gemi_CustodialFeesReceivableMember_documentation_en-US" xlink:label="lab_gemi_CustodialFeesReceivableMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Custodial Fees Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CustodialFeesReceivableMember" xlink:href="gemi-20260930.xsd#gemi_CustodialFeesReceivableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CustodialFeesReceivableMember" xlink:to="lab_gemi_CustodialFeesReceivableMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingRecoveryCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryCompAmt" xlink:to="lab_ecd_OutstandingRecoveryCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_IndividualAxis_terseLabel_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individual:</link:label>
    <link:label id="lab_ecd_IndividualAxis_label_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Individual [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_IndividualAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_IndividualAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_IndividualAxis" xlink:to="lab_ecd_IndividualAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_01a015a8-8a6b-7ab9-a8c0-e64ab0549a37_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average shares outstanding - diluted (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_01a015a8-8a6b-7478-9107-524a5dc0548f_verboseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Weighted average common stock outstanding, diluted (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_FoundersMember_01a015a8-8b8d-78b0-9af2-338471fd2c4d_terseLabel_en-US" xlink:label="lab_gemi_FoundersMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Founders</link:label>
    <link:label id="lab_gemi_FoundersMember_label_en-US" xlink:label="lab_gemi_FoundersMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Founders [Member]</link:label>
    <link:label id="lab_gemi_FoundersMember_documentation_en-US" xlink:label="lab_gemi_FoundersMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Founders</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_FoundersMember" xlink:href="gemi-20260930.xsd#gemi_FoundersMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_FoundersMember" xlink:to="lab_gemi_FoundersMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_DebtInstrumentAmountOfCryptoCurrencyUnitsLoaned_01a015a8-8a6b-793a-8ad4-9bf12fa6b2a5_terseLabel_en-US" xlink:label="lab_gemi_DebtInstrumentAmountOfCryptoCurrencyUnitsLoaned" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amount of crypto loaned (in units)</link:label>
    <link:label id="lab_gemi_DebtInstrumentAmountOfCryptoCurrencyUnitsLoaned_label_en-US" xlink:label="lab_gemi_DebtInstrumentAmountOfCryptoCurrencyUnitsLoaned" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Amount Of Crypto Currency Units Loaned</link:label>
    <link:label id="lab_gemi_DebtInstrumentAmountOfCryptoCurrencyUnitsLoaned_documentation_en-US" xlink:label="lab_gemi_DebtInstrumentAmountOfCryptoCurrencyUnitsLoaned" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Amount Of Crypto Currency Units Loaned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_DebtInstrumentAmountOfCryptoCurrencyUnitsLoaned" xlink:href="gemi-20260930.xsd#gemi_DebtInstrumentAmountOfCryptoCurrencyUnitsLoaned"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_DebtInstrumentAmountOfCryptoCurrencyUnitsLoaned" xlink:to="lab_gemi_DebtInstrumentAmountOfCryptoCurrencyUnitsLoaned" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems_01a015a8-8b08-7eb8-b3bc-3d564170164c_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts, Notes, Loans and Financing Receivable [Line Items]</link:label>
    <link:label id="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems_label_en-US" xlink:label="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts, Notes, Loans and Financing Receivable [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsNotesAndLoansReceivableLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:to="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueLineItems_01a015a8-8b8d-757d-bf79-cd24935b552f_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Line Items]</link:label>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueLineItems_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisaggregationOfRevenueLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueLineItems" xlink:to="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ServiceCustodialFeeRevenueMember_01a015a8-8b8d-72f1-adea-054aafe54c83_terseLabel_en-US" xlink:label="lab_gemi_ServiceCustodialFeeRevenueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Custodial fee revenue</link:label>
    <link:label id="lab_gemi_ServiceCustodialFeeRevenueMember_label_en-US" xlink:label="lab_gemi_ServiceCustodialFeeRevenueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Service, Custodial Fee Revenue [Member]</link:label>
    <link:label id="lab_gemi_ServiceCustodialFeeRevenueMember_documentation_en-US" xlink:label="lab_gemi_ServiceCustodialFeeRevenueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Service, Custodial Fee Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ServiceCustodialFeeRevenueMember" xlink:href="gemi-20260930.xsd#gemi_ServiceCustodialFeeRevenueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ServiceCustodialFeeRevenueMember" xlink:to="lab_gemi_ServiceCustodialFeeRevenueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_A5280ETHFebruary282025Member_01a015a8-8b08-7ffc-84d1-21b776df9ae3_terseLabel_en-US" xlink:label="lab_gemi_A5280ETHFebruary282025Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">5,280 ETH, February 28, 2025</link:label>
    <link:label id="lab_gemi_A5280ETHFebruary282025Member_label_en-US" xlink:label="lab_gemi_A5280ETHFebruary282025Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">5,280 ETH, February 28, 2025 [Member]</link:label>
    <link:label id="lab_gemi_A5280ETHFebruary282025Member_documentation_en-US" xlink:label="lab_gemi_A5280ETHFebruary282025Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">5,280 ETH, February 28, 2025</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_A5280ETHFebruary282025Member" xlink:href="gemi-20260930.xsd#gemi_A5280ETHFebruary282025Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_A5280ETHFebruary282025Member" xlink:to="lab_gemi_A5280ETHFebruary282025Member" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_01a015a8-8b08-7dc1-b3fa-14a17d0a347f_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_01a015a8-8b08-7217-9c83-ef8f55f1690f_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:to="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_terseLabel_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change</link:label>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_label_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_UndrlygSecurityMktPriceChngPct"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:to="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_01a015a8-8b8d-7ede-89cf-5f52648649a8_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivatives</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:to="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ReceivableCryptoAssetPledgedUnrealizedGainLossOperating_01a015a8-8a6b-792d-8c0f-24bb4bf19a7a_negatedTerseLabel_en-US" xlink:label="lab_gemi_ReceivableCryptoAssetPledgedUnrealizedGainLossOperating" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Unrealized loss on receivable, crypto assets pledged</link:label>
    <link:label id="lab_gemi_ReceivableCryptoAssetPledgedUnrealizedGainLossOperating_label_en-US" xlink:label="lab_gemi_ReceivableCryptoAssetPledgedUnrealizedGainLossOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivable Crypto Asset Pledged, Unrealized Gain (Loss), Operating</link:label>
    <link:label id="lab_gemi_ReceivableCryptoAssetPledgedUnrealizedGainLossOperating_documentation_en-US" xlink:label="lab_gemi_ReceivableCryptoAssetPledgedUnrealizedGainLossOperating" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Receivable Crypto Asset Pledged, Unrealized Gain (Loss), Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ReceivableCryptoAssetPledgedUnrealizedGainLossOperating" xlink:href="gemi-20260930.xsd#gemi_ReceivableCryptoAssetPledgedUnrealizedGainLossOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ReceivableCryptoAssetPledgedUnrealizedGainLossOperating" xlink:to="lab_gemi_ReceivableCryptoAssetPledgedUnrealizedGainLossOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_01a015a8-8a6b-7fb6-9730-c784390bf8c7_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: imputed interest</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CryptoAssetNumberOfRestrictedUnits_01a015a8-8b08-737b-bbbe-903ceb47d862_verboseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetNumberOfRestrictedUnits" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Number of restricted crypto assets held (in units)</link:label>
    <link:label id="lab_us-gaap_CryptoAssetNumberOfRestrictedUnits_label_en-US" xlink:label="lab_us-gaap_CryptoAssetNumberOfRestrictedUnits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Number of Units, Restricted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetNumberOfRestrictedUnits" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetNumberOfRestrictedUnits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CryptoAssetNumberOfRestrictedUnits" xlink:to="lab_us-gaap_CryptoAssetNumberOfRestrictedUnits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShortTermBorrowings_01a015a8-8b8d-7056-9095-99ad5066bbf2_periodStartLabel_en-US" xlink:label="lab_us-gaap_ShortTermBorrowings" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Principal Outstanding beginning balance</link:label>
    <link:label id="lab_us-gaap_ShortTermBorrowings_01a015a8-8b8d-75bd-9a75-35ed7a4aa28d_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShortTermBorrowings" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Principal Outstanding ending balance</link:label>
    <link:label id="lab_us-gaap_ShortTermBorrowings_label_en-US" xlink:label="lab_us-gaap_ShortTermBorrowings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermBorrowings" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShortTermBorrowings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortTermBorrowings" xlink:to="lab_us-gaap_ShortTermBorrowings" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerAbstract_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromContractWithCustomerAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCashCurrent_01a015a8-8a6b-7eea-ae0f-f50e3944c6e2_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_RestrictedCashCurrent_label_en-US" xlink:label="lab_us-gaap_RestrictedCashCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestrictedCashCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCashCurrent" xlink:to="lab_us-gaap_RestrictedCashCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockCommonMember_01a015a8-8b08-7760-90fa-0f6de659b40b_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury Stock</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonMember_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockCommonMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonMember" xlink:to="lab_us-gaap_TreasuryStockCommonMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Goodwill and Other [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:to="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_IncreaseDecreaseInCryptoAssetAddition_01a015a8-8b08-7dda-ae84-9eb920f9b801_negatedTerseLabel_en-US" xlink:label="lab_gemi_IncreaseDecreaseInCryptoAssetAddition" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchase of crypto assets</link:label>
    <link:label id="lab_gemi_IncreaseDecreaseInCryptoAssetAddition_label_en-US" xlink:label="lab_gemi_IncreaseDecreaseInCryptoAssetAddition" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) In Crypto Asset, Addition</link:label>
    <link:label id="lab_gemi_IncreaseDecreaseInCryptoAssetAddition_documentation_en-US" xlink:label="lab_gemi_IncreaseDecreaseInCryptoAssetAddition" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Increase (Decrease) In Crypto Asset, Addition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_IncreaseDecreaseInCryptoAssetAddition" xlink:href="gemi-20260930.xsd#gemi_IncreaseDecreaseInCryptoAssetAddition"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_IncreaseDecreaseInCryptoAssetAddition" xlink:to="lab_gemi_IncreaseDecreaseInCryptoAssetAddition" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_01a015a8-8a6b-7932-8212-cbac8adaa734_totalLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total undiscounted lease payments</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LitigationStatusDomain_01a015a8-8b8e-7c76-9c61-331580f04e24_terseLabel_en-US" xlink:label="lab_us-gaap_LitigationStatusDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Litigation Status [Domain]</link:label>
    <link:label id="lab_us-gaap_LitigationStatusDomain_label_en-US" xlink:label="lab_us-gaap_LitigationStatusDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Litigation Status [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LitigationStatusDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LitigationStatusDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LitigationStatusDomain" xlink:to="lab_us-gaap_LitigationStatusDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CustomerCustodialFundsFairValueDisclosure_01a015a8-8a6b-7dbc-82c8-3ec10f85d8fd_terseLabel_en-US" xlink:label="lab_gemi_CustomerCustodialFundsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer custodial funds</link:label>
    <link:label id="lab_gemi_CustomerCustodialFundsFairValueDisclosure_label_en-US" xlink:label="lab_gemi_CustomerCustodialFundsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer Custodial Funds, Fair Value Disclosure</link:label>
    <link:label id="lab_gemi_CustomerCustodialFundsFairValueDisclosure_documentation_en-US" xlink:label="lab_gemi_CustomerCustodialFundsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Customer Custodial Funds, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CustomerCustodialFundsFairValueDisclosure" xlink:href="gemi-20260930.xsd#gemi_CustomerCustodialFundsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CustomerCustodialFundsFairValueDisclosure" xlink:to="lab_gemi_CustomerCustodialFundsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_A10000ETHApril72025Member_01a015a8-8b08-7422-8db1-b6489202b8fc_terseLabel_en-US" xlink:label="lab_gemi_A10000ETHApril72025Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">10,000 ETH, April 7, 2025</link:label>
    <link:label id="lab_gemi_A10000ETHApril72025Member_label_en-US" xlink:label="lab_gemi_A10000ETHApril72025Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">10,000 ETH, April 7, 2025 [Member]</link:label>
    <link:label id="lab_gemi_A10000ETHApril72025Member_documentation_en-US" xlink:label="lab_gemi_A10000ETHApril72025Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">10,000 ETH, April 7, 2025</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_A10000ETHApril72025Member" xlink:href="gemi-20260930.xsd#gemi_A10000ETHApril72025Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_A10000ETHApril72025Member" xlink:to="lab_gemi_A10000ETHApril72025Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_01a015a8-8b08-7bc2-a947-f09625be056e_periodStartLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Unvested beginning balance (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_01a015a8-8b08-714d-ba43-1a313b099784_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Unvested ending balance (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_terseLabel_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Executive Categories</link:label>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_label_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Executive Categories [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllExecutiveCategoriesMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllExecutiveCategoriesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllExecutiveCategoriesMember" xlink:to="lab_ecd_AllExecutiveCategoriesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_TemporaryEquitySharesConversionOfConvertibleSecurities_01a015a8-8b08-77df-9f0f-494ca582522e_negatedTerseLabel_en-US" xlink:label="lab_gemi_TemporaryEquitySharesConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Conversion of convertible preferred units to common stock in connection with IPO (in shares)</link:label>
    <link:label id="lab_gemi_TemporaryEquitySharesConversionOfConvertibleSecurities_label_en-US" xlink:label="lab_gemi_TemporaryEquitySharesConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares, Conversion Of Convertible Securities</link:label>
    <link:label id="lab_gemi_TemporaryEquitySharesConversionOfConvertibleSecurities_documentation_en-US" xlink:label="lab_gemi_TemporaryEquitySharesConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Temporary Equity, Shares, Conversion Of Convertible Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_TemporaryEquitySharesConversionOfConvertibleSecurities" xlink:href="gemi-20260930.xsd#gemi_TemporaryEquitySharesConversionOfConvertibleSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_TemporaryEquitySharesConversionOfConvertibleSecurities" xlink:to="lab_gemi_TemporaryEquitySharesConversionOfConvertibleSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsSvcCstMember" xlink:to="lab_ecd_PnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfLongTermLinesOfCredit_01a015a8-8b8d-7a18-9dfc-bc8359afb670_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermLinesOfCredit" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repayment of funding debt</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfLongTermLinesOfCredit_01a015a8-8b8d-7bae-a69f-6f00dac91978_terseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repayments of funding debt</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfLongTermLinesOfCredit_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Long-Term Lines of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfLongTermLinesOfCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfLongTermLinesOfCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfLongTermLinesOfCredit" xlink:to="lab_us-gaap_RepaymentsOfLongTermLinesOfCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_RelatedPartyDebtDenominatedInCryptoAssetRepaid_01a015a8-8b8d-717d-97dc-f0cfaeb3fa6e_terseLabel_en-US" xlink:label="lab_gemi_RelatedPartyDebtDenominatedInCryptoAssetRepaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repayments of related party loans denominated in crypto assets</link:label>
    <link:label id="lab_gemi_RelatedPartyDebtDenominatedInCryptoAssetRepaid_01a015a8-8b8d-7cae-b6ab-807dc3a37103_verboseLabel_en-US" xlink:label="lab_gemi_RelatedPartyDebtDenominatedInCryptoAssetRepaid" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Amount Repaid</link:label>
    <link:label id="lab_gemi_RelatedPartyDebtDenominatedInCryptoAssetRepaid_label_en-US" xlink:label="lab_gemi_RelatedPartyDebtDenominatedInCryptoAssetRepaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Debt, Denominated In Crypto Asset, Repaid</link:label>
    <link:label id="lab_gemi_RelatedPartyDebtDenominatedInCryptoAssetRepaid_documentation_en-US" xlink:label="lab_gemi_RelatedPartyDebtDenominatedInCryptoAssetRepaid" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loans Payable, Denominated In Crypto Asset, Repaid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_RelatedPartyDebtDenominatedInCryptoAssetRepaid" xlink:href="gemi-20260930.xsd#gemi_RelatedPartyDebtDenominatedInCryptoAssetRepaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_RelatedPartyDebtDenominatedInCryptoAssetRepaid" xlink:to="lab_gemi_RelatedPartyDebtDenominatedInCryptoAssetRepaid" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TangibleAssetImpairmentCharges_01a015a8-8b08-7649-b07e-6786f9b5dfbe_terseLabel_en-US" xlink:label="lab_us-gaap_TangibleAssetImpairmentCharges" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Impairment</link:label>
    <link:label id="lab_us-gaap_TangibleAssetImpairmentCharges_label_en-US" xlink:label="lab_us-gaap_TangibleAssetImpairmentCharges" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tangible Asset Impairment Charges</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TangibleAssetImpairmentCharges" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TangibleAssetImpairmentCharges"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TangibleAssetImpairmentCharges" xlink:to="lab_us-gaap_TangibleAssetImpairmentCharges" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CommonStockConvertibleMinimumOwnershipPercentageTriggeringConversion_01a015a8-8b8d-7209-9c2f-51fd5f242e10_terseLabel_en-US" xlink:label="lab_gemi_CommonStockConvertibleMinimumOwnershipPercentageTriggeringConversion" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum percentage of outstanding common stock held, triggering automatic conversion of stock</link:label>
    <link:label id="lab_gemi_CommonStockConvertibleMinimumOwnershipPercentageTriggeringConversion_label_en-US" xlink:label="lab_gemi_CommonStockConvertibleMinimumOwnershipPercentageTriggeringConversion" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Convertible, Minimum Ownership Percentage Triggering Conversion</link:label>
    <link:label id="lab_gemi_CommonStockConvertibleMinimumOwnershipPercentageTriggeringConversion_documentation_en-US" xlink:label="lab_gemi_CommonStockConvertibleMinimumOwnershipPercentageTriggeringConversion" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock, Convertible, Minimum Ownership Percentage Triggering Conversion</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CommonStockConvertibleMinimumOwnershipPercentageTriggeringConversion" xlink:href="gemi-20260930.xsd#gemi_CommonStockConvertibleMinimumOwnershipPercentageTriggeringConversion"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CommonStockConvertibleMinimumOwnershipPercentageTriggeringConversion" xlink:to="lab_gemi_CommonStockConvertibleMinimumOwnershipPercentageTriggeringConversion" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConversionOfStockAmountIssued1_01a015a8-8a6b-776a-a72c-37228f1557d8_terseLabel_en-US" xlink:label="lab_us-gaap_ConversionOfStockAmountIssued1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion of convertible preferred units to common stock in connection with initial public offering</link:label>
    <link:label id="lab_us-gaap_ConversionOfStockAmountIssued1_label_en-US" xlink:label="lab_us-gaap_ConversionOfStockAmountIssued1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Conversion of Stock, Amount Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConversionOfStockAmountIssued1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConversionOfStockAmountIssued1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConversionOfStockAmountIssued1" xlink:to="lab_us-gaap_ConversionOfStockAmountIssued1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract_01a015a8-8a6b-7774-b2be-79c2a22f320f_terseLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash, cash equivalents, restricted cash and cash equivalents consisted of the following:</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SellingAndMarketingExpense_01a015a8-8b8d-73a7-915d-0f2b16fe66c2_terseLabel_en-US" xlink:label="lab_us-gaap_SellingAndMarketingExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sales and marketing</link:label>
    <link:label id="lab_us-gaap_SellingAndMarketingExpense_label_en-US" xlink:label="lab_us-gaap_SellingAndMarketingExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Selling and Marketing Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SellingAndMarketingExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SellingAndMarketingExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SellingAndMarketingExpense" xlink:to="lab_us-gaap_SellingAndMarketingExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_FinancingAgreementsInterestExpenseAmount_01a015a8-8b8d-7cec-abf6-2b105d56824a_terseLabel_en-US" xlink:label="lab_gemi_FinancingAgreementsInterestExpenseAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Expense</link:label>
    <link:label id="lab_gemi_FinancingAgreementsInterestExpenseAmount_label_en-US" xlink:label="lab_gemi_FinancingAgreementsInterestExpenseAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Agreements, Interest Expense Amount</link:label>
    <link:label id="lab_gemi_FinancingAgreementsInterestExpenseAmount_documentation_en-US" xlink:label="lab_gemi_FinancingAgreementsInterestExpenseAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Agreements, Interest Expense Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_FinancingAgreementsInterestExpenseAmount" xlink:href="gemi-20260930.xsd#gemi_FinancingAgreementsInterestExpenseAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_FinancingAgreementsInterestExpenseAmount" xlink:to="lab_gemi_FinancingAgreementsInterestExpenseAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CryptoAssetRollForward_01a015a8-8b8d-7d47-98ce-59d826eba944_terseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto Asset [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_CryptoAssetRollForward_label_en-US" xlink:label="lab_us-gaap_CryptoAssetRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CryptoAssetRollForward" xlink:to="lab_us-gaap_CryptoAssetRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_01a015a8-8a6b-772f-8872-8b86e960c506_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Basic and Diluted Net Loss Per Share</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureAbstract" xlink:to="lab_us-gaap_DebtDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_InterestPaidAmountPreviouslyAccrued_01a015a8-8a6b-71e2-84eb-216c51b8f52a_terseLabel_en-US" xlink:label="lab_gemi_InterestPaidAmountPreviouslyAccrued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior year interest accrued that was paid during the year</link:label>
    <link:label id="lab_gemi_InterestPaidAmountPreviouslyAccrued_label_en-US" xlink:label="lab_gemi_InterestPaidAmountPreviouslyAccrued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Paid, Amount Previously Accrued</link:label>
    <link:label id="lab_gemi_InterestPaidAmountPreviouslyAccrued_documentation_en-US" xlink:label="lab_gemi_InterestPaidAmountPreviouslyAccrued" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Paid, Amount Previously Accrued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_InterestPaidAmountPreviouslyAccrued" xlink:href="gemi-20260930.xsd#gemi_InterestPaidAmountPreviouslyAccrued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_InterestPaidAmountPreviouslyAccrued" xlink:to="lab_gemi_InterestPaidAmountPreviouslyAccrued" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CapitalSharesReservedForFutureIssuanceAmount_01a12fc7-acba-7f2e-ace6-d91e893175af_terseLabel_en-US" xlink:label="lab_gemi_CapitalSharesReservedForFutureIssuanceAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate initial offering price</link:label>
    <link:label id="lab_gemi_CapitalSharesReservedForFutureIssuanceAmount_label_en-US" xlink:label="lab_gemi_CapitalSharesReservedForFutureIssuanceAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital Shares Reserved For Future Issuance, Amount</link:label>
    <link:label id="lab_gemi_CapitalSharesReservedForFutureIssuanceAmount_documentation_en-US" xlink:label="lab_gemi_CapitalSharesReservedForFutureIssuanceAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Capital Shares Reserved For Future Issuance, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CapitalSharesReservedForFutureIssuanceAmount" xlink:href="gemi-20260930.xsd#gemi_CapitalSharesReservedForFutureIssuanceAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CapitalSharesReservedForFutureIssuanceAmount" xlink:to="lab_gemi_CapitalSharesReservedForFutureIssuanceAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CryptoAssetCost_01a015a8-8b8d-77ae-a862-87a020b94642_terseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cost Basis</link:label>
    <link:label id="lab_us-gaap_CryptoAssetCost_label_en-US" xlink:label="lab_us-gaap_CryptoAssetCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CryptoAssetCost" xlink:to="lab_us-gaap_CryptoAssetCost" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MinimumMember_01a015a8-8b08-7410-a621-ad535621c5be_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum</link:label>
    <link:label id="lab_srt_MinimumMember_label_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Minimum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MinimumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MinimumMember" xlink:to="lab_srt_MinimumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_DerivativeAssetMember_01a015a8-8b08-71d8-bbd6-47f5588ab18a_terseLabel_en-US" xlink:label="lab_gemi_DerivativeAssetMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative assets</link:label>
    <link:label id="lab_gemi_DerivativeAssetMember_label_en-US" xlink:label="lab_gemi_DerivativeAssetMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset [Member]</link:label>
    <link:label id="lab_gemi_DerivativeAssetMember_documentation_en-US" xlink:label="lab_gemi_DerivativeAssetMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_DerivativeAssetMember" xlink:href="gemi-20260930.xsd#gemi_DerivativeAssetMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_DerivativeAssetMember" xlink:to="lab_gemi_DerivativeAssetMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable_01a015a8-8a6b-79be-9526-f52565f65ec7_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTableTextBlock_01a015a8-8a6b-7a81-adf3-61439c49f84f_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Disaggregation of Revenue</link:label>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTableTextBlock_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisaggregationOfRevenueTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:to="lab_us-gaap_DisaggregationOfRevenueTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightAxis_01a015a8-8b08-7c27-a473-8ad484d32bec_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Axis]</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightAxis_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfWarrantOrRightAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightAxis" xlink:to="lab_us-gaap_ClassOfWarrantOrRightAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfIncomeLocationBalanceAxis_01a015a8-8b08-7a21-90e0-bc6e2cc5f728_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Location, Statement of Income, Balance [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementOfIncomeLocationBalanceAxis_label_en-US" xlink:label="lab_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Location, Statement of Income, Balance [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfIncomeLocationBalanceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:to="lab_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonRule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:to="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_01a015a8-8b8d-793b-ab47-70b329b2e058_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average remaining contractual life of options outstanding (in years)</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted-Average Remaining Contractual Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2" xlink:to="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_01a015a8-8b8d-712a-b1fd-c12220115025_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_OriginalPhantomUnitsMember_01a015a8-8a6b-7d03-88b4-52ff51fb9697_terseLabel_en-US" xlink:label="lab_gemi_OriginalPhantomUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Original Phantom Units</link:label>
    <link:label id="lab_gemi_OriginalPhantomUnitsMember_label_en-US" xlink:label="lab_gemi_OriginalPhantomUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Original Phantom Units [Member]</link:label>
    <link:label id="lab_gemi_OriginalPhantomUnitsMember_documentation_en-US" xlink:label="lab_gemi_OriginalPhantomUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Original Phantom Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_OriginalPhantomUnitsMember" xlink:href="gemi-20260930.xsd#gemi_OriginalPhantomUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_OriginalPhantomUnitsMember" xlink:to="lab_gemi_OriginalPhantomUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_01a015a8-8a6b-765d-86eb-3e94b3a98158_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesAuthorized" xlink:to="lab_us-gaap_CommonStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_DerivativeLiabilityMember_01a015a8-8b08-7993-9093-ec2d08b63343_terseLabel_en-US" xlink:label="lab_gemi_DerivativeLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative liabilities</link:label>
    <link:label id="lab_gemi_DerivativeLiabilityMember_label_en-US" xlink:label="lab_gemi_DerivativeLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability [Member]</link:label>
    <link:label id="lab_gemi_DerivativeLiabilityMember_documentation_en-US" xlink:label="lab_gemi_DerivativeLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_DerivativeLiabilityMember" xlink:href="gemi-20260930.xsd#gemi_DerivativeLiabilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_DerivativeLiabilityMember" xlink:to="lab_gemi_DerivativeLiabilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_01a015a8-8b08-7785-93b3-b940a1a2e1df_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of shares (in shares)</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_01a015a8-8b08-7d39-89c7-eb1abf2b8b8a_verboseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Shares issued and sold (in shares)</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_label_en-US" xlink:label="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Number of Shares Issued in Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:to="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock_01a015a8-8b8d-73fe-8aee-de3580b4e8b3_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Restricted Stock Unit Activity</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Restricted Stock Unit, Activity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfShareBasedCompensationRestrictedStockUnitsAwardActivityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_A340BTCOctober312023Member_01a015a8-8b8d-7080-b280-5f13780cd45a_terseLabel_en-US" xlink:label="lab_gemi_A340BTCOctober312023Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">340 BTC October 31, 2023</link:label>
    <link:label id="lab_gemi_A340BTCOctober312023Member_label_en-US" xlink:label="lab_gemi_A340BTCOctober312023Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">340 BTC October 31, 2023 [Member]</link:label>
    <link:label id="lab_gemi_A340BTCOctober312023Member_documentation_en-US" xlink:label="lab_gemi_A340BTCOctober312023Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">340 BTC October 31, 2023</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_A340BTCOctober312023Member" xlink:href="gemi-20260930.xsd#gemi_A340BTCOctober312023Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_A340BTCOctober312023Member" xlink:to="lab_gemi_A340BTCOctober312023Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardExrcPrice_terseLabel_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise Price</link:label>
    <link:label id="lab_ecd_AwardExrcPrice_label_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardExrcPrice" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardExrcPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardExrcPrice" xlink:to="lab_ecd_AwardExrcPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRestructuringAndRelatedCostsTable_01a015a8-8a6b-7518-a63b-5bc453bbf6ff_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRestructuringAndRelatedCostsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restructuring Cost [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRestructuringAndRelatedCostsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRestructuringAndRelatedCostsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restructuring Cost [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRestructuringAndRelatedCostsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRestructuringAndRelatedCostsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRestructuringAndRelatedCostsTable" xlink:to="lab_us-gaap_ScheduleOfRestructuringAndRelatedCostsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardNetOfForfeitures_01a015a8-8b08-7b92-bc12-cb391b2cd270_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardNetOfForfeitures" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common stock upon settlement of RSUs, net of shares withheld</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardNetOfForfeitures_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardNetOfForfeitures" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Restricted Stock Award, Net of Forfeitures</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardNetOfForfeitures" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardNetOfForfeitures"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardNetOfForfeitures" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardNetOfForfeitures" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FacilityClosingMember_01a015a8-8b8d-7291-819f-a437b4c4722b_terseLabel_en-US" xlink:label="lab_us-gaap_FacilityClosingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Facilities Consolidation</link:label>
    <link:label id="lab_us-gaap_FacilityClosingMember_label_en-US" xlink:label="lab_us-gaap_FacilityClosingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Facility Closing [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FacilityClosingMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FacilityClosingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FacilityClosingMember" xlink:to="lab_us-gaap_FacilityClosingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentQuarterlyReport_01a015a8-8b08-7607-830f-92dc3fae697b_terseLabel_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:label id="lab_dei_DocumentQuarterlyReport_label_en-US" xlink:label="lab_dei_DocumentQuarterlyReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Quarterly Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentQuarterlyReport" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentQuarterlyReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentQuarterlyReport" xlink:to="lab_dei_DocumentQuarterlyReport" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_label_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:to="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrentAbstract_01a015a8-8b08-7c53-894f-b89cb0667c58_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses:</link:label>
    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Liabilities, Current [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedLiabilitiesCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedLiabilitiesCurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedLiabilitiesCurrentAbstract" xlink:to="lab_us-gaap_AccruedLiabilitiesCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_01a015a8-8a6b-7b62-9788-91d4f8594f9f_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Payable</link:label>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestPayableCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:to="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetNetNoncurrent_01a015a8-8b8d-7196-8407-bf0dce9a4a23_verboseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetNetNoncurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Warrant receivable</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetNetNoncurrent_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetNetNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Asset, after Allowance for Credit Loss, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerAssetNetNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractWithCustomerAssetNetNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerAssetNetNoncurrent" xlink:to="lab_us-gaap_ContractWithCustomerAssetNetNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_StakingFeesReceivableMember_01a015a8-8b08-70f0-94e1-1d0aff43fdfc_verboseLabel_en-US" xlink:label="lab_gemi_StakingFeesReceivableMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Staking fees receivable</link:label>
    <link:label id="lab_gemi_StakingFeesReceivableMember_01a015a8-8b08-787e-9177-0159e1f3e2da_terseLabel_en-US" xlink:label="lab_gemi_StakingFeesReceivableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Staking fees receivable</link:label>
    <link:label id="lab_gemi_StakingFeesReceivableMember_label_en-US" xlink:label="lab_gemi_StakingFeesReceivableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Staking Fees Receivable [Member]</link:label>
    <link:label id="lab_gemi_StakingFeesReceivableMember_documentation_en-US" xlink:label="lab_gemi_StakingFeesReceivableMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Staking Fees Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_StakingFeesReceivableMember" xlink:href="gemi-20260930.xsd#gemi_StakingFeesReceivableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_StakingFeesReceivableMember" xlink:to="lab_gemi_StakingFeesReceivableMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Table</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseContractualTermAxis_01a015a8-8b08-7ce5-99b1-96ea83bb6099_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseContractualTermAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease Contractual Term [Axis]</link:label>
    <link:label id="lab_us-gaap_LeaseContractualTermAxis_label_en-US" xlink:label="lab_us-gaap_LeaseContractualTermAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease Contractual Term [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseContractualTermAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LeaseContractualTermAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseContractualTermAxis" xlink:to="lab_us-gaap_LeaseContractualTermAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_IncreaseDecreaseInDueToThirdParties_01a015a8-8b8d-70be-b6f2-851ae653ab4b_terseLabel_en-US" xlink:label="lab_gemi_IncreaseDecreaseInDueToThirdParties" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payables due to third parties</link:label>
    <link:label id="lab_gemi_IncreaseDecreaseInDueToThirdParties_label_en-US" xlink:label="lab_gemi_IncreaseDecreaseInDueToThirdParties" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) In Due To Third Parties</link:label>
    <link:label id="lab_gemi_IncreaseDecreaseInDueToThirdParties_documentation_en-US" xlink:label="lab_gemi_IncreaseDecreaseInDueToThirdParties" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Increase (Decrease) In Due To Third Parties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_IncreaseDecreaseInDueToThirdParties" xlink:href="gemi-20260930.xsd#gemi_IncreaseDecreaseInDueToThirdParties"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_IncreaseDecreaseInDueToThirdParties" xlink:to="lab_gemi_IncreaseDecreaseInDueToThirdParties" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityComponentDomain_01a015a8-8b08-772d-9eb0-f9767d45ad55_terseLabel_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:label id="lab_us-gaap_EquityComponentDomain_label_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityComponentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityComponentDomain" xlink:to="lab_us-gaap_EquityComponentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputTypeDomain_01a015a8-8a6b-75f5-84a9-4df7527e3e5b_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Domain]</link:label>
    <link:label id="lab_us-gaap_MeasurementInputTypeDomain_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputTypeDomain" xlink:to="lab_us-gaap_MeasurementInputTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction_01a015a8-8b08-77c3-85b3-d32d7f0fe000_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net proceeds from shares issued and sold</link:label>
    <link:label id="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction_label_en-US" xlink:label="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Consideration Received on Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockConsiderationReceivedOnTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:to="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableGrossCurrent_01a015a8-8b08-746a-9881-02f31c1d697b_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableGrossCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable, before allowances</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableGrossCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableGrossCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, before Allowance for Credit Loss, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableGrossCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableGrossCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableGrossCurrent" xlink:to="lab_us-gaap_AccountsReceivableGrossCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrAdoptionDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adoption Date</link:label>
    <link:label id="lab_ecd_TrdArrAdoptionDate_label_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Adoption Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrAdoptionDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrAdoptionDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrAdoptionDate" xlink:to="lab_ecd_TrdArrAdoptionDate" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_01a015a8-8b08-74e7-b403-8f6d480ab082_terseLabel_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_label_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RepurchaseAgreementCounterpartyNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:to="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpense_01a015a8-8b08-7cee-a889-299062d279e5_totalLabel_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total other income (expense), net</link:label>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpense_label_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonoperating Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonoperatingIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonoperatingIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonoperatingIncomeExpense" xlink:to="lab_us-gaap_NonoperatingIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestructuringCostAndReserveAxis_01a015a8-8b8d-7714-a715-6b7f5ea88c06_terseLabel_en-US" xlink:label="lab_us-gaap_RestructuringCostAndReserveAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restructuring Type [Axis]</link:label>
    <link:label id="lab_us-gaap_RestructuringCostAndReserveAxis_label_en-US" xlink:label="lab_us-gaap_RestructuringCostAndReserveAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restructuring Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestructuringCostAndReserveAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestructuringCostAndReserveAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestructuringCostAndReserveAxis" xlink:to="lab_us-gaap_RestructuringCostAndReserveAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNi_01a015a8-8a6b-7952-a2fb-d669e8269c7b_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNi" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity securities</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNi_01a015a8-8a6b-72f2-bf08-13a2a89d0544_verboseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNi" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Equity securities</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNi_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNi" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNi" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecuritiesFvNi"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesFvNi" xlink:to="lab_us-gaap_EquitySecuritiesFvNi" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndTitle_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title</link:label>
    <link:label id="lab_ecd_TrdArrIndTitle_label_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Title</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndTitle" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrIndTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndTitle" xlink:to="lab_ecd_TrdArrIndTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_PaymentsForCustodialFundsDueToCustomersNetOfRedemptions_01a015a8-8b8d-7505-a903-2625658a5f81_negatedTerseLabel_en-US" xlink:label="lab_gemi_PaymentsForCustodialFundsDueToCustomersNetOfRedemptions" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Custodial funds due to customers, net of redemptions</link:label>
    <link:label id="lab_gemi_PaymentsForCustodialFundsDueToCustomersNetOfRedemptions_label_en-US" xlink:label="lab_gemi_PaymentsForCustodialFundsDueToCustomersNetOfRedemptions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments For Custodial Funds Due To Customers, Net Of Redemptions</link:label>
    <link:label id="lab_gemi_PaymentsForCustodialFundsDueToCustomersNetOfRedemptions_documentation_en-US" xlink:label="lab_gemi_PaymentsForCustodialFundsDueToCustomersNetOfRedemptions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments For Custodial Funds Due To Customers, Net Of Redemptions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_PaymentsForCustodialFundsDueToCustomersNetOfRedemptions" xlink:href="gemi-20260930.xsd#gemi_PaymentsForCustodialFundsDueToCustomersNetOfRedemptions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_PaymentsForCustodialFundsDueToCustomersNetOfRedemptions" xlink:to="lab_gemi_PaymentsForCustodialFundsDueToCustomersNetOfRedemptions" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoAssetStablecoinCurrent_01a015a8-8b8d-7c6b-b562-d20e361bbb20_terseLabel_en-US" xlink:label="lab_gemi_CryptoAssetStablecoinCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stablecoin</link:label>
    <link:label id="lab_gemi_CryptoAssetStablecoinCurrent_label_en-US" xlink:label="lab_gemi_CryptoAssetStablecoinCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Stablecoin, Current</link:label>
    <link:label id="lab_gemi_CryptoAssetStablecoinCurrent_documentation_en-US" xlink:label="lab_gemi_CryptoAssetStablecoinCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Asset, Stablecoin, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoAssetStablecoinCurrent" xlink:href="gemi-20260930.xsd#gemi_CryptoAssetStablecoinCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoAssetStablecoinCurrent" xlink:to="lab_gemi_CryptoAssetStablecoinCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_label_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountingPoliciesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountingPoliciesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountingPoliciesAbstract" xlink:to="lab_us-gaap_AccountingPoliciesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_terseLabel_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement does not require Recovery</link:label>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_label_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Does Not Require Recovery [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDoesNotRequireRecoveryTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:to="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_01a015a8-8b8d-7579-bb53-f0f972ca78cb_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Risk-free rate</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Risk Free Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CryptoAssetCumulativeRealizedLossFromDisposition_01a1a6d3-eb35-70f0-a90c-369847c0c813_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetCumulativeRealizedLossFromDisposition" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Realized losses</link:label>
    <link:label id="lab_us-gaap_CryptoAssetCumulativeRealizedLossFromDisposition_label_en-US" xlink:label="lab_us-gaap_CryptoAssetCumulativeRealizedLossFromDisposition" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Cumulative Realized Loss from Disposition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetCumulativeRealizedLossFromDisposition" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetCumulativeRealizedLossFromDisposition"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CryptoAssetCumulativeRealizedLossFromDisposition" xlink:to="lab_us-gaap_CryptoAssetCumulativeRealizedLossFromDisposition" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_01a015a8-8b08-7d97-a8db-7d008e418c4c_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total lease liabilities</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiability" xlink:to="lab_us-gaap_OperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_01a015a8-8b08-7178-91e0-c187c0ef55c9_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Options outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_01a015a8-8b08-7d25-90fc-46ee97575d22_periodStartLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Outstanding beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_01a015a8-8b08-7617-af75-1389dba89aec_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Outstanding ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestIncomeOperating_01a015a8-8b08-7677-a523-14ee3630ae0b_terseLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Corporate interest</link:label>
    <link:label id="lab_us-gaap_InterestIncomeOperating_label_en-US" xlink:label="lab_us-gaap_InterestIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestIncomeOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestIncomeOperating" xlink:to="lab_us-gaap_InterestIncomeOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTrdPoliciesProcAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:to="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PatentsMember_01a015a8-8a6b-7844-b26b-180ec89c8026_verboseLabel_en-US" xlink:label="lab_us-gaap_PatentsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Patents</link:label>
    <link:label id="lab_us-gaap_PatentsMember_label_en-US" xlink:label="lab_us-gaap_PatentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Patents [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PatentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PatentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PatentsMember" xlink:to="lab_us-gaap_PatentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TypeOfRestructuringDomain_01a015a8-8b08-7d6e-aa15-a713cbdd05d4_terseLabel_en-US" xlink:label="lab_us-gaap_TypeOfRestructuringDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Type of Restructuring [Domain]</link:label>
    <link:label id="lab_us-gaap_TypeOfRestructuringDomain_label_en-US" xlink:label="lab_us-gaap_TypeOfRestructuringDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Type of Restructuring [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TypeOfRestructuringDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TypeOfRestructuringDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TypeOfRestructuringDomain" xlink:to="lab_us-gaap_TypeOfRestructuringDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_01a015a8-8b08-7e92-b5bb-60a255ff7458_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsNetIncomeTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_DebtInstrumentAmountOfCryptoCurrencyUnitsLoanedRepaidDuringThePeriod_01a015a8-8b08-7f03-beb5-683286c513ee_verboseLabel_en-US" xlink:label="lab_gemi_DebtInstrumentAmountOfCryptoCurrencyUnitsLoanedRepaidDuringThePeriod" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Amount of crypto repaid (in units)</link:label>
    <link:label id="lab_gemi_DebtInstrumentAmountOfCryptoCurrencyUnitsLoanedRepaidDuringThePeriod_label_en-US" xlink:label="lab_gemi_DebtInstrumentAmountOfCryptoCurrencyUnitsLoanedRepaidDuringThePeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Amount Of Crypto Currency Units Loaned, Repaid During The Period</link:label>
    <link:label id="lab_gemi_DebtInstrumentAmountOfCryptoCurrencyUnitsLoanedRepaidDuringThePeriod_documentation_en-US" xlink:label="lab_gemi_DebtInstrumentAmountOfCryptoCurrencyUnitsLoanedRepaidDuringThePeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Amount Of Crypto Currency Units Loaned, Repaid During The Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_DebtInstrumentAmountOfCryptoCurrencyUnitsLoanedRepaidDuringThePeriod" xlink:href="gemi-20260930.xsd#gemi_DebtInstrumentAmountOfCryptoCurrencyUnitsLoanedRepaidDuringThePeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_DebtInstrumentAmountOfCryptoCurrencyUnitsLoanedRepaidDuringThePeriod" xlink:to="lab_gemi_DebtInstrumentAmountOfCryptoCurrencyUnitsLoanedRepaidDuringThePeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain_01a015a8-8b8d-7342-9f86-7f01cb19bd6a_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Asset, Aging [Domain]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Aging [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivablesPeriodPastDueDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:to="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_01a015a8-8b08-7452-b86e-cf997bbfb004_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Potentially Dilutive Units Not Included in Calculation of Diluted Shares Outstanding</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock"/>
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    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_01a015a8-8b8d-77fd-bc37-3d802d0035e7_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">RSUs</link:label>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_01a015a8-8b8d-7ace-a2c7-33b2ee19fd33_verboseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unvested RSUs</link:label>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_label_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock Units (RSUs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockUnitsRSUMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestrictedStockUnitsRSUMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedStockUnitsRSUMember" xlink:to="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CryptoAssetFairValue_01a015a8-8b08-7c54-bb3a-347499c893f1_terseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto assets held:</link:label>
    <link:label id="lab_us-gaap_CryptoAssetFairValue_01a015a8-8b08-76b2-9bd9-04a8b8ea48ad_verboseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetFairValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_CryptoAssetFairValue_01a015a8-8b08-7948-be8f-be9eb2ea2ed6_periodStartLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetFairValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Crypto assets held beginning balance</link:label>
    <link:label id="lab_us-gaap_CryptoAssetFairValue_01a015a8-8b08-7335-ac9f-85faeb13d16a_periodEndLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetFairValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Crypto assets held, ending balance</link:label>
    <link:label id="lab_us-gaap_CryptoAssetFairValue_label_en-US" xlink:label="lab_us-gaap_CryptoAssetFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CryptoAssetFairValue" xlink:to="lab_us-gaap_CryptoAssetFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllAdjToCompMember_terseLabel_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation</link:label>
    <link:label id="lab_ecd_AllAdjToCompMember_label_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllAdjToCompMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllAdjToCompMember"/>
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    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfPrivatePlacement_01a015a8-8b8d-7cbd-b3e8-07dcb715b07a_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfPrivatePlacement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from issuance of common stock in connection with concurrent private placement with Nasdaq</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfPrivatePlacement_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfPrivatePlacement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Private Placement</link:label>
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    <link:label id="lab_gemi_PaymentsToAcquireCreditCardReceivable_01a015a8-8b8d-7583-b9a9-53ecea7e415d_negatedTerseLabel_en-US" xlink:label="lab_gemi_PaymentsToAcquireCreditCardReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of credit card receivables</link:label>
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    <link:label id="lab_gemi_PaymentsToAcquireCreditCardReceivable_documentation_en-US" xlink:label="lab_gemi_PaymentsToAcquireCreditCardReceivable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payments To Acquire Credit Card Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_PaymentsToAcquireCreditCardReceivable" xlink:href="gemi-20260930.xsd#gemi_PaymentsToAcquireCreditCardReceivable"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_01a015a8-8b08-7a1b-8338-9706a0466149_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash used in operating activities</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueNetPriceAdjustmentAbstract_01a015a8-8b8d-79b6-a46c-0927464523ae_terseLabel_en-US" xlink:label="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueNetPriceAdjustmentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net reductions</link:label>
    <link:label id="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueNetPriceAdjustmentAbstract_label_en-US" xlink:label="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueNetPriceAdjustmentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities Without Readily Determinable Fair Value, Net Price Adjustment [Abstract]</link:label>
    <link:label id="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueNetPriceAdjustmentAbstract_documentation_en-US" xlink:label="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueNetPriceAdjustmentAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Securities Without Readily Determinable Fair Value, Net Price Adjustment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueNetPriceAdjustmentAbstract" xlink:href="gemi-20260930.xsd#gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueNetPriceAdjustmentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueNetPriceAdjustmentAbstract" xlink:to="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueNetPriceAdjustmentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeStatementAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementAbstract" xlink:to="lab_us-gaap_IncomeStatementAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityAbstract_01a015a8-8b8d-7f79-b4cf-4ee572ec6554_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stockholders' equity:</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityAbstract" xlink:to="lab_us-gaap_StockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentTransitionReport_01a015a8-8a6b-77ad-a254-e12d9baf34d3_terseLabel_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:label id="lab_dei_DocumentTransitionReport_label_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentTransitionReport" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentTransitionReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentTransitionReport" xlink:to="lab_dei_DocumentTransitionReport" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueOptionQuantitativeDisclosuresLineItems_01a015a8-8b8d-7947-a888-f36b601c5fb8_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOptionQuantitativeDisclosuresLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Option, Quantitative Disclosures [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueOptionQuantitativeDisclosuresLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueOptionQuantitativeDisclosuresLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Option, Quantitative Disclosures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueOptionQuantitativeDisclosuresLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueOptionQuantitativeDisclosuresLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueOptionQuantitativeDisclosuresLineItems" xlink:to="lab_us-gaap_FairValueOptionQuantitativeDisclosuresLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestructuringPlanDomain_01a015a8-8a6b-7b3c-a997-acde37995f5a_terseLabel_en-US" xlink:label="lab_us-gaap_RestructuringPlanDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restructuring Plan [Domain]</link:label>
    <link:label id="lab_us-gaap_RestructuringPlanDomain_label_en-US" xlink:label="lab_us-gaap_RestructuringPlanDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restructuring Plan [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestructuringPlanDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestructuringPlanDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestructuringPlanDomain" xlink:to="lab_us-gaap_RestructuringPlanDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_01a015a8-8b08-7933-9b6f-a5b44e51d436_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating expenses:</link:label>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpensesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpensesAbstract" xlink:to="lab_us-gaap_OperatingExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_terseLabel_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs)</link:label>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_label_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockAppreciationRightsSARSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:to="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_01a015a8-8b08-76b1-b29c-54e361540aff_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Finite-Lived Intangible Assets</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_WarrantFairValueDisclosure_01a015a8-8b08-7eab-b225-b081011aec8a_terseLabel_en-US" xlink:label="lab_gemi_WarrantFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants</link:label>
    <link:label id="lab_gemi_WarrantFairValueDisclosure_label_en-US" xlink:label="lab_gemi_WarrantFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrant, Fair Value Disclosure</link:label>
    <link:label id="lab_gemi_WarrantFairValueDisclosure_documentation_en-US" xlink:label="lab_gemi_WarrantFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Warrants, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_WarrantFairValueDisclosure" xlink:href="gemi-20260930.xsd#gemi_WarrantFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_WarrantFairValueDisclosure" xlink:to="lab_gemi_WarrantFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_AccountsReceivableAllowanceForCreditLossWriteOffAccruedInterestAndFeeReceivable_01a015a8-8b8d-7be4-ac52-60cf9b02851a_terseLabel_en-US" xlink:label="lab_gemi_AccountsReceivableAllowanceForCreditLossWriteOffAccruedInterestAndFeeReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest receivable included in write-offs</link:label>
    <link:label id="lab_gemi_AccountsReceivableAllowanceForCreditLossWriteOffAccruedInterestAndFeeReceivable_label_en-US" xlink:label="lab_gemi_AccountsReceivableAllowanceForCreditLossWriteOffAccruedInterestAndFeeReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss, Write-Off, Accrued Interest And Fee Receivable</link:label>
    <link:label id="lab_gemi_AccountsReceivableAllowanceForCreditLossWriteOffAccruedInterestAndFeeReceivable_documentation_en-US" xlink:label="lab_gemi_AccountsReceivableAllowanceForCreditLossWriteOffAccruedInterestAndFeeReceivable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss, Write-Off, Accrued Interest And Fee Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_AccountsReceivableAllowanceForCreditLossWriteOffAccruedInterestAndFeeReceivable" xlink:href="gemi-20260930.xsd#gemi_AccountsReceivableAllowanceForCreditLossWriteOffAccruedInterestAndFeeReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_AccountsReceivableAllowanceForCreditLossWriteOffAccruedInterestAndFeeReceivable" xlink:to="lab_gemi_AccountsReceivableAllowanceForCreditLossWriteOffAccruedInterestAndFeeReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CityAreaCode_01a015a8-8b8d-72d1-8206-f78211c3b5a7_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CityAreaCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CityAreaCode" xlink:to="lab_dei_CityAreaCode" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_A1275BTCJuly242025Member_01a015a8-8a6b-7846-a139-c388aac2fb3e_terseLabel_en-US" xlink:label="lab_gemi_A1275BTCJuly242025Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">1, 275 BTC, July 24, 2025</link:label>
    <link:label id="lab_gemi_A1275BTCJuly242025Member_label_en-US" xlink:label="lab_gemi_A1275BTCJuly242025Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">1, 275 BTC, July 24, 2025 [Member]</link:label>
    <link:label id="lab_gemi_A1275BTCJuly242025Member_documentation_en-US" xlink:label="lab_gemi_A1275BTCJuly242025Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">1, 275 BTC, July 24, 2025</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_A1275BTCJuly242025Member" xlink:href="gemi-20260930.xsd#gemi_A1275BTCJuly242025Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_A1275BTCJuly242025Member" xlink:to="lab_gemi_A1275BTCJuly242025Member" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentInformationTable_01a015a8-8b08-7b0d-a674-766d177362e8_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Table]</link:label>
    <link:label id="lab_dei_DocumentInformationTable_label_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Information [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationTable" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentInformationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentInformationTable" xlink:to="lab_dei_DocumentInformationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_01a015a8-8b8e-7385-90b7-0163f197b501_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, right-of-use asset, periodic reduction</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset, Periodic Reduction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_01a015a8-8b08-7b33-9c50-5295e2e9acf7_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Events</link:label>
    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Events [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsTextBlock" xlink:to="lab_us-gaap_SubsequentEventsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryIndName" xlink:to="lab_ecd_ForgoneRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_BitcoinMember_01a015a8-8a6b-7ba4-b6b8-ac95144d978c_terseLabel_en-US" xlink:label="lab_gemi_BitcoinMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Bitcoin</link:label>
    <link:label id="lab_gemi_BitcoinMember_01a015a8-8a6b-7c17-a4a9-6df281a45108_verboseLabel_en-US" xlink:label="lab_gemi_BitcoinMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Bitcoin</link:label>
    <link:label id="lab_gemi_BitcoinMember_label_en-US" xlink:label="lab_gemi_BitcoinMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Bitcoin [Member]</link:label>
    <link:label id="lab_gemi_BitcoinMember_documentation_en-US" xlink:label="lab_gemi_BitcoinMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Bitcoin</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_BitcoinMember" xlink:href="gemi-20260930.xsd#gemi_BitcoinMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_BitcoinMember" xlink:to="lab_gemi_BitcoinMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureLineItems_01a015a8-8b08-73d9-b06a-f4b0b33f2d5b_terseLabel_en-US" xlink:label="lab_gemi_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred Costs, Capitalized, Prepaid And Other Assets Disclosure [Line Items]</link:label>
    <link:label id="lab_gemi_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureLineItems_label_en-US" xlink:label="lab_gemi_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Costs, Capitalized, Prepaid And Other Assets Disclosure [Line Items]</link:label>
    <link:label id="lab_gemi_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureLineItems_documentation_en-US" xlink:label="lab_gemi_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Costs, Capitalized, Prepaid And Other Assets Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureLineItems" xlink:href="gemi-20260930.xsd#gemi_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureLineItems" xlink:to="lab_gemi_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description</link:label>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_label_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonGaapMeasureDescriptionTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:to="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_01a015a8-8b08-7ff7-bfec-981666eac6da_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-Average Grant Date Fair Value per Share</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValueRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityDomain_01a015a8-8b8e-7908-8a53-2806868aa73f_terseLabel_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:label id="lab_dei_EntityDomain_label_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityDomain"/>
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    <link:label id="lab_gemi_ServiceStakingRevenueMember_01a015a8-8b8d-73d4-91f2-656bcd335398_terseLabel_en-US" xlink:label="lab_gemi_ServiceStakingRevenueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Staking revenue</link:label>
    <link:label id="lab_gemi_ServiceStakingRevenueMember_label_en-US" xlink:label="lab_gemi_ServiceStakingRevenueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Service, Staking Revenue [Member]</link:label>
    <link:label id="lab_gemi_ServiceStakingRevenueMember_documentation_en-US" xlink:label="lab_gemi_ServiceStakingRevenueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Service, Staking Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ServiceStakingRevenueMember" xlink:href="gemi-20260930.xsd#gemi_ServiceStakingRevenueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ServiceStakingRevenueMember" xlink:to="lab_gemi_ServiceStakingRevenueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_01a015a8-8b8d-7c99-99de-bb3f68016f12_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesIssued" xlink:to="lab_us-gaap_PreferredStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CreditCardReceivablesPledgedCurrent_01a015a8-8a6b-775a-be89-2df0bc33f218_terseLabel_en-US" xlink:label="lab_gemi_CreditCardReceivablesPledgedCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit card receivables pledged, net</link:label>
    <link:label id="lab_gemi_CreditCardReceivablesPledgedCurrent_label_en-US" xlink:label="lab_gemi_CreditCardReceivablesPledgedCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Card Receivables Pledged, Current</link:label>
    <link:label id="lab_gemi_CreditCardReceivablesPledgedCurrent_documentation_en-US" xlink:label="lab_gemi_CreditCardReceivablesPledgedCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Credit Card Receivables Pledged, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CreditCardReceivablesPledgedCurrent" xlink:href="gemi-20260930.xsd#gemi_CreditCardReceivablesPledgedCurrent"/>
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    <link:label id="lab_gemi_DebtTermsAxis_01a015a8-8b08-72e9-8b84-dc28116252d9_terseLabel_en-US" xlink:label="lab_gemi_DebtTermsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Terms [Axis]</link:label>
    <link:label id="lab_gemi_DebtTermsAxis_label_en-US" xlink:label="lab_gemi_DebtTermsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Terms [Axis]</link:label>
    <link:label id="lab_gemi_DebtTermsAxis_documentation_en-US" xlink:label="lab_gemi_DebtTermsAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Terms</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_DebtTermsAxis" xlink:href="gemi-20260930.xsd#gemi_DebtTermsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_DebtTermsAxis" xlink:to="lab_gemi_DebtTermsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermPurchaseCommitmentCategoryOfItemPurchasedDomain_01a015a8-8b8d-70b9-81ba-e806266eabbd_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermPurchaseCommitmentCategoryOfItemPurchasedDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Purchase Commitment, Category of Item Purchased [Domain]</link:label>
    <link:label id="lab_us-gaap_LongTermPurchaseCommitmentCategoryOfItemPurchasedDomain_label_en-US" xlink:label="lab_us-gaap_LongTermPurchaseCommitmentCategoryOfItemPurchasedDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Purchase Commitment, Category of Item Purchased [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermPurchaseCommitmentCategoryOfItemPurchasedDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermPurchaseCommitmentCategoryOfItemPurchasedDomain"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_01a015a8-8b8d-781c-9feb-a71ba372d027_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOtherOperatingAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilitiesCurrent_01a015a8-8b8d-747d-a7e5-5056a7f90578_totalLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total accrued expenses and other current liabilities</link:label>
    <link:label id="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsPayableAndOtherAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable and Other Accrued Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableAndOtherAccruedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsPayableAndOtherAccruedLiabilitiesCurrent"/>
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    <link:label id="lab_us-gaap_NatureOfOperations_01a015a8-8b08-77b5-bc44-984d080b5604_terseLabel_en-US" xlink:label="lab_us-gaap_NatureOfOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Description of Business</link:label>
    <link:label id="lab_us-gaap_NatureOfOperations_label_en-US" xlink:label="lab_us-gaap_NatureOfOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nature of Operations [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NatureOfOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NatureOfOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NatureOfOperations" xlink:to="lab_us-gaap_NatureOfOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_01a015a8-8b08-71cc-9f7b-a871788a5cc2_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common stock in exchange for crypto assets (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_01a015a8-8b08-7c27-9e07-a8314af420a4_verboseLabel_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net benefit related to stock-based compensation</link:label>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_01a015a8-8b08-7152-9dc9-76a48a71b9ba_terseLabel_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation expense</link:label>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_label_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllocatedShareBasedCompensationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AllocatedShareBasedCompensationExpense"/>
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    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByMeasurementBasisAxis"/>
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    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercises in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised"/>
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    <link:label id="lab_gemi_IntangibleAssetFiniteLivedEstimatedAmortizationExpenseAfterYearFour_01a015a8-8b8d-7028-9d35-37e4d977e254_terseLabel_en-US" xlink:label="lab_gemi_IntangibleAssetFiniteLivedEstimatedAmortizationExpenseAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_gemi_IntangibleAssetFiniteLivedEstimatedAmortizationExpenseAfterYearFour_label_en-US" xlink:label="lab_gemi_IntangibleAssetFiniteLivedEstimatedAmortizationExpenseAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, After Year Four</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_gemi_IntangibleAssetFiniteLivedEstimatedAmortizationExpenseAfterYearFour" xlink:href="gemi-20260930.xsd#gemi_IntangibleAssetFiniteLivedEstimatedAmortizationExpenseAfterYearFour"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_01a015a8-8b08-7a4a-adae-0f48139614f7_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Granted (in dollars per share)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_A822BTCMarch182026Member_01a015a8-8b8d-79d1-b0cc-5bf363c833aa_terseLabel_en-US" xlink:label="lab_gemi_A822BTCMarch182026Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">822 BTC, March 18, 2026</link:label>
    <link:label id="lab_gemi_A822BTCMarch182026Member_label_en-US" xlink:label="lab_gemi_A822BTCMarch182026Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">822 BTC March 18, 2026 [Member]</link:label>
    <link:label id="lab_gemi_A822BTCMarch182026Member_documentation_en-US" xlink:label="lab_gemi_A822BTCMarch182026Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">822 BTC March 18, 2026</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_A822BTCMarch182026Member" xlink:href="gemi-20260930.xsd#gemi_A822BTCMarch182026Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_A822BTCMarch182026Member" xlink:to="lab_gemi_A822BTCMarch182026Member" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTable_01a015a8-8b8d-7ef8-80fb-be5fb797ab4f_terseLabel_en-US" xlink:label="lab_gemi_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred Costs, Capitalized, Prepaid And Other Assets Disclosure [Table]</link:label>
    <link:label id="lab_gemi_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTable_label_en-US" xlink:label="lab_gemi_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Costs, Capitalized, Prepaid And Other Assets Disclosure [Table]</link:label>
    <link:label id="lab_gemi_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTable_documentation_en-US" xlink:label="lab_gemi_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Costs, Capitalized, Prepaid And Other Assets Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTable" xlink:href="gemi-20260930.xsd#gemi_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTable" xlink:to="lab_gemi_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_01a015a8-8b8d-7a73-9fec-3d036359dd91_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeDomain" xlink:to="lab_us-gaap_SubsequentEventTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PayablesAndAccrualsAbstract_label_en-US" xlink:label="lab_us-gaap_PayablesAndAccrualsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payables and Accruals [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PayablesAndAccrualsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PayablesAndAccrualsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PayablesAndAccrualsAbstract" xlink:to="lab_us-gaap_PayablesAndAccrualsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_TransactionRevenueOtherMember_01a015a8-8b08-786b-8d7b-3d243e8feb12_terseLabel_en-US" xlink:label="lab_gemi_TransactionRevenueOtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other transaction revenue</link:label>
    <link:label id="lab_gemi_TransactionRevenueOtherMember_label_en-US" xlink:label="lab_gemi_TransactionRevenueOtherMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transaction Revenue, Other [Member]</link:label>
    <link:label id="lab_gemi_TransactionRevenueOtherMember_documentation_en-US" xlink:label="lab_gemi_TransactionRevenueOtherMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Transaction Revenue, Other</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_TransactionRevenueOtherMember" xlink:href="gemi-20260930.xsd#gemi_TransactionRevenueOtherMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_TransactionRevenueOtherMember" xlink:to="lab_gemi_TransactionRevenueOtherMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue_01a015a8-8b08-7453-9340-fc2eca58eff7_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forfeited (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Forfeitures, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompRecoveryTable_terseLabel_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery</link:label>
    <link:label id="lab_ecd_ErrCompRecoveryTable_label_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompRecoveryTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ErrCompRecoveryTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompRecoveryTable" xlink:to="lab_ecd_ErrCompRecoveryTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod_01a015a8-8a6b-7b6f-87b3-3ae18112914d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Forfeited (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Forfeitures in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_AccountsReceivableCreditLossExpenseReversalDiscreteFraudReserves_01a015a8-8a6b-71a4-a952-35c9ddccfd22_terseLabel_en-US" xlink:label="lab_gemi_AccountsReceivableCreditLossExpenseReversalDiscreteFraudReserves" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discrete fraud reserves included in provision for (reversal of) credit losses</link:label>
    <link:label id="lab_gemi_AccountsReceivableCreditLossExpenseReversalDiscreteFraudReserves_label_en-US" xlink:label="lab_gemi_AccountsReceivableCreditLossExpenseReversalDiscreteFraudReserves" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Credit Loss Expense (Reversal), Discrete Fraud Reserves</link:label>
    <link:label id="lab_gemi_AccountsReceivableCreditLossExpenseReversalDiscreteFraudReserves_documentation_en-US" xlink:label="lab_gemi_AccountsReceivableCreditLossExpenseReversalDiscreteFraudReserves" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Credit Loss Expense (Reversal), Discrete Fraud Reserves</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_AccountsReceivableCreditLossExpenseReversalDiscreteFraudReserves" xlink:href="gemi-20260930.xsd#gemi_AccountsReceivableCreditLossExpenseReversalDiscreteFraudReserves"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_AccountsReceivableCreditLossExpenseReversalDiscreteFraudReserves" xlink:to="lab_gemi_AccountsReceivableCreditLossExpenseReversalDiscreteFraudReserves" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditCardReceivablesMember_01a015a8-8b8d-7f57-8298-4a853f4ae062_terseLabel_en-US" xlink:label="lab_us-gaap_CreditCardReceivablesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit card receivables</link:label>
    <link:label id="lab_us-gaap_CreditCardReceivablesMember_label_en-US" xlink:label="lab_us-gaap_CreditCardReceivablesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Card Receivable [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditCardReceivablesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CreditCardReceivablesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditCardReceivablesMember" xlink:to="lab_us-gaap_CreditCardReceivablesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCurrentReportingStatus_01a015a8-8a6b-76e7-a5d7-d55fdd527b9e_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:label id="lab_dei_EntityCurrentReportingStatus_label_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCurrentReportingStatus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCurrentReportingStatus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCurrentReportingStatus" xlink:to="lab_dei_EntityCurrentReportingStatus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_01a015a8-8a6b-7748-8795-366d062c197f_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by (used in) financing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnAmt" xlink:to="lab_ecd_TotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation_01a015a8-8b8d-779d-ac05-681c82ce1680_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Shares withheld for employee tax withholdings</link:label>
    <link:label id="lab_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Decrease for Tax Withholding Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:to="lab_us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract_01a015a8-8b8d-7d18-a6e5-0ee98d1552b2_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract_01a015a8-8b8d-71ff-a7f8-4ac35e2044eb_verboseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Financial Liabilities:</link:label>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Fair Value Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesFairValueDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:to="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CryptoAssetHoldingLineItems_01a015a8-8b08-78bc-b47c-3c9ac7002534_terseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetHoldingLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto Asset, Holding [Line Items]</link:label>
    <link:label id="lab_us-gaap_CryptoAssetHoldingLineItems_label_en-US" xlink:label="lab_us-gaap_CryptoAssetHoldingLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Holding [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetHoldingLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetHoldingLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CryptoAssetHoldingLineItems" xlink:to="lab_us-gaap_CryptoAssetHoldingLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssetsNoncurrentAbstract_01a015a8-8a6b-7935-8e0b-3e40c260a9e6_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other non-current assets</link:label>
    <link:label id="lab_us-gaap_OtherAssetsNoncurrentAbstract_label_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets, Noncurrent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsNoncurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAssetsNoncurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsNoncurrentAbstract" xlink:to="lab_us-gaap_OtherAssetsNoncurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoAssetPaymentsForExpenses_01a015a8-8b08-7ee6-8626-332e144dca44_negatedTerseLabel_en-US" xlink:label="lab_gemi_CryptoAssetPaymentsForExpenses" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Crypto asset payments for expenses</link:label>
    <link:label id="lab_gemi_CryptoAssetPaymentsForExpenses_label_en-US" xlink:label="lab_gemi_CryptoAssetPaymentsForExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset Payments For Expenses</link:label>
    <link:label id="lab_gemi_CryptoAssetPaymentsForExpenses_documentation_en-US" xlink:label="lab_gemi_CryptoAssetPaymentsForExpenses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Asset Payments For Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoAssetPaymentsForExpenses" xlink:href="gemi-20260930.xsd#gemi_CryptoAssetPaymentsForExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoAssetPaymentsForExpenses" xlink:to="lab_gemi_CryptoAssetPaymentsForExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_01a015a8-8b08-72f4-813f-6406a9c502c8_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustments to reconcile net loss to net cash used in operating activities</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs_01a015a8-8b8d-76f0-821e-de48759b270e_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Write-offs</link:label>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs_label_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs" xlink:to="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_01a015a8-8b8d-7772-b4a3-b96dfb00bec1_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from financing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_01a015a8-8b08-7396-9226-144b8d7a0c2b_verboseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Software, property and equipment, net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_01a015a8-8b08-7644-bc90-036b32da57c9_totalLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Software, property and equipment, net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment, after Accumulated Depreciation, Depletion, and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentNet" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_01a015a8-8b8d-7a0d-8936-bfa6b30f9c8c_terseLabel_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_label_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:to="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_AccountsReceivablePercentPastDue_01a015a8-8a6b-77b2-a5c5-2857e9077917_terseLabel_en-US" xlink:label="lab_gemi_AccountsReceivablePercentPastDue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage of receivables current and past due</link:label>
    <link:label id="lab_gemi_AccountsReceivablePercentPastDue_label_en-US" xlink:label="lab_gemi_AccountsReceivablePercentPastDue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Percent Past Due</link:label>
    <link:label id="lab_gemi_AccountsReceivablePercentPastDue_documentation_en-US" xlink:label="lab_gemi_AccountsReceivablePercentPastDue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Percent Past Due</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_AccountsReceivablePercentPastDue" xlink:href="gemi-20260930.xsd#gemi_AccountsReceivablePercentPastDue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_AccountsReceivablePercentPastDue" xlink:to="lab_gemi_AccountsReceivablePercentPastDue" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoAssetFuturesLiabilityMember_01a015a8-8b08-7cd1-bacc-24fabdf239bb_terseLabel_en-US" xlink:label="lab_gemi_CryptoAssetFuturesLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto asset futures</link:label>
    <link:label id="lab_gemi_CryptoAssetFuturesLiabilityMember_label_en-US" xlink:label="lab_gemi_CryptoAssetFuturesLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset Futures, Liability [Member]</link:label>
    <link:label id="lab_gemi_CryptoAssetFuturesLiabilityMember_documentation_en-US" xlink:label="lab_gemi_CryptoAssetFuturesLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Asset Futures, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoAssetFuturesLiabilityMember" xlink:href="gemi-20260930.xsd#gemi_CryptoAssetFuturesLiabilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoAssetFuturesLiabilityMember" xlink:to="lab_gemi_CryptoAssetFuturesLiabilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract_01a015a8-8b8d-7a80-ab8a-be03b4bf33a5_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Numerator:</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssets_01a015a8-8b8d-74aa-9425-f30a49fbf91e_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto asset futures</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_01a015a8-8b8d-78fc-896f-d530291fa638_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_label_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssets" xlink:to="lab_us-gaap_DerivativeAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_LineOfCreditFacilityThresholdMaximumBorrowingCapacityTriggeringInterestRateIncrease_01a015a8-8a6b-7839-afbb-ea55dff2f660_terseLabel_en-US" xlink:label="lab_gemi_LineOfCreditFacilityThresholdMaximumBorrowingCapacityTriggeringInterestRateIncrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding balance threshold for interest rate increase</link:label>
    <link:label id="lab_gemi_LineOfCreditFacilityThresholdMaximumBorrowingCapacityTriggeringInterestRateIncrease_label_en-US" xlink:label="lab_gemi_LineOfCreditFacilityThresholdMaximumBorrowingCapacityTriggeringInterestRateIncrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line Of Credit Facility, Threshold Maximum Borrowing Capacity Triggering Interest Rate Increase</link:label>
    <link:label id="lab_gemi_LineOfCreditFacilityThresholdMaximumBorrowingCapacityTriggeringInterestRateIncrease_documentation_en-US" xlink:label="lab_gemi_LineOfCreditFacilityThresholdMaximumBorrowingCapacityTriggeringInterestRateIncrease" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line Of Credit Facility, Maximum Borrowing Capacity Threshold Triggering Interest Rate Increase</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_LineOfCreditFacilityThresholdMaximumBorrowingCapacityTriggeringInterestRateIncrease" xlink:href="gemi-20260930.xsd#gemi_LineOfCreditFacilityThresholdMaximumBorrowingCapacityTriggeringInterestRateIncrease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_LineOfCreditFacilityThresholdMaximumBorrowingCapacityTriggeringInterestRateIncrease" xlink:to="lab_gemi_LineOfCreditFacilityThresholdMaximumBorrowingCapacityTriggeringInterestRateIncrease" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_01a015a8-8b08-733e-a5be-80ebddf68dc3_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_A5200ETHJanuary272025Member_01a015a8-8b08-732c-a650-0bf76ae4e54b_terseLabel_en-US" xlink:label="lab_gemi_A5200ETHJanuary272025Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">5,200 ETH January 27, 2025</link:label>
    <link:label id="lab_gemi_A5200ETHJanuary272025Member_label_en-US" xlink:label="lab_gemi_A5200ETHJanuary272025Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">5,200 ETH January 27, 2025 [Member]</link:label>
    <link:label id="lab_gemi_A5200ETHJanuary272025Member_documentation_en-US" xlink:label="lab_gemi_A5200ETHJanuary272025Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">5,200 ETH January 27, 2025</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_A5200ETHJanuary272025Member" xlink:href="gemi-20260930.xsd#gemi_A5200ETHJanuary272025Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_A5200ETHJanuary272025Member" xlink:to="lab_gemi_A5200ETHJanuary272025Member" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_TransactionAndServiceRevenueMember_01a015a8-8b08-7ec1-abd3-7a68dfd179c9_terseLabel_en-US" xlink:label="lab_gemi_TransactionAndServiceRevenueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transaction And Service Revenue</link:label>
    <link:label id="lab_gemi_TransactionAndServiceRevenueMember_label_en-US" xlink:label="lab_gemi_TransactionAndServiceRevenueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transaction And Service Revenue [Member]</link:label>
    <link:label id="lab_gemi_TransactionAndServiceRevenueMember_documentation_en-US" xlink:label="lab_gemi_TransactionAndServiceRevenueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Transaction And Service Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_TransactionAndServiceRevenueMember" xlink:href="gemi-20260930.xsd#gemi_TransactionAndServiceRevenueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_TransactionAndServiceRevenueMember" xlink:to="lab_gemi_TransactionAndServiceRevenueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_terseLabel_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Securities</link:label>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_label_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Underlying Securities Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardUndrlygSecuritiesAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:to="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_PrepaidExpenseAndOtherAssetsDisclosureTextBlock_01a015a8-8b8d-7255-8c10-132077be1cda_terseLabel_en-US" xlink:label="lab_gemi_PrepaidExpenseAndOtherAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepaid Expenses and Other Assets</link:label>
    <link:label id="lab_gemi_PrepaidExpenseAndOtherAssetsDisclosureTextBlock_label_en-US" xlink:label="lab_gemi_PrepaidExpenseAndOtherAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepaid Expense And Other Assets Disclosure [Text Block]</link:label>
    <link:label id="lab_gemi_PrepaidExpenseAndOtherAssetsDisclosureTextBlock_documentation_en-US" xlink:label="lab_gemi_PrepaidExpenseAndOtherAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Prepaid Expense And Other Assets Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_PrepaidExpenseAndOtherAssetsDisclosureTextBlock" xlink:href="gemi-20260930.xsd#gemi_PrepaidExpenseAndOtherAssetsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_PrepaidExpenseAndOtherAssetsDisclosureTextBlock" xlink:to="lab_gemi_PrepaidExpenseAndOtherAssetsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerTextBlock_01a015a8-8b08-73bb-ad32-e5957e4920a9_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerTextBlock_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromContractWithCustomerTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_01a015a8-8b08-77a8-9691-a85903640061_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common stock in exchange for crypto assets</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CashPledgedAsCollateralCurrent_01a015a8-8a6b-76a0-b4e3-e3eb6d121ecf_terseLabel_en-US" xlink:label="lab_gemi_CashPledgedAsCollateralCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash collateral pledged</link:label>
    <link:label id="lab_gemi_CashPledgedAsCollateralCurrent_label_en-US" xlink:label="lab_gemi_CashPledgedAsCollateralCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Pledged As Collateral, Current</link:label>
    <link:label id="lab_gemi_CashPledgedAsCollateralCurrent_documentation_en-US" xlink:label="lab_gemi_CashPledgedAsCollateralCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cash, Pledged As Collateral, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CashPledgedAsCollateralCurrent" xlink:href="gemi-20260930.xsd#gemi_CashPledgedAsCollateralCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CashPledgedAsCollateralCurrent" xlink:to="lab_gemi_CashPledgedAsCollateralCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable_01a015a8-8b8d-79c8-8eb4-9a0fa8c5c7da_terseLabel_en-US" xlink:label="lab_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Values Derivatives, Balance Sheet Location, by Derivative Contract Type [Table]</link:label>
    <link:label id="lab_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable_label_en-US" xlink:label="lab_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Values Derivatives, Balance Sheet Location, by Derivative Contract Type [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable" xlink:to="lab_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrepaidExpenseCurrent_01a015a8-8b08-7d09-86ff-b9b0fa6888b5_terseLabel_en-US" xlink:label="lab_us-gaap_PrepaidExpenseCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepaid expenses</link:label>
    <link:label id="lab_us-gaap_PrepaidExpenseCurrent_label_en-US" xlink:label="lab_us-gaap_PrepaidExpenseCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepaid Expense, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidExpenseCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrepaidExpenseCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrepaidExpenseCurrent" xlink:to="lab_us-gaap_PrepaidExpenseCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_GainLossOnChangeInFairValueOfRelatedPartyDebt_01a015a8-8a6b-7c53-9fbd-8dd9b6179ccd_terseLabel_en-US" xlink:label="lab_gemi_GainLossOnChangeInFairValueOfRelatedPartyDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value on related party loans</link:label>
    <link:label id="lab_gemi_GainLossOnChangeInFairValueOfRelatedPartyDebt_01a015a8-8a6b-7aa3-817e-f7c15a61416a_negatedTerseLabel_en-US" xlink:label="lab_gemi_GainLossOnChangeInFairValueOfRelatedPartyDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value on related party loans</link:label>
    <link:label id="lab_gemi_GainLossOnChangeInFairValueOfRelatedPartyDebt_label_en-US" xlink:label="lab_gemi_GainLossOnChangeInFairValueOfRelatedPartyDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) On Change In Fair Value Of Related Party Debt</link:label>
    <link:label id="lab_gemi_GainLossOnChangeInFairValueOfRelatedPartyDebt_documentation_en-US" xlink:label="lab_gemi_GainLossOnChangeInFairValueOfRelatedPartyDebt" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gain (Loss) On Change In Fair Value Of Related Party Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_GainLossOnChangeInFairValueOfRelatedPartyDebt" xlink:href="gemi-20260930.xsd#gemi_GainLossOnChangeInFairValueOfRelatedPartyDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_GainLossOnChangeInFairValueOfRelatedPartyDebt" xlink:to="lab_gemi_GainLossOnChangeInFairValueOfRelatedPartyDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice_01a015a8-8b8d-74a9-944a-ca888ce85b8d_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forfeited (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Forfeitures in Period, Weighted Average Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_InterestExpenseRelatedPartyDebt_01a015a8-8b08-739c-ab7d-ef8850afe5a5_negatedTerseLabel_en-US" xlink:label="lab_gemi_InterestExpenseRelatedPartyDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Interest expense on related party loans</link:label>
    <link:label id="lab_gemi_InterestExpenseRelatedPartyDebt_label_en-US" xlink:label="lab_gemi_InterestExpenseRelatedPartyDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Related Party Debt</link:label>
    <link:label id="lab_gemi_InterestExpenseRelatedPartyDebt_documentation_en-US" xlink:label="lab_gemi_InterestExpenseRelatedPartyDebt" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Expense, Debt, Related Party Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_InterestExpenseRelatedPartyDebt" xlink:href="gemi-20260930.xsd#gemi_InterestExpenseRelatedPartyDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_InterestExpenseRelatedPartyDebt" xlink:to="lab_gemi_InterestExpenseRelatedPartyDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_01a015a8-8b08-71bf-bc6a-21ee451edeb8_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other investing activities, net</link:label>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_label_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment for (Proceeds from) Other Investing Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsForProceedsFromOtherInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:to="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_01a015a8-8a6b-7bdf-bb48-9a4136757740_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average discount rate</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Weighted Average Discount Rate, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:to="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_A3000ETHFebruary72025Member_01a015a8-8b08-7e31-a856-4848dda3f84c_terseLabel_en-US" xlink:label="lab_gemi_A3000ETHFebruary72025Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">3,000 ETH, February 7, 2025</link:label>
    <link:label id="lab_gemi_A3000ETHFebruary72025Member_label_en-US" xlink:label="lab_gemi_A3000ETHFebruary72025Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">3,000 ETH, February 7, 2025 [Member]</link:label>
    <link:label id="lab_gemi_A3000ETHFebruary72025Member_documentation_en-US" xlink:label="lab_gemi_A3000ETHFebruary72025Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">3,000 ETH, February 7, 2025</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_A3000ETHFebruary72025Member" xlink:href="gemi-20260930.xsd#gemi_A3000ETHFebruary72025Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_A3000ETHFebruary72025Member" xlink:to="lab_gemi_A3000ETHFebruary72025Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonvestedRestrictedStockSharesActivityTableTextBlock_01a015a8-8b8d-7443-9454-e8b80e92d92e_terseLabel_en-US" xlink:label="lab_us-gaap_NonvestedRestrictedStockSharesActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Restricted Stock Award Activity</link:label>
    <link:label id="lab_us-gaap_NonvestedRestrictedStockSharesActivityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_NonvestedRestrictedStockSharesActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonvested Restricted Stock Shares Activity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonvestedRestrictedStockSharesActivityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonvestedRestrictedStockSharesActivityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonvestedRestrictedStockSharesActivityTableTextBlock" xlink:to="lab_us-gaap_NonvestedRestrictedStockSharesActivityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_FundingDebtIncludingAccruedInterestCurrent_01a015a8-8b08-74a8-a756-e2e894c0edc5_terseLabel_en-US" xlink:label="lab_gemi_FundingDebtIncludingAccruedInterestCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Funding debt</link:label>
    <link:label id="lab_gemi_FundingDebtIncludingAccruedInterestCurrent_label_en-US" xlink:label="lab_gemi_FundingDebtIncludingAccruedInterestCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Funding Debt, Including Accrued Interest, Current</link:label>
    <link:label id="lab_gemi_FundingDebtIncludingAccruedInterestCurrent_documentation_en-US" xlink:label="lab_gemi_FundingDebtIncludingAccruedInterestCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Funding Debt, Including Accrued Interest, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_FundingDebtIncludingAccruedInterestCurrent" xlink:href="gemi-20260930.xsd#gemi_FundingDebtIncludingAccruedInterestCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_FundingDebtIncludingAccruedInterestCurrent" xlink:to="lab_gemi_FundingDebtIncludingAccruedInterestCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_01a015a8-8b08-7cd3-bfac-78ffd201c49b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseCostTableTextBlock_01a015a8-8b08-7f79-9f96-cd95b5e3951e_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseCostTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Components of Lease Expense and Other Information</link:label>
    <link:label id="lab_us-gaap_LeaseCostTableTextBlock_label_en-US" xlink:label="lab_us-gaap_LeaseCostTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease, Cost [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseCostTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LeaseCostTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseCostTableTextBlock" xlink:to="lab_us-gaap_LeaseCostTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssetsCurrent_01a015a8-8b8d-7e4e-aadc-342eff8034b6_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_OtherAssetsCurrent_label_en-US" xlink:label="lab_us-gaap_OtherAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAssetsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsCurrent" xlink:to="lab_us-gaap_OtherAssetsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllTradingArrangementsMember_terseLabel_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Trading Arrangements</link:label>
    <link:label id="lab_ecd_AllTradingArrangementsMember_label_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Trading Arrangements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllTradingArrangementsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllTradingArrangementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllTradingArrangementsMember" xlink:to="lab_ecd_AllTradingArrangementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_LesseeOperatingLeaseLeaseNotYetCommencedMonthlyRent_01a1c837-8daf-74fb-85ad-2b2ac6a86cad_terseLabel_en-US" xlink:label="lab_gemi_LesseeOperatingLeaseLeaseNotYetCommencedMonthlyRent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, lease not yet commenced, monthly rent</link:label>
    <link:label id="lab_gemi_LesseeOperatingLeaseLeaseNotYetCommencedMonthlyRent_label_en-US" xlink:label="lab_gemi_LesseeOperatingLeaseLeaseNotYetCommencedMonthlyRent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Lease Not Yet Commenced, Monthly Rent</link:label>
    <link:label id="lab_gemi_LesseeOperatingLeaseLeaseNotYetCommencedMonthlyRent_documentation_en-US" xlink:label="lab_gemi_LesseeOperatingLeaseLeaseNotYetCommencedMonthlyRent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Lease Not Yet Commenced, Monthly Rent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_LesseeOperatingLeaseLeaseNotYetCommencedMonthlyRent" xlink:href="gemi-20260930.xsd#gemi_LesseeOperatingLeaseLeaseNotYetCommencedMonthlyRent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_LesseeOperatingLeaseLeaseNotYetCommencedMonthlyRent" xlink:to="lab_gemi_LesseeOperatingLeaseLeaseNotYetCommencedMonthlyRent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_01a015a8-8b08-7d2b-b11a-49c2e21441db_periodStartLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_01a015a8-8b08-7b81-8b9e-422629aedb2f_periodEndLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_label_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OtherPerfMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OtherPerfMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OtherPerfMeasureAmt" xlink:to="lab_ecd_OtherPerfMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMnpiCnsdrdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:to="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_DebtTermsDomain_01a015a8-8b8d-73f4-95ad-d6de7ed8df26_terseLabel_en-US" xlink:label="lab_gemi_DebtTermsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Terms [Domain]</link:label>
    <link:label id="lab_gemi_DebtTermsDomain_label_en-US" xlink:label="lab_gemi_DebtTermsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Terms [Domain]</link:label>
    <link:label id="lab_gemi_DebtTermsDomain_documentation_en-US" xlink:label="lab_gemi_DebtTermsDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Terms [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_DebtTermsDomain" xlink:href="gemi-20260930.xsd#gemi_DebtTermsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_DebtTermsDomain" xlink:to="lab_gemi_DebtTermsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ThirdPartyDebtDenominatedInCryptoAssetRepaid_01a015a8-8b08-7fe8-9046-ea54a92859a3_terseLabel_en-US" xlink:label="lab_gemi_ThirdPartyDebtDenominatedInCryptoAssetRepaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repayment of third party loan interest denominated in crypto</link:label>
    <link:label id="lab_gemi_ThirdPartyDebtDenominatedInCryptoAssetRepaid_label_en-US" xlink:label="lab_gemi_ThirdPartyDebtDenominatedInCryptoAssetRepaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Third Party Debt, Denominated In Crypto Asset, Repaid</link:label>
    <link:label id="lab_gemi_ThirdPartyDebtDenominatedInCryptoAssetRepaid_documentation_en-US" xlink:label="lab_gemi_ThirdPartyDebtDenominatedInCryptoAssetRepaid" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Third Party Debt, Denominated In Crypto Asset, Repaid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ThirdPartyDebtDenominatedInCryptoAssetRepaid" xlink:href="gemi-20260930.xsd#gemi_ThirdPartyDebtDenominatedInCryptoAssetRepaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ThirdPartyDebtDenominatedInCryptoAssetRepaid" xlink:to="lab_gemi_ThirdPartyDebtDenominatedInCryptoAssetRepaid" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_01a015a8-8b8d-7379-b134-e37d7fd8f549_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CurrentFiscalYearEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CurrentFiscalYearEndDate" xlink:to="lab_dei_CurrentFiscalYearEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoAvgTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:to="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLineItems_01a015a8-8a6b-773a-b61c-2fb71d081ce0_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativeLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLineItems" xlink:to="lab_us-gaap_DerivativeLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount_01a1c83a-972b-705b-8625-a2a497d11e7a_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Base rent</link:label>
    <link:label id="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount_label_en-US" xlink:label="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecorded Unconditional Purchase Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:to="lab_us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestructuringReserveRollForward_01a015a8-8a6b-79b9-a989-82724c3d6673_terseLabel_en-US" xlink:label="lab_us-gaap_RestructuringReserveRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restructuring Reserve [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_RestructuringReserveRollForward_label_en-US" xlink:label="lab_us-gaap_RestructuringReserveRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restructuring Reserve [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestructuringReserveRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestructuringReserveRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestructuringReserveRollForward" xlink:to="lab_us-gaap_RestructuringReserveRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year</link:label>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:to="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFileNumber_01a015a8-8b08-7bfe-a5af-069ddbcff905_terseLabel_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:label id="lab_dei_EntityFileNumber_label_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFileNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFileNumber" xlink:to="lab_dei_EntityFileNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_01a015a8-8b8d-755f-b3aa-628e25d99e10_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common stock upon settlement of stock awards, net of shares withheld</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Issued, Value, Share-Based Payment Arrangement, after Forfeiture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_01a015a8-8b8d-7f5a-ac0c-9b9e31c8724d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Stock Option Activity</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option, Activity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CommonUnitsMember_01a015a8-8b08-7cad-9af0-4e2de0efc954_terseLabel_en-US" xlink:label="lab_gemi_CommonUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Units</link:label>
    <link:label id="lab_gemi_CommonUnitsMember_label_en-US" xlink:label="lab_gemi_CommonUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Units [Member]</link:label>
    <link:label id="lab_gemi_CommonUnitsMember_documentation_en-US" xlink:label="lab_gemi_CommonUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CommonUnitsMember" xlink:href="gemi-20260930.xsd#gemi_CommonUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CommonUnitsMember" xlink:to="lab_gemi_CommonUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward_01a015a8-8b8d-780c-ba00-ba43722f1588_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-Average Exercise Price</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Exercise Price [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour_01a015a8-8a6b-7ed6-b117-e18080aa43f0_terseLabel_en-US" xlink:label="lab_gemi_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_gemi_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour_label_en-US" xlink:label="lab_gemi_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, To Be Paid, After Year Four</link:label>
    <link:label id="lab_gemi_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour_documentation_en-US" xlink:label="lab_gemi_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, To Be Paid, After Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:href="gemi-20260930.xsd#gemi_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:to="lab_gemi_LesseeOperatingLeaseLiabilityToBePaidAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RecoveryOfErrCompDisclosureLineItems_label_en-US" xlink:label="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Erroneously Awarded Compensation Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RecoveryOfErrCompDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:to="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureAxis_terseLabel_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measure:</link:label>
    <link:label id="lab_ecd_MeasureAxis_label_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MeasureAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureAxis" xlink:to="lab_ecd_MeasureAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_RestrictedCashAndCashEquivalentsFairValueDisclosure_01a015a8-8b08-782a-a9c3-67fae73d76f4_terseLabel_en-US" xlink:label="lab_gemi_RestrictedCashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash equivalents:</link:label>
    <link:label id="lab_gemi_RestrictedCashAndCashEquivalentsFairValueDisclosure_01a015a8-8b08-714d-99c4-40d98d01499d_verboseLabel_en-US" xlink:label="lab_gemi_RestrictedCashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash and cash equivalents</link:label>
    <link:label id="lab_gemi_RestrictedCashAndCashEquivalentsFairValueDisclosure_label_en-US" xlink:label="lab_gemi_RestrictedCashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash And Cash Equivalents, Fair Value Disclosure</link:label>
    <link:label id="lab_gemi_RestrictedCashAndCashEquivalentsFairValueDisclosure_documentation_en-US" xlink:label="lab_gemi_RestrictedCashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restricted Cash And Cash Equivalents, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_RestrictedCashAndCashEquivalentsFairValueDisclosure" xlink:href="gemi-20260930.xsd#gemi_RestrictedCashAndCashEquivalentsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_RestrictedCashAndCashEquivalentsFairValueDisclosure" xlink:to="lab_gemi_RestrictedCashAndCashEquivalentsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CryptoAssetAddition_01a015a8-8a6b-7051-8d61-17438d527bda_terseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetAddition" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Addition of crypto assets</link:label>
    <link:label id="lab_us-gaap_CryptoAssetAddition_label_en-US" xlink:label="lab_us-gaap_CryptoAssetAddition" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Addition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetAddition" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetAddition"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CryptoAssetAddition" xlink:to="lab_us-gaap_CryptoAssetAddition" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_RecognitionCriteriaMetMember_01a015a8-8a6b-73ac-a57b-c8d355d4cfc9_terseLabel_en-US" xlink:label="lab_gemi_RecognitionCriteriaMetMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recognition Criteria, Met</link:label>
    <link:label id="lab_gemi_RecognitionCriteriaMetMember_label_en-US" xlink:label="lab_gemi_RecognitionCriteriaMetMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recognition Criteria, Met [Member]</link:label>
    <link:label id="lab_gemi_RecognitionCriteriaMetMember_documentation_en-US" xlink:label="lab_gemi_RecognitionCriteriaMetMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Recognition Criteria, Met</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_RecognitionCriteriaMetMember" xlink:href="gemi-20260930.xsd#gemi_RecognitionCriteriaMetMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_RecognitionCriteriaMetMember" xlink:to="lab_gemi_RecognitionCriteriaMetMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_01a015a8-8b8d-7aed-a7d7-10547efa5b61_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury stock (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_01a015a8-8b8d-7aa9-bc66-7a2bdf413c72_negatedPeriodStartLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2009/role/negatedPeriodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning treasury balance (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_01a015a8-8b8d-7201-93ea-342faf99d340_negatedPeriodEndLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2009/role/negatedPeriodEndLabel" xlink:type="resource" xml:lang="en-US">Ending treasury balance (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonShares" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockCommonShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonShares" xlink:to="lab_us-gaap_TreasuryStockCommonShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_01a015a8-8b08-7375-bcbc-bd2f71da49d1_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyMember_01a015a8-8b08-79bf-a0f0-4947c16001eb_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party</link:label>
    <link:label id="lab_us-gaap_RelatedPartyMember_label_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyMember" xlink:to="lab_us-gaap_RelatedPartyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_01a015a8-8b8d-75c0-9298-45b6245a0e02_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash paid during the period for income taxes, net of refunds</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_label_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Paid, after Refund Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxesPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxesPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxesPaidNet" xlink:to="lab_us-gaap_IncomeTaxesPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConversionOfStockByUniqueDescriptionAxis_01a015a8-8b08-73a5-91f3-92f00a2d3f72_terseLabel_en-US" xlink:label="lab_us-gaap_ConversionOfStockByUniqueDescriptionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Conversion Description [Axis]</link:label>
    <link:label id="lab_us-gaap_ConversionOfStockByUniqueDescriptionAxis_label_en-US" xlink:label="lab_us-gaap_ConversionOfStockByUniqueDescriptionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Conversion Description [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConversionOfStockByUniqueDescriptionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConversionOfStockByUniqueDescriptionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConversionOfStockByUniqueDescriptionAxis" xlink:to="lab_us-gaap_ConversionOfStockByUniqueDescriptionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonClassAMember_01a015a8-8b8d-7a2f-b9c5-2205f2e2a142_terseLabel_en-US" xlink:label="lab_us-gaap_CommonClassAMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Class A</link:label>
    <link:label id="lab_us-gaap_CommonClassAMember_label_en-US" xlink:label="lab_us-gaap_CommonClassAMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Class A [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassAMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassAMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonClassAMember" xlink:to="lab_us-gaap_CommonClassAMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_01a015a8-8b8d-7e54-9002-73babdeab99d_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_label_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityInteractiveDataCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitySmallBusiness_01a015a8-8b08-7d4c-a252-04f30b53864f_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitySmallBusiness" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntitySmallBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitySmallBusiness" xlink:to="lab_dei_EntitySmallBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_01a015a8-8b08-70e0-852c-0f341514806e_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Comprehensive loss</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation_01a0f315-dbe6-76d1-8168-2b180a675634_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Shares withheld for employee tax withholdings (in shares)</link:label>
    <link:label id="lab_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Shares Withheld for Tax Withholding Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" xlink:to="lab_us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_01a015a8-8b08-73da-987d-71deb54661a1_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Line Items]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_terseLabel_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value</link:label>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_label_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MnpiDiscTimedForCompValFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:to="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_01a015a8-8a6b-7c74-90aa-9fb05db6a59e_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other non-current assets, net</link:label>
    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_01a015a8-8a6b-7d41-8f24-e2897df9a172_totalLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total other non-current assets</link:label>
    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_label_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAssetsNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsNoncurrent" xlink:to="lab_us-gaap_OtherAssetsNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentType_01a015a8-8a6b-7d7d-8570-8329a1d057c7_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:label id="lab_dei_DocumentType_label_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentType"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentType" xlink:to="lab_dei_DocumentType" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_OtherRevenueAndCorporateInterestMember_01a015a8-8a6b-7985-a642-ac8c65ef2685_terseLabel_en-US" xlink:label="lab_gemi_OtherRevenueAndCorporateInterestMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other revenue</link:label>
    <link:label id="lab_gemi_OtherRevenueAndCorporateInterestMember_label_en-US" xlink:label="lab_gemi_OtherRevenueAndCorporateInterestMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Revenue And Corporate Interest [Member]</link:label>
    <link:label id="lab_gemi_OtherRevenueAndCorporateInterestMember_documentation_en-US" xlink:label="lab_gemi_OtherRevenueAndCorporateInterestMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Revenue And Interest Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_OtherRevenueAndCorporateInterestMember" xlink:href="gemi-20260930.xsd#gemi_OtherRevenueAndCorporateInterestMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_OtherRevenueAndCorporateInterestMember" xlink:to="lab_gemi_OtherRevenueAndCorporateInterestMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_01a015a8-8b8d-77b5-9d29-3d6a58ee69fc_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CryptoAssetActivityLineItems_01a015a8-8b08-7dc7-b51a-76eaeb583d1b_terseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetActivityLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto Asset, Activity [Line Items]</link:label>
    <link:label id="lab_us-gaap_CryptoAssetActivityLineItems_label_en-US" xlink:label="lab_us-gaap_CryptoAssetActivityLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Activity [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetActivityLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetActivityLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CryptoAssetActivityLineItems" xlink:to="lab_us-gaap_CryptoAssetActivityLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_01a015a8-8b08-7152-96b7-e22bc008a7c3_terseLabel_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Significant Accounting Policies</link:label>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_label_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Significant Accounting Policies [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SignificantAccountingPoliciesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1_01a015a8-8b08-7b92-9e02-7c15ba1ad8d7_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate intrinsic value of options exercisable</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercisable, Intrinsic Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1" xlink:to="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueImpairmentsLossAndDownwardPriceAdjustmentAnnualAmount_01a015a8-8a6b-7b0d-9233-dc9afe908b0d_negatedTerseLabel_en-US" xlink:label="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueImpairmentsLossAndDownwardPriceAdjustmentAnnualAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Impairments and downward adjustments</link:label>
    <link:label id="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueImpairmentsLossAndDownwardPriceAdjustmentAnnualAmount_label_en-US" xlink:label="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueImpairmentsLossAndDownwardPriceAdjustmentAnnualAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities Without Readily Determinable Fair Value, Impairments Loss And Downward Price Adjustment, Annual Amount</link:label>
    <link:label id="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueImpairmentsLossAndDownwardPriceAdjustmentAnnualAmount_documentation_en-US" xlink:label="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueImpairmentsLossAndDownwardPriceAdjustmentAnnualAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Securities Without Readily Determinable Fair Value, Impairments Loss And Downward Price Adjustment, Annual Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueImpairmentsLossAndDownwardPriceAdjustmentAnnualAmount" xlink:href="gemi-20260930.xsd#gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueImpairmentsLossAndDownwardPriceAdjustmentAnnualAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueImpairmentsLossAndDownwardPriceAdjustmentAnnualAmount" xlink:to="lab_gemi_EquitySecuritiesWithoutReadilyDeterminableFairValueImpairmentsLossAndDownwardPriceAdjustmentAnnualAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventLineItems_01a015a8-8a6b-7cc3-bb31-d0989142eb9f_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Line Items]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventLineItems_label_en-US" xlink:label="lab_us-gaap_SubsequentEventLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventLineItems" xlink:to="lab_us-gaap_SubsequentEventLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CreditCardReceivablesPledgedMember_01a015a8-8b8e-789a-8b0a-6d4704c7b415_terseLabel_en-US" xlink:label="lab_gemi_CreditCardReceivablesPledgedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit card receivables, pledged</link:label>
    <link:label id="lab_gemi_CreditCardReceivablesPledgedMember_label_en-US" xlink:label="lab_gemi_CreditCardReceivablesPledgedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Card Receivables, Pledged [Member]</link:label>
    <link:label id="lab_gemi_CreditCardReceivablesPledgedMember_documentation_en-US" xlink:label="lab_gemi_CreditCardReceivablesPledgedMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Credit Card Receivables, Pledged</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CreditCardReceivablesPledgedMember" xlink:href="gemi-20260930.xsd#gemi_CreditCardReceivablesPledgedMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CreditCardReceivablesPledgedMember" xlink:to="lab_gemi_CreditCardReceivablesPledgedMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_01a015a8-8b08-782c-bd70-9672a48813fb_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LocalPhoneNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LocalPhoneNumber" xlink:to="lab_dei_LocalPhoneNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_01a015a8-8b8d-7d09-a1ed-2788e0b05fa7_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net loss before income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_01a015a8-8b08-7d5d-ba24-c9f5fdd403ff_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and contingencies (Note 22)</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingencies" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingencies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingencies" xlink:to="lab_us-gaap_CommitmentsAndContingencies" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_01a015a8-8b08-73d4-9f7b-2ecbcca42a8f_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:to="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_RepurchaseAgreementsCollateralRate_01a015a8-8a6b-7c75-809e-49e36d998db6_terseLabel_en-US" xlink:label="lab_gemi_RepurchaseAgreementsCollateralRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral rate</link:label>
    <link:label id="lab_gemi_RepurchaseAgreementsCollateralRate_01a015a8-8a6b-7585-a6a5-45f2d90b15b0_verboseLabel_en-US" xlink:label="lab_gemi_RepurchaseAgreementsCollateralRate" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Collateral Rate</link:label>
    <link:label id="lab_gemi_RepurchaseAgreementsCollateralRate_label_en-US" xlink:label="lab_gemi_RepurchaseAgreementsCollateralRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repurchase Agreements, Collateral Rate</link:label>
    <link:label id="lab_gemi_RepurchaseAgreementsCollateralRate_documentation_en-US" xlink:label="lab_gemi_RepurchaseAgreementsCollateralRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Repurchase Agreements, Collateral Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_RepurchaseAgreementsCollateralRate" xlink:href="gemi-20260930.xsd#gemi_RepurchaseAgreementsCollateralRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_RepurchaseAgreementsCollateralRate" xlink:to="lab_gemi_RepurchaseAgreementsCollateralRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentGross_01a015a8-8b08-76a3-bc18-a81dba321b03_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Software, property and equipment, gross</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentGross_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment, before Accumulated Depreciation, Depletion, and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentGross" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentGross" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote</link:label>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_label_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChangedPeerGroupFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:to="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_01a015a8-8b08-705b-903a-556102d3defa_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_terseLabel_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Executive Category:</link:label>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_label_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Executive Category [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ExecutiveCategoryAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ExecutiveCategoryAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ExecutiveCategoryAxis" xlink:to="lab_ecd_ExecutiveCategoryAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis_01a015a8-8b08-7d14-96ad-40ba821c78fe_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivable Type [Axis]</link:label>
    <link:label id="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis_label_en-US" xlink:label="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivable Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:to="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_CounterpartyNameAxis_01a015a8-8a6b-7dd2-90df-23a8e95c5ed9_terseLabel_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Axis]</link:label>
    <link:label id="lab_srt_CounterpartyNameAxis_label_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CounterpartyNameAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_CounterpartyNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_CounterpartyNameAxis" xlink:to="lab_srt_CounterpartyNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_01a015a8-8a6b-7d7a-a79c-c88118074cf9_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities and Stockholders&#8217; Equity</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_AccountsReceivableNettingFairValueDisclosure_01a015a8-8a6b-7fa3-aab6-78498560137c_terseLabel_en-US" xlink:label="lab_gemi_AccountsReceivableNettingFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable, net:</link:label>
    <link:label id="lab_gemi_AccountsReceivableNettingFairValueDisclosure_label_en-US" xlink:label="lab_gemi_AccountsReceivableNettingFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Netting, Fair Value Disclosure</link:label>
    <link:label id="lab_gemi_AccountsReceivableNettingFairValueDisclosure_documentation_en-US" xlink:label="lab_gemi_AccountsReceivableNettingFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Netting, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_AccountsReceivableNettingFairValueDisclosure" xlink:href="gemi-20260930.xsd#gemi_AccountsReceivableNettingFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_AccountsReceivableNettingFairValueDisclosure" xlink:to="lab_gemi_AccountsReceivableNettingFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoAvgCompActuallyPaidAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:to="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_01a015a8-8a6b-732e-a124-0f1432e82efd_terseLabel_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental disclosure of cash flow information</link:label>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_label_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supplemental Cash Flow Information [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SupplementalCashFlowInformationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:to="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoName_terseLabel_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:label id="lab_ecd_PeoName_label_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoName" xlink:to="lab_ecd_PeoName" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoAssetPurchaseNumberOfUnits_01a015a8-8a6b-7b2e-a2b4-2a6b625698fb_terseLabel_en-US" xlink:label="lab_gemi_CryptoAssetPurchaseNumberOfUnits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of crypto assets acquired (in units)</link:label>
    <link:label id="lab_gemi_CryptoAssetPurchaseNumberOfUnits_label_en-US" xlink:label="lab_gemi_CryptoAssetPurchaseNumberOfUnits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Purchase, Number Of Units</link:label>
    <link:label id="lab_gemi_CryptoAssetPurchaseNumberOfUnits_documentation_en-US" xlink:label="lab_gemi_CryptoAssetPurchaseNumberOfUnits" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Asset, Purchase, Number Of Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoAssetPurchaseNumberOfUnits" xlink:href="gemi-20260930.xsd#gemi_CryptoAssetPurchaseNumberOfUnits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoAssetPurchaseNumberOfUnits" xlink:to="lab_gemi_CryptoAssetPurchaseNumberOfUnits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseholdImprovementsMember_01a015a8-8b8d-7d48-a8cc-4950861803d0_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseholdImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leasehold improvements</link:label>
    <link:label id="lab_us-gaap_LeaseholdImprovementsMember_label_en-US" xlink:label="lab_us-gaap_LeaseholdImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leasehold Improvements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseholdImprovementsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LeaseholdImprovementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseholdImprovementsMember" xlink:to="lab_us-gaap_LeaseholdImprovementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_SecuredDebtFinancingFacility_01a015a8-8b8d-7264-836f-acb57fea1f93_terseLabel_en-US" xlink:label="lab_gemi_SecuredDebtFinancingFacility" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Secured debt, financing facility</link:label>
    <link:label id="lab_gemi_SecuredDebtFinancingFacility_label_en-US" xlink:label="lab_gemi_SecuredDebtFinancingFacility" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secured Debt, Financing Facility</link:label>
    <link:label id="lab_gemi_SecuredDebtFinancingFacility_documentation_en-US" xlink:label="lab_gemi_SecuredDebtFinancingFacility" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Secured Debt, Financing Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_SecuredDebtFinancingFacility" xlink:href="gemi-20260930.xsd#gemi_SecuredDebtFinancingFacility"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_SecuredDebtFinancingFacility" xlink:to="lab_gemi_SecuredDebtFinancingFacility" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_01a015a8-8b8d-7164-b77c-7da8a4fc54ac_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Lived Asset, Class [Axis]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Asset, Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method</link:label>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_label_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_StkPrcOrTsrEstimationMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:to="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_01a015a8-8b8d-7fb8-b466-003307189a4a_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_label_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityTaxIdentificationNumber" xlink:to="lab_dei_EntityTaxIdentificationNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward_01a015a8-8b08-7374-b8d0-62a684a43eb6_terseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward_label_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward" xlink:to="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialAssetNotPastDueMember_01a015a8-8b8e-794b-a796-96995fda2ca7_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialAssetNotPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current</link:label>
    <link:label id="lab_us-gaap_FinancialAssetNotPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancialAssetNotPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Not Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialAssetNotPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancialAssetNotPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialAssetNotPastDueMember" xlink:to="lab_us-gaap_FinancialAssetNotPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ProceedsFromCreditCardReceivables_01a015a8-8b08-7fe5-be89-8bc59e3e1780_terseLabel_en-US" xlink:label="lab_gemi_ProceedsFromCreditCardReceivables" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from repayments of credit card receivables</link:label>
    <link:label id="lab_gemi_ProceedsFromCreditCardReceivables_label_en-US" xlink:label="lab_gemi_ProceedsFromCreditCardReceivables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From Credit Card Receivables</link:label>
    <link:label id="lab_gemi_ProceedsFromCreditCardReceivables_documentation_en-US" xlink:label="lab_gemi_ProceedsFromCreditCardReceivables" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds From Credit Card Receivables</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ProceedsFromCreditCardReceivables" xlink:href="gemi-20260930.xsd#gemi_ProceedsFromCreditCardReceivables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ProceedsFromCreditCardReceivables" xlink:to="lab_gemi_ProceedsFromCreditCardReceivables" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense_01a015a8-8b8d-7541-9efd-7c6aa8a069c3_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income tax benefit (expense) related to stock-based compensation expense</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Expense, Tax Benefit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense" xlink:to="lab_us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice_01a015a8-8a6b-75c9-90a9-d4be6587c4e5_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercised (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Exercises in Period, Weighted Average Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueRecognitionPolicyTextBlock_01a015a8-8b08-7767-b7e4-71ae03af2977_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue recognition</link:label>
    <link:label id="lab_us-gaap_RevenueRecognitionPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueRecognitionPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:to="lab_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAccruedLiabilitiesCurrent_01a015a8-8a6b-72e9-99e8-947b8c5fce69_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses</link:label>
    <link:label id="lab_us-gaap_OtherAccruedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Accrued Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAccruedLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:to="lab_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_01a015a8-8b08-742d-9f64-3e5bac7430b0_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityIncorporationStateCountryCode" xlink:to="lab_dei_EntityIncorporationStateCountryCode" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined</link:label>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_label_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtErrCompNotYetDeterminedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:to="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases_01a015a8-8a6b-7187-84cc-88690cd16836_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additions</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Purchases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_terseLabel_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement</link:label>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_label_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MtrlTermsOfTrdArrTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:to="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalentsAtCarryingValue_01a015a8-8b08-7449-9a5d-41c38aba3a41_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalentsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash and Cash Equivalent, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashAndCashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestrictedCashAndCashEquivalentsAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCashAndCashEquivalentsAtCarryingValue" xlink:to="lab_us-gaap_RestrictedCashAndCashEquivalentsAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year</link:label>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:to="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestructuringAndRelatedCostNumberOfPositionsEliminated_01a015a8-8b08-7caa-9079-d1b12c80542b_terseLabel_en-US" xlink:label="lab_us-gaap_RestructuringAndRelatedCostNumberOfPositionsEliminated" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of employees included in reduction in force</link:label>
    <link:label id="lab_us-gaap_RestructuringAndRelatedCostNumberOfPositionsEliminated_label_en-US" xlink:label="lab_us-gaap_RestructuringAndRelatedCostNumberOfPositionsEliminated" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restructuring and Related Cost, Number of Positions Eliminated</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestructuringAndRelatedCostNumberOfPositionsEliminated" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestructuringAndRelatedCostNumberOfPositionsEliminated"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestructuringAndRelatedCostNumberOfPositionsEliminated" xlink:to="lab_us-gaap_RestructuringAndRelatedCostNumberOfPositionsEliminated" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_01a015a8-8b8d-73e6-ba3a-c1a4cea3cd73_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentAxis" xlink:to="lab_us-gaap_DebtInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTable_01a015a8-8b08-7cbf-984f-705c5f367a4f_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTable_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTable" xlink:to="lab_us-gaap_SubsequentEventTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensation_01a015a8-8b08-70ec-8f52-b20647cd6088_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock-based compensation</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Noncash Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensation" xlink:to="lab_us-gaap_ShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LaborAndRelatedExpense_01a015a8-8b8d-7475-ab9d-233b9540d6fb_terseLabel_en-US" xlink:label="lab_us-gaap_LaborAndRelatedExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Salaries and compensation</link:label>
    <link:label id="lab_us-gaap_LaborAndRelatedExpense_label_en-US" xlink:label="lab_us-gaap_LaborAndRelatedExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Labor and Related Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LaborAndRelatedExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LaborAndRelatedExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LaborAndRelatedExpense" xlink:to="lab_us-gaap_LaborAndRelatedExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseCost_01a015a8-8b8d-754c-9ac2-6894bdb1b9b5_totalLabel_en-US" xlink:label="lab_us-gaap_LeaseCost" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total lease expense</link:label>
    <link:label id="lab_us-gaap_LeaseCost_label_en-US" xlink:label="lab_us-gaap_LeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseCost" xlink:to="lab_us-gaap_LeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_A35000ETHMarch12023Member_01a015a8-8b08-7632-8d7f-8848a3834494_terseLabel_en-US" xlink:label="lab_gemi_A35000ETHMarch12023Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">35,000 ETH March 1, 2023</link:label>
    <link:label id="lab_gemi_A35000ETHMarch12023Member_label_en-US" xlink:label="lab_gemi_A35000ETHMarch12023Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">35,000 ETH March 1, 2023 [Member]</link:label>
    <link:label id="lab_gemi_A35000ETHMarch12023Member_documentation_en-US" xlink:label="lab_gemi_A35000ETHMarch12023Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">35,000 ETH March 1, 2023</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_A35000ETHMarch12023Member" xlink:href="gemi-20260930.xsd#gemi_A35000ETHMarch12023Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_A35000ETHMarch12023Member" xlink:to="lab_gemi_A35000ETHMarch12023Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_01a015a8-8a6b-7dba-bb97-be31e9484550_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion in connection with IPO (in shares) (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Conversion of Convertible Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockMember_01a015a8-8a6b-72e9-95d4-7cee9caab668_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ESPP</link:label>
    <link:label id="lab_us-gaap_EmployeeStockMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Employee Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockMember" xlink:to="lab_us-gaap_EmployeeStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_01a015a8-8b8d-752d-83cf-c9f219df7931_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasic" xlink:to="lab_us-gaap_EarningsPerShareBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_01a015a8-8a6b-788c-87ad-6184f45da249_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MeasurementInputTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputTypeAxis" xlink:to="lab_us-gaap_MeasurementInputTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsCurrent_01a015a8-8b08-7429-8e40-cf74f2c8bd03_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total current assets</link:label>
    <link:label id="lab_us-gaap_AssetsCurrent_label_en-US" xlink:label="lab_us-gaap_AssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsCurrent" xlink:to="lab_us-gaap_AssetsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoAssetFuturesAssetMember_01a015a8-8b08-7c31-ac7f-ea035c23824a_terseLabel_en-US" xlink:label="lab_gemi_CryptoAssetFuturesAssetMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto asset futures</link:label>
    <link:label id="lab_gemi_CryptoAssetFuturesAssetMember_label_en-US" xlink:label="lab_gemi_CryptoAssetFuturesAssetMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset Futures, Asset [Member]</link:label>
    <link:label id="lab_gemi_CryptoAssetFuturesAssetMember_documentation_en-US" xlink:label="lab_gemi_CryptoAssetFuturesAssetMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Asset Futures, Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoAssetFuturesAssetMember" xlink:href="gemi-20260930.xsd#gemi_CryptoAssetFuturesAssetMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoAssetFuturesAssetMember" xlink:to="lab_gemi_CryptoAssetFuturesAssetMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDueToRelatedParties_01a015a8-8b08-7237-8c8e-847a8f4df661_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDueToRelatedParties" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Payables due to related parties</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInDueToRelatedParties_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInDueToRelatedParties" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Due to Related Parties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInDueToRelatedParties" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInDueToRelatedParties"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInDueToRelatedParties" xlink:to="lab_us-gaap_IncreaseDecreaseInDueToRelatedParties" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingArrLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingArrLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Arrangements [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingArrLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTradingArrLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingArrLineItems" xlink:to="lab_ecd_InsiderTradingArrLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShortTermLeaseCost_01a015a8-8b8d-7141-b56c-af82dbc5669a_terseLabel_en-US" xlink:label="lab_us-gaap_ShortTermLeaseCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Short-term lease expense</link:label>
    <link:label id="lab_us-gaap_ShortTermLeaseCost_label_en-US" xlink:label="lab_us-gaap_ShortTermLeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Term Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortTermLeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShortTermLeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortTermLeaseCost" xlink:to="lab_us-gaap_ShortTermLeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_01a015a8-8b8d-7444-8d43-a9d58617fdfb_verboseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable, net</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_01a015a8-8b8d-736f-8e27-46d04a4fe06a_totalLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total accounts receivable, net of allowance</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, after Allowance for Credit Loss, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableNetCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableNetCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableNetCurrent" xlink:to="lab_us-gaap_AccountsReceivableNetCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_OtherAssetsInTransitOverTheCounterTradesCurrent_01a1c851-ade8-7307-89d7-4eb7d502d0aa_terseLabel_en-US" xlink:label="lab_gemi_OtherAssetsInTransitOverTheCounterTradesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">In transit OTC trades</link:label>
    <link:label id="lab_gemi_OtherAssetsInTransitOverTheCounterTradesCurrent_label_en-US" xlink:label="lab_gemi_OtherAssetsInTransitOverTheCounterTradesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets, In-Transit Over The Counter Trades, Current</link:label>
    <link:label id="lab_gemi_OtherAssetsInTransitOverTheCounterTradesCurrent_documentation_en-US" xlink:label="lab_gemi_OtherAssetsInTransitOverTheCounterTradesCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Assets, In-Transit Over The Counter Trades, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_OtherAssetsInTransitOverTheCounterTradesCurrent" xlink:href="gemi-20260930.xsd#gemi_OtherAssetsInTransitOverTheCounterTradesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_OtherAssetsInTransitOverTheCounterTradesCurrent" xlink:to="lab_gemi_OtherAssetsInTransitOverTheCounterTradesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_TechnologyExpense_01a015a8-8a6b-7a79-8ae6-bc5bdb39379d_terseLabel_en-US" xlink:label="lab_gemi_TechnologyExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Technology</link:label>
    <link:label id="lab_gemi_TechnologyExpense_01a015a8-8a6b-7feb-87ab-c01f6153309f_verboseLabel_en-US" xlink:label="lab_gemi_TechnologyExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Technology expense</link:label>
    <link:label id="lab_gemi_TechnologyExpense_label_en-US" xlink:label="lab_gemi_TechnologyExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Technology Expense</link:label>
    <link:label id="lab_gemi_TechnologyExpense_documentation_en-US" xlink:label="lab_gemi_TechnologyExpense" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Technology Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_TechnologyExpense" xlink:href="gemi-20260930.xsd#gemi_TechnologyExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_TechnologyExpense" xlink:to="lab_gemi_TechnologyExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfShortTermDebtTextBlock_01a015a8-8b8d-7ab8-bcdb-642c1ab13f4b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShortTermDebtTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Crypto Asset Loans</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShortTermDebtTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShortTermDebtTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Short-Term Debt [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShortTermDebtTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfShortTermDebtTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfShortTermDebtTextBlock" xlink:to="lab_us-gaap_ScheduleOfShortTermDebtTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_AssembledWorkforceMember_01a015a8-8b8d-79f7-a44d-a53a23b001ec_verboseLabel_en-US" xlink:label="lab_gemi_AssembledWorkforceMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Assembled workforce</link:label>
    <link:label id="lab_gemi_AssembledWorkforceMember_label_en-US" xlink:label="lab_gemi_AssembledWorkforceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assembled Workforce [Member]</link:label>
    <link:label id="lab_gemi_AssembledWorkforceMember_documentation_en-US" xlink:label="lab_gemi_AssembledWorkforceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Assembled Workforce</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_AssembledWorkforceMember" xlink:href="gemi-20260930.xsd#gemi_AssembledWorkforceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_AssembledWorkforceMember" xlink:to="lab_gemi_AssembledWorkforceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdvertisingCostsPolicyTextBlock_01a015a8-8b08-77aa-9ffc-6d846301a2fa_terseLabel_en-US" xlink:label="lab_us-gaap_AdvertisingCostsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sales and marketing</link:label>
    <link:label id="lab_us-gaap_AdvertisingCostsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_AdvertisingCostsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Advertising Cost [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdvertisingCostsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdvertisingCostsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdvertisingCostsPolicyTextBlock" xlink:to="lab_us-gaap_AdvertisingCostsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_ConversionOfRelatedPartyDebtToConvertibleDebt_01a015a8-8b08-7665-b593-930e98652c88_terseLabel_en-US" xlink:label="lab_gemi_ConversionOfRelatedPartyDebtToConvertibleDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion of related party loans into related party convertible notes</link:label>
    <link:label id="lab_gemi_ConversionOfRelatedPartyDebtToConvertibleDebt_label_en-US" xlink:label="lab_gemi_ConversionOfRelatedPartyDebtToConvertibleDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Conversion Of Related Party Debt To Convertible Debt</link:label>
    <link:label id="lab_gemi_ConversionOfRelatedPartyDebtToConvertibleDebt_documentation_en-US" xlink:label="lab_gemi_ConversionOfRelatedPartyDebtToConvertibleDebt" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Conversion Of Related Party Debt To Convertible Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_ConversionOfRelatedPartyDebtToConvertibleDebt" xlink:href="gemi-20260930.xsd#gemi_ConversionOfRelatedPartyDebtToConvertibleDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_ConversionOfRelatedPartyDebtToConvertibleDebt" xlink:to="lab_gemi_ConversionOfRelatedPartyDebtToConvertibleDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_LoansReceivableCurrent_01a015a8-8b8d-71e3-a50c-d2095fbfff8b_terseLabel_en-US" xlink:label="lab_gemi_LoansReceivableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan receivables</link:label>
    <link:label id="lab_gemi_LoansReceivableCurrent_label_en-US" xlink:label="lab_gemi_LoansReceivableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Receivable, Current</link:label>
    <link:label id="lab_gemi_LoansReceivableCurrent_documentation_en-US" xlink:label="lab_gemi_LoansReceivableCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loans Receivable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_LoansReceivableCurrent" xlink:href="gemi-20260930.xsd#gemi_LoansReceivableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_LoansReceivableCurrent" xlink:to="lab_gemi_LoansReceivableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate_01a015a8-8b08-7d05-bb94-7a62137a097b_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Volatility</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Volatility Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_01a015a8-8a6b-76dd-8bd5-06e1f00ca4aa_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosureItemAmountsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:to="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CoverAbstract_label_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CoverAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CoverAbstract" xlink:to="lab_dei_CoverAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription_01a015a8-8b8d-75c4-93ff-53350ad9b5a6_terseLabel_en-US" xlink:label="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassification</link:label>
    <link:label id="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription_label_en-US" xlink:label="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification, Comparability Adjustment [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PriorPeriodReclassificationAdjustmentDescription"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:to="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CustodialFundsDueToCustomerFairValueDisclosure_01a015a8-8a6b-7fbe-aedb-3c91520c839b_terseLabel_en-US" xlink:label="lab_gemi_CustodialFundsDueToCustomerFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Custodial funds due to customers</link:label>
    <link:label id="lab_gemi_CustodialFundsDueToCustomerFairValueDisclosure_label_en-US" xlink:label="lab_gemi_CustodialFundsDueToCustomerFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Custodial Funds Due To Customer, Fair Value Disclosure</link:label>
    <link:label id="lab_gemi_CustodialFundsDueToCustomerFairValueDisclosure_documentation_en-US" xlink:label="lab_gemi_CustodialFundsDueToCustomerFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Custodial Funds Due To Customer, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CustodialFundsDueToCustomerFairValueDisclosure" xlink:href="gemi-20260930.xsd#gemi_CustodialFundsDueToCustomerFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CustodialFundsDueToCustomerFairValueDisclosure" xlink:to="lab_gemi_CustodialFundsDueToCustomerFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt_01a015a8-8b08-7fda-829c-576a56c21e78_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from third party loan, net of discount</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Other Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfOtherLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivables1To29DaysPastDueMember_01a015a8-8b08-7784-ba66-7e3bbd4023f7_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivables1To29DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Asset, 1 to 29 Days Past Due</link:label>
    <link:label id="lab_us-gaap_FinancingReceivables1To29DaysPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancingReceivables1To29DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, 1 to 29 Days Past Due [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivables1To29DaysPastDueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivables1To29DaysPastDueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivables1To29DaysPastDueMember" xlink:to="lab_us-gaap_FinancingReceivables1To29DaysPastDueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueUpwardPriceAdjustmentAnnualAmount_01a015a8-8b08-711e-bbd6-8451ac880942_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueUpwardPriceAdjustmentAnnualAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Upward adjustments</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueUpwardPriceAdjustmentAnnualAmount_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueUpwardPriceAdjustmentAnnualAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities without Readily Determinable Fair Value, Upward Price Adjustment, Annual Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueUpwardPriceAdjustmentAnnualAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueUpwardPriceAdjustmentAnnualAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueUpwardPriceAdjustmentAnnualAmount" xlink:to="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueUpwardPriceAdjustmentAnnualAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansPayableMember_01a015a8-8a6b-7ac6-800e-980c0a4cab88_terseLabel_en-US" xlink:label="lab_us-gaap_LoansPayableMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term Loans</link:label>
    <link:label id="lab_us-gaap_LoansPayableMember_label_en-US" xlink:label="lab_us-gaap_LoansPayableMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Payable [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansPayableMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LoansPayableMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansPayableMember" xlink:to="lab_us-gaap_LoansPayableMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueTableTextBlock_01a015a8-8b8d-7bbc-8854-68ba65809efc_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Carrying Value of Strategic Investments Accounted for under the Measurement Alternative</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueTableTextBlock_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities without Readily Determinable Fair Value [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueTableTextBlock" xlink:to="lab_us-gaap_EquitySecuritiesWithoutReadilyDeterminableFairValueTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsMember" xlink:to="lab_ecd_EqtyAwrdsAdjsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CryptoAssetTextBlock_01a015a8-8b08-7149-9542-8829c1dbb5fc_terseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto Assets Held</link:label>
    <link:label id="lab_us-gaap_CryptoAssetTextBlock_label_en-US" xlink:label="lab_us-gaap_CryptoAssetTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CryptoAssetTextBlock" xlink:to="lab_us-gaap_CryptoAssetTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_01a015a8-8b8d-7e72-9e6c-cebf7da1b857_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:to="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_01a015a8-8b08-723b-888b-3f26610bdba7_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOtherOperatingLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherOperatingLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_01a015a8-8b08-7b0c-bd83-93614b0f6113_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Accounts Receivable, Net of Allowance</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accounts, Notes, Loans and Financing Receivable [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_InterestExpenseThirdPartyDebt_01a015a8-8b8d-7f42-b2e8-26c515bd9f2e_negatedTerseLabel_en-US" xlink:label="lab_gemi_InterestExpenseThirdPartyDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Interest expense on third party loans</link:label>
    <link:label id="lab_gemi_InterestExpenseThirdPartyDebt_label_en-US" xlink:label="lab_gemi_InterestExpenseThirdPartyDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Third Party Debt</link:label>
    <link:label id="lab_gemi_InterestExpenseThirdPartyDebt_documentation_en-US" xlink:label="lab_gemi_InterestExpenseThirdPartyDebt" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Expense, Debt, Third Party Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_InterestExpenseThirdPartyDebt" xlink:href="gemi-20260930.xsd#gemi_InterestExpenseThirdPartyDebt"/>
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    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_01a015a8-8b08-7415-9847-0f310e026dad_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income (expense), net</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Nonoperating Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherNonoperatingIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:to="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock_01a015a8-8a6b-7765-9c8e-39eb6cdd3e98_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Accrued Expenses and Other Current Liabilities</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accounts Payable and Accrued Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAccountsPayableAndAccruedLiabilitiesTableTextBlock"/>
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    <link:label id="lab_gemi_CryptoAssetCollateralPayableFairValueDisclosure_01a015a8-8b8d-77db-b0b7-e665151d89f6_terseLabel_en-US" xlink:label="lab_gemi_CryptoAssetCollateralPayableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto asset collateral payable</link:label>
    <link:label id="lab_gemi_CryptoAssetCollateralPayableFairValueDisclosure_label_en-US" xlink:label="lab_gemi_CryptoAssetCollateralPayableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset Collateral Payable, Fair Value Disclosure</link:label>
    <link:label id="lab_gemi_CryptoAssetCollateralPayableFairValueDisclosure_documentation_en-US" xlink:label="lab_gemi_CryptoAssetCollateralPayableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Asset Collateral Payable, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoAssetCollateralPayableFairValueDisclosure" xlink:href="gemi-20260930.xsd#gemi_CryptoAssetCollateralPayableFairValueDisclosure"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_01a015a8-8b8d-73a4-a3c8-77af83082800_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Forfeited (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Forfeited in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromDisposalCryptoAsset_01a015a8-8b08-7f32-a836-f4433f988cc6_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromDisposalCryptoAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from disposal of crypto assets</link:label>
    <link:label id="lab_us-gaap_ProceedsFromDisposalCryptoAsset_label_en-US" xlink:label="lab_us-gaap_ProceedsFromDisposalCryptoAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Disposal, Crypto Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromDisposalCryptoAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromDisposalCryptoAsset"/>
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    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_01a015a8-8b08-775e-9d48-1339020e55f0_terseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General and administrative expense</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_01a015a8-8b08-7183-b135-e9cf01b72d8e_verboseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">General and administrative</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:to="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities_01a015a8-8b8d-73a9-8821-9d70f5c5e44e_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion in connection with IPO</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Conversion of Convertible Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_01a015a8-8a6b-7839-ab61-5e98c07f79f7_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesAuthorized" xlink:to="lab_us-gaap_PreferredStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativesFairValueLineItems_01a015a8-8a6b-7a86-adbf-8cc30a426b9c_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativesFairValueLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivatives, Fair Value [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativesFairValueLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativesFairValueLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivatives, Fair Value [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativesFairValueLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativesFairValueLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativesFairValueLineItems" xlink:to="lab_us-gaap_DerivativesFairValueLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CustomerCustodialFundsCurrent_01a015a8-8b8d-7117-90ed-7498498b484f_terseLabel_en-US" xlink:label="lab_gemi_CustomerCustodialFundsCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer custodial funds</link:label>
    <link:label id="lab_gemi_CustomerCustodialFundsCurrent_01a015a8-8b8d-75c8-af2b-4fe7123c7bf5_verboseLabel_en-US" xlink:label="lab_gemi_CustomerCustodialFundsCurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Customer custodial funds</link:label>
    <link:label id="lab_gemi_CustomerCustodialFundsCurrent_label_en-US" xlink:label="lab_gemi_CustomerCustodialFundsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer Custodial Funds, Current</link:label>
    <link:label id="lab_gemi_CustomerCustodialFundsCurrent_documentation_en-US" xlink:label="lab_gemi_CustomerCustodialFundsCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Customer Custodial Funds, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CustomerCustodialFundsCurrent" xlink:href="gemi-20260930.xsd#gemi_CustomerCustodialFundsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CustomerCustodialFundsCurrent" xlink:to="lab_gemi_CustomerCustodialFundsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockDomain_01a015a8-8b08-713c-b7d2-468e113db4da_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockDomain" xlink:to="lab_us-gaap_ClassOfStockDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:to="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OciMarketRiskBenefitInstrumentSpecificCreditRiskGainLossAfterAdjustmentsAndTaxParent_01a015a8-8b8d-7fa9-ac1f-159b4dd470d5_terseLabel_en-US" xlink:label="lab_us-gaap_OciMarketRiskBenefitInstrumentSpecificCreditRiskGainLossAfterAdjustmentsAndTaxParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value attributable to instrument-specific credit risk</link:label>
    <link:label id="lab_us-gaap_OciMarketRiskBenefitInstrumentSpecificCreditRiskGainLossAfterAdjustmentsAndTaxParent_label_en-US" xlink:label="lab_us-gaap_OciMarketRiskBenefitInstrumentSpecificCreditRiskGainLossAfterAdjustmentsAndTaxParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OCI, Market Risk Benefit, Instrument-Specific Credit Risk, Gain (Loss), after Adjustments and Tax, Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OciMarketRiskBenefitInstrumentSpecificCreditRiskGainLossAfterAdjustmentsAndTaxParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OciMarketRiskBenefitInstrumentSpecificCreditRiskGainLossAfterAdjustmentsAndTaxParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OciMarketRiskBenefitInstrumentSpecificCreditRiskGainLossAfterAdjustmentsAndTaxParent" xlink:to="lab_us-gaap_OciMarketRiskBenefitInstrumentSpecificCreditRiskGainLossAfterAdjustmentsAndTaxParent" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_TransactionProcessingExpense_01a015a8-8b8d-7d38-b43b-f3571cc23618_terseLabel_en-US" xlink:label="lab_gemi_TransactionProcessingExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transaction processing</link:label>
    <link:label id="lab_gemi_TransactionProcessingExpense_label_en-US" xlink:label="lab_gemi_TransactionProcessingExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transaction Processing Expense</link:label>
    <link:label id="lab_gemi_TransactionProcessingExpense_documentation_en-US" xlink:label="lab_gemi_TransactionProcessingExpense" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Transaction Processing Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_TransactionProcessingExpense" xlink:href="gemi-20260930.xsd#gemi_TransactionProcessingExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_TransactionProcessingExpense" xlink:to="lab_gemi_TransactionProcessingExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_terseLabel_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Available</link:label>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_label_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Securities Aggregate Available Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrSecuritiesAggAvailAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:to="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CryptoAssetsConsiderationPaidOnTransaction_01a015a8-8b8d-7bdc-a4b7-2d0927a4c8a0_terseLabel_en-US" xlink:label="lab_gemi_CryptoAssetsConsiderationPaidOnTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Crypto assets , consideration paid on transaction</link:label>
    <link:label id="lab_gemi_CryptoAssetsConsiderationPaidOnTransaction_label_en-US" xlink:label="lab_gemi_CryptoAssetsConsiderationPaidOnTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Assets , Consideration Paid On Transaction</link:label>
    <link:label id="lab_gemi_CryptoAssetsConsiderationPaidOnTransaction_documentation_en-US" xlink:label="lab_gemi_CryptoAssetsConsiderationPaidOnTransaction" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Crypto Assets , Consideration Paid On Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CryptoAssetsConsiderationPaidOnTransaction" xlink:href="gemi-20260930.xsd#gemi_CryptoAssetsConsiderationPaidOnTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CryptoAssetsConsiderationPaidOnTransaction" xlink:to="lab_gemi_CryptoAssetsConsiderationPaidOnTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CryptoAssetDisposition_01a015a8-8b8d-72cb-936e-46a5cf0a9cb5_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetDisposition" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Disposition of crypto assets</link:label>
    <link:label id="lab_us-gaap_CryptoAssetDisposition_01a015a8-8b8d-7b80-88bd-e961c4328f5a_terseLabel_en-US" xlink:label="lab_us-gaap_CryptoAssetDisposition" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposition of crypto assets</link:label>
    <link:label id="lab_us-gaap_CryptoAssetDisposition_label_en-US" xlink:label="lab_us-gaap_CryptoAssetDisposition" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Crypto Asset, Disposition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CryptoAssetDisposition" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CryptoAssetDisposition"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CryptoAssetDisposition" xlink:to="lab_us-gaap_CryptoAssetDisposition" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_01a015a8-8a6b-795f-b14b-241b19603f98_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:to="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableCurrent_01a015a8-8a6b-7837-9708-8ec67f538659_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable</link:label>
    <link:label id="lab_us-gaap_AccountsPayableCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsPayableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableCurrent" xlink:to="lab_us-gaap_AccountsPayableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNoncashIncomeExpense_01a015a8-8b08-7a95-b54c-91cf8506be40_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other operating activities, net</link:label>
    <link:label id="lab_us-gaap_OtherNoncashIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Noncash Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNoncashIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherNoncashIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNoncashIncomeExpense" xlink:to="lab_us-gaap_OtherNoncashIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_A2500ETHMarch282025Member_01a015a8-8b08-7a39-9a81-280926a3e711_terseLabel_en-US" xlink:label="lab_gemi_A2500ETHMarch282025Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2,500 ETH, March 28, 2025</link:label>
    <link:label id="lab_gemi_A2500ETHMarch282025Member_label_en-US" xlink:label="lab_gemi_A2500ETHMarch282025Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2,500 ETH, March 28, 2025 [Member]</link:label>
    <link:label id="lab_gemi_A2500ETHMarch282025Member_documentation_en-US" xlink:label="lab_gemi_A2500ETHMarch282025Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2,500 ETH, March 28, 2025</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_A2500ETHMarch282025Member" xlink:href="gemi-20260930.xsd#gemi_A2500ETHMarch282025Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_A2500ETHMarch282025Member" xlink:to="lab_gemi_A2500ETHMarch282025Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTable_terseLabel_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure</link:label>
    <link:label id="lab_ecd_PvpTable_label_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PvpTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTable" xlink:to="lab_ecd_PvpTable" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CommissionsPayableCurrent_01a015a8-8b08-7a65-ba1a-a2f7578c6258_terseLabel_en-US" xlink:label="lab_gemi_CommissionsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commissions to NFT artists payable</link:label>
    <link:label id="lab_gemi_CommissionsPayableCurrent_label_en-US" xlink:label="lab_gemi_CommissionsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commissions Payable, Current</link:label>
    <link:label id="lab_gemi_CommissionsPayableCurrent_documentation_en-US" xlink:label="lab_gemi_CommissionsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commissions Payable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CommissionsPayableCurrent" xlink:href="gemi-20260930.xsd#gemi_CommissionsPayableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CommissionsPayableCurrent" xlink:to="lab_gemi_CommissionsPayableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFilerCategory_01a015a8-8b08-72a6-87e4-81e8d62ac01b_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:label id="lab_dei_EntityFilerCategory_label_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFilerCategory"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFilerCategory" xlink:to="lab_dei_EntityFilerCategory" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToDevelopSoftware_01a015a8-8a6b-7f66-92b0-cff5186e7d7e_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToDevelopSoftware" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Capitalization of internally developed software costs</link:label>
    <link:label id="lab_us-gaap_PaymentsToDevelopSoftware_label_en-US" xlink:label="lab_us-gaap_PaymentsToDevelopSoftware" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Develop Software</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToDevelopSoftware" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToDevelopSoftware"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToDevelopSoftware" xlink:to="lab_us-gaap_PaymentsToDevelopSoftware" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableAllowanceForCreditLossExcludingAccruedInterestNoncurrent_01a015a8-8b8e-7ca7-bfd9-946605a8ac56_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableAllowanceForCreditLossExcludingAccruedInterestNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Excludes from disputed receivables</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableAllowanceForCreditLossExcludingAccruedInterestNoncurrent_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableAllowanceForCreditLossExcludingAccruedInterestNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss, Excluding Accrued Interest, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableAllowanceForCreditLossExcludingAccruedInterestNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableAllowanceForCreditLossExcludingAccruedInterestNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableAllowanceForCreditLossExcludingAccruedInterestNoncurrent" xlink:to="lab_us-gaap_AccountsReceivableAllowanceForCreditLossExcludingAccruedInterestNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdvertisingExpense_01a015a8-8b08-7e05-9751-0e3cdfadd12b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AdvertisingExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Advertising expense</link:label>
    <link:label id="lab_us-gaap_AdvertisingExpense_label_en-US" xlink:label="lab_us-gaap_AdvertisingExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Advertising Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdvertisingExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdvertisingExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdvertisingExpense" xlink:to="lab_us-gaap_AdvertisingExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod_01a015a8-8a6b-749b-adea-b17b7272036a_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of Common Units due to equity awards granted, net of forfeitures (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Net of Forfeitures</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_01a015a8-8a6b-72d9-9b13-21c50261859c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Realized and unrealized gain on derivatives</link:label>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_label_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Derivative Instruments, Net, Pretax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainLossOnDerivativeInstrumentsNetPretax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:to="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrentAbstract_01a015a8-8b8d-7fe8-ac07-e84d2b2c1a13_terseLabel_en-US" xlink:label="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepaid expenses and other current assets</link:label>
    <link:label id="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepaid Expense and Other Assets, Current [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrepaidExpenseAndOtherAssetsCurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrepaidExpenseAndOtherAssetsCurrentAbstract" xlink:to="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList_01a015a8-8b8d-7ab8-b59f-51f1bf2e25e0_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Current, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Current, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis_01a015a8-8a6b-7864-a2ef-dd47fdc7ee94_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Asset, Aging [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Aging [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivablesPeriodPastDueAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:to="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_OtherRevenueMember_01a015a8-8b08-7c6e-a05f-437e48e85b50_terseLabel_en-US" xlink:label="lab_gemi_OtherRevenueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other revenue</link:label>
    <link:label id="lab_gemi_OtherRevenueMember_label_en-US" xlink:label="lab_gemi_OtherRevenueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Revenue [Member]</link:label>
    <link:label id="lab_gemi_OtherRevenueMember_documentation_en-US" xlink:label="lab_gemi_OtherRevenueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_OtherRevenueMember" xlink:href="gemi-20260930.xsd#gemi_OtherRevenueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_OtherRevenueMember" xlink:to="lab_gemi_OtherRevenueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine2_01a015a8-8a6b-7c4d-a4b3-12a49ad52292_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line Two</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine2_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine2" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine2" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine2"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine2" xlink:to="lab_dei_EntityAddressAddressLine2" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_CommonStockConvertibleConversionRatio_01a015a8-8b08-70f3-ad6a-acddac3bfa14_terseLabel_en-US" xlink:label="lab_gemi_CommonStockConvertibleConversionRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock conversion ratio</link:label>
    <link:label id="lab_gemi_CommonStockConvertibleConversionRatio_label_en-US" xlink:label="lab_gemi_CommonStockConvertibleConversionRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Convertible, Conversion Ratio</link:label>
    <link:label id="lab_gemi_CommonStockConvertibleConversionRatio_documentation_en-US" xlink:label="lab_gemi_CommonStockConvertibleConversionRatio" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock, Convertible, Conversion Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_CommonStockConvertibleConversionRatio" xlink:href="gemi-20260930.xsd#gemi_CommonStockConvertibleConversionRatio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_CommonStockConvertibleConversionRatio" xlink:to="lab_gemi_CommonStockConvertibleConversionRatio" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsCurrentAbstract_01a015a8-8a6b-7da6-8c58-cff3782f60b7_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current assets:</link:label>
    <link:label id="lab_us-gaap_AssetsCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Current [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsCurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsCurrentAbstract" xlink:to="lab_us-gaap_AssetsCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilities_01a015a8-8b8d-7e3e-aa1f-0ea449e9131b_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative liability</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_01a015a8-8b8d-76e0-a8cb-ee998eee7567_negatedLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilities" xlink:to="lab_us-gaap_DerivativeLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_01a015a8-8b08-79ff-8302-b2fdad55140b_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_NovemberGalaxyLoanMember_01a1cd63-74a3-7c5d-9b1c-3393152c2f81_terseLabel_en-US" xlink:label="lab_gemi_NovemberGalaxyLoanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">November Galaxy Loan</link:label>
    <link:label id="lab_gemi_NovemberGalaxyLoanMember_label_en-US" xlink:label="lab_gemi_NovemberGalaxyLoanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">November Galaxy Loan [Member]</link:label>
    <link:label id="lab_gemi_NovemberGalaxyLoanMember_documentation_en-US" xlink:label="lab_gemi_NovemberGalaxyLoanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">November Galaxy Loan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_NovemberGalaxyLoanMember" xlink:href="gemi-20260930.xsd#gemi_NovemberGalaxyLoanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_NovemberGalaxyLoanMember" xlink:to="lab_gemi_NovemberGalaxyLoanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue_01a015a8-8b08-7814-9467-ab24a0ba69ec_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vested (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Vested in Period, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_01a015a8-8b08-7273-9b95-602d1a38473d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Income tax benefit (provision)</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_01a015a8-8b8d-7e68-a6a9-b662605cccad_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation</link:label>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConsolidationPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:to="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_TransactionRevenueMember_01a015a8-8a6b-7119-8fdf-640ded28fa1c_terseLabel_en-US" xlink:label="lab_gemi_TransactionRevenueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transaction revenue</link:label>
    <link:label id="lab_gemi_TransactionRevenueMember_label_en-US" xlink:label="lab_gemi_TransactionRevenueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transaction Revenue [Member]</link:label>
    <link:label id="lab_gemi_TransactionRevenueMember_documentation_en-US" xlink:label="lab_gemi_TransactionRevenueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Transaction Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_TransactionRevenueMember" xlink:href="gemi-20260930.xsd#gemi_TransactionRevenueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_gemi_TransactionRevenueMember" xlink:to="lab_gemi_TransactionRevenueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_gemi_WindDownWorkforceReductionLeaseRelatedActionsAndExecutiveDeparturesMember_01a015a8-8b8d-74a4-8f1c-0d797b0f5b84_terseLabel_en-US" xlink:label="lab_gemi_WindDownWorkforceReductionLeaseRelatedActionsAndExecutiveDeparturesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restructuring</link:label>
    <link:label id="lab_gemi_WindDownWorkforceReductionLeaseRelatedActionsAndExecutiveDeparturesMember_label_en-US" xlink:label="lab_gemi_WindDownWorkforceReductionLeaseRelatedActionsAndExecutiveDeparturesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Wind-Down, Workforce Reduction, Lease-Related Actions And Executive Departures [Member]</link:label>
    <link:label id="lab_gemi_WindDownWorkforceReductionLeaseRelatedActionsAndExecutiveDeparturesMember_documentation_en-US" xlink:label="lab_gemi_WindDownWorkforceReductionLeaseRelatedActionsAndExecutiveDeparturesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Wind-Down, Workforce Reduction, Lease-Related Actions And Executive Departures</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_WindDownWorkforceReductionLeaseRelatedActionsAndExecutiveDeparturesMember" xlink:href="gemi-20260930.xsd#gemi_WindDownWorkforceReductionLeaseRelatedActionsAndExecutiveDeparturesMember"/>
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    <link:label id="lab_gemi_ReceivableCryptoAssetPledgedRealizedGainLossOperating_documentation_en-US" xlink:label="lab_gemi_ReceivableCryptoAssetPledgedRealizedGainLossOperating" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Receivable, Crypto Asset Pledged, Realized Gain (Loss), Operating</link:label>
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    <link:label id="lab_us-gaap_StatementTable_01a015a8-8b8d-7600-9eea-44da67fca022_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromIssuanceInitialPublicOffering_01a015a8-8b08-794b-95e1-5fdf4f84a6c7_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceInitialPublicOffering" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from issuance of common stock in connection with initial public offering, net of underwriting discounts and commissions and offering costs</link:label>
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    <link:label id="lab_gemi_FinancingAgreementsSecuritiesTransferredNominalValue_documentation_en-US" xlink:label="lab_gemi_FinancingAgreementsSecuritiesTransferredNominalValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Agreements, Securities Transferred, Nominal Value</link:label>
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    <link:label id="lab_us-gaap_InvestmentIncomeInterest_01a015a8-8b08-7ac3-9c64-8a70dd09740b_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest income</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeInterest_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income, Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentIncomeInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeInterest" xlink:to="lab_us-gaap_InvestmentIncomeInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtConversionConvertedInstrumentAmount1_01a015a8-8b08-7f90-9d9b-e918b9cf283f_terseLabel_en-US" xlink:label="lab_us-gaap_DebtConversionConvertedInstrumentAmount1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Conversion of related party loans and related party convertible notes to common stock in connection with initial public offering</link:label>
    <link:label id="lab_us-gaap_DebtConversionConvertedInstrumentAmount1_label_en-US" xlink:label="lab_us-gaap_DebtConversionConvertedInstrumentAmount1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Conversion, Converted Instrument, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtConversionConvertedInstrumentAmount1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtConversionConvertedInstrumentAmount1"/>
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    <link:label id="lab_gemi_WarehouseCreditAgreementMember_01a015a8-8b8d-7e09-9ef8-b23104e53ab3_terseLabel_en-US" xlink:label="lab_gemi_WarehouseCreditAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warehouse Credit Agreement</link:label>
    <link:label id="lab_gemi_WarehouseCreditAgreementMember_label_en-US" xlink:label="lab_gemi_WarehouseCreditAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warehouse Credit Agreement [Member]</link:label>
    <link:label id="lab_gemi_WarehouseCreditAgreementMember_documentation_en-US" xlink:label="lab_gemi_WarehouseCreditAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Warehouse Credit Agreement</link:label>
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    <link:label id="lab_us-gaap_StockCompensationPlanMember_01a015a8-8b08-754b-bfd0-02b808a8a1ad_terseLabel_en-US" xlink:label="lab_us-gaap_StockCompensationPlanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity awards</link:label>
    <link:label id="lab_us-gaap_StockCompensationPlanMember_label_en-US" xlink:label="lab_us-gaap_StockCompensationPlanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockCompensationPlanMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockCompensationPlanMember"/>
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    <link:label id="lab_gemi_SecuredDebtFinancingAgreements_01a015a8-8b8d-79dd-86af-4af85013486c_terseLabel_en-US" xlink:label="lab_gemi_SecuredDebtFinancingAgreements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principal Outstanding</link:label>
    <link:label id="lab_gemi_SecuredDebtFinancingAgreements_label_en-US" xlink:label="lab_gemi_SecuredDebtFinancingAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secured Debt, Financing Agreements</link:label>
    <link:label id="lab_gemi_SecuredDebtFinancingAgreements_documentation_en-US" xlink:label="lab_gemi_SecuredDebtFinancingAgreements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Secured Debt, Financing Agreements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_gemi_SecuredDebtFinancingAgreements" xlink:href="gemi-20260930.xsd#gemi_SecuredDebtFinancingAgreements"/>
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    <link:label id="lab_us-gaap_LossContingencyDamagesSoughtValue_01a015a8-8b8e-7d6e-9530-bb588ce1d093_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingencyDamagesSoughtValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amount to be paid</link:label>
    <link:label id="lab_us-gaap_LossContingencyDamagesSoughtValue_label_en-US" xlink:label="lab_us-gaap_LossContingencyDamagesSoughtValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency, Damages Sought, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingencyDamagesSoughtValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingencyDamagesSoughtValue"/>
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    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableRecoveries_01a015a8-8a6b-70ef-9309-7c5ae7a9256b_terseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableRecoveries" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recoveries and reversals of write-offs</link:label>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableRecoveries_label_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableRecoveries" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss, Recovery</link:label>
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