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<!--Created on: 3/31/2026 7:37:59 PM-->
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  <xsd:element name="TransferAssignOrSellSharesSharesPercentage" id="fgmc_TransferAssignOrSellSharesSharesPercentage" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" />
  <xsd:element name="RestrictionsOnTransferPeriodOfTimeAfterBusinessCombinationCompletion" id="fgmc_RestrictionsOnTransferPeriodOfTimeAfterBusinessCombinationCompletion" type="xbrli:durationItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" />
  <xsd:element name="TransferAssignOrSellSharesAfterCompletionOfInitialBusinessCombinationStockPriceTrigger" id="fgmc_TransferAssignOrSellSharesAfterCompletionOfInitialBusinessCombinationStockPriceTrigger" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" />
  <xsd:element name="TransferAssignOrSellSharesAfterCompletionOfInitialBusinessCombinationThresholdTradingDays" id="fgmc_TransferAssignOrSellSharesAfterCompletionOfInitialBusinessCombinationThresholdTradingDays" type="xbrli:integerItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" />
  <xsd:element name="TransferAssignOrSellSharesAfterCompletionOfInitialBusinessCombinationThresholdConsecutiveTradingDays" id="fgmc_TransferAssignOrSellSharesAfterCompletionOfInitialBusinessCombinationThresholdConsecutiveTradingDays" type="xbrli:integerItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" />
  <xsd:element name="PromissoryNotesMember" id="fgmc_PromissoryNotesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="true" />
  <xsd:element name="AdministrativeServicesAgreementMember" id="fgmc_AdministrativeServicesAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="true" />
  <xsd:element name="MonthlyFeesForServicesRendered" id="fgmc_MonthlyFeesForServicesRendered" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" xbrli:balance="debit" />
  <xsd:element name="UnitsMember" id="fgmc_UnitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="true" />
  <xsd:element name="CommitmentsAndContingenciesTable" id="fgmc_CommitmentsAndContingenciesTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" nillable="true" xbrli:periodType="duration" abstract="true" />
  <xsd:element name="CommitmentsAndContingenciesLineItems" id="fgmc_CommitmentsAndContingenciesLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="true" />
  <xsd:element name="OverAllotmentPeriod" id="fgmc_OverAllotmentPeriod" type="xbrli:durationItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" />
  <xsd:element name="NumberOfAdditionalUnitsToBePurchased" id="fgmc_NumberOfAdditionalUnitsToBePurchased" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="instant" abstract="false" />
  <xsd:element name="UnderwritingDiscountPaid" id="fgmc_UnderwritingDiscountPaid" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" xbrli:balance="credit" />
  <xsd:element name="PercentageOfDiscountToUnderwriterOnGrossProceedsFromOverAllotment" id="fgmc_PercentageOfDiscountToUnderwriterOnGrossProceedsFromOverAllotment" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" />
  <xsd:element name="UnitsIssuedDuringPeriodValueNewIssues" id="fgmc_UnitsIssuedDuringPeriodValueNewIssues" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" xbrli:balance="credit" />
  <xsd:element name="PaymentForAdvisoryServices" id="fgmc_PaymentForAdvisoryServices" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" xbrli:balance="credit" />
  <xsd:element name="UnitsIssuedDuringPeriodSharesIssuedForServices" id="fgmc_UnitsIssuedDuringPeriodSharesIssuedForServices" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" />
  <xsd:element name="NominalPricePerUnit" id="fgmc_NominalPricePerUnit" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" />
  <xsd:element name="SaleOfStockPricePerUnit" id="fgmc_SaleOfStockPricePerUnit" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" />
  <xsd:element name="NumberOfUnitsForfeited" id="fgmc_NumberOfUnitsForfeited" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" />
  <xsd:element name="PricePerUnitPlacedIntoTrustAccount" id="fgmc_PricePerUnitPlacedIntoTrustAccount" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" />
  <xsd:element name="StockIssuedDuringPeriodStockDividendValue" id="fgmc_StockIssuedDuringPeriodStockDividendValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" xbrli:balance="credit" />
  <xsd:element name="CommonStockSharesSubjectToPossibleRedemptionMember" id="fgmc_CommonStockSharesSubjectToPossibleRedemptionMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="true" />
  <xsd:element name="CommonStockSharesNotSubjectToPossibleRedemptionMember" id="fgmc_CommonStockSharesNotSubjectToPossibleRedemptionMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="true" />
  <xsd:element name="ProceedsFromIssuanceOfSharesToUnderwriter" id="fgmc_ProceedsFromIssuanceOfSharesToUnderwriter" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" xbrli:balance="debit" />
  <xsd:element name="CommonStockSharesSubjectToPossibleRedemptionPolicyTextBlock" id="fgmc_CommonStockSharesSubjectToPossibleRedemptionPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" />
  <xsd:element name="CashWithdrawnFromTrustAccount" id="fgmc_CashWithdrawnFromTrustAccount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" xbrli:balance="credit" />
  <xsd:element name="CommonStockSharesOutstandingBasic" id="fgmc_CommonStockSharesOutstandingBasic" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" />
  <xsd:element name="PercentageOfCommonStockBasic" id="fgmc_PercentageOfCommonStockBasic" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" />
  <xsd:element name="AccretionApplicableToRedeemableClassBasic" id="fgmc_AccretionApplicableToRedeemableClassBasic" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" xbrli:balance="credit" />
  <xsd:element name="CommonStockSharesOutstandingDiluted" id="fgmc_CommonStockSharesOutstandingDiluted" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" />
  <xsd:element name="PercentageOfCommonStockDiluted" id="fgmc_PercentageOfCommonStockDiluted" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" />
  <xsd:element name="AccretionApplicableToRedeemableClassDiluted" id="fgmc_AccretionApplicableToRedeemableClassDiluted" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" xbrli:balance="credit" />
  <xsd:element name="InitialPublicOfferingAbstract" id="fgmc_InitialPublicOfferingAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="true" />
  <xsd:element name="InitialPublicOfferingTextBlock" id="fgmc_InitialPublicOfferingTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" />
  <xsd:element name="InitialPublicOfferingTable" id="fgmc_InitialPublicOfferingTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" nillable="true" xbrli:periodType="duration" abstract="true" />
  <xsd:element name="InitialPublicOfferingLineItems" id="fgmc_InitialPublicOfferingLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="true" />
  <xsd:element name="PaymentsToAcquireInvestmentsInTrustAccount" id="fgmc_PaymentsToAcquireInvestmentsInTrustAccount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" xbrli:balance="credit" />
  <xsd:element name="PromissoryNotesIssuedOnOctober62023Member" id="fgmc_PromissoryNotesIssuedOnOctober62023Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="true" />
  <xsd:element name="PromissoryNotesIssuedOnJanuary302025Member" id="fgmc_PromissoryNotesIssuedOnJanuary302025Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="true" />
  <xsd:element name="PercentageOfAdditionalUnderwriterFeeForDeferment" id="fgmc_PercentageOfAdditionalUnderwriterFeeForDeferment" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" />
  <xsd:element name="PercentageOfRightToAllocateAdditionalUnderwriterFeeOtherFinancialInstitution" id="fgmc_PercentageOfRightToAllocateAdditionalUnderwriterFeeOtherFinancialInstitution" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" />
  <xsd:element name="PublicRightMember" id="fgmc_PublicRightMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="true" />
  <xsd:element name="NumberOfWarrantsIssued" id="fgmc_NumberOfWarrantsIssued" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" />
  <xsd:element name="ReclassificationsOfPermanentToTemporaryEquity" id="fgmc_ReclassificationsOfPermanentToTemporaryEquity" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" xbrli:balance="debit" />
  <xsd:element name="OfferingCosts" id="fgmc_OfferingCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" xbrli:balance="debit" />
  <xsd:element name="RepaymentsOfNotesPayablePrincipal" id="fgmc_RepaymentsOfNotesPayablePrincipal" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" xbrli:balance="credit" />
  <xsd:element name="RepaymentsOfNotesPayableInterest" id="fgmc_RepaymentsOfNotesPayableInterest" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" xbrli:balance="credit" />
  <xsd:element name="IncomeAllocatedByClassBasic" id="fgmc_IncomeAllocatedByClassBasic" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" xbrli:balance="credit" />
  <xsd:element name="AccretionAllocatedBasedOnOwnershipPercentageBasic" id="fgmc_AccretionAllocatedBasedOnOwnershipPercentageBasic" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" xbrli:balance="debit" />
  <xsd:element name="IncomeAllocatedByClassDiluted" id="fgmc_IncomeAllocatedByClassDiluted" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" xbrli:balance="credit" />
  <xsd:element name="AccretionAllocatedBasedOnOwnershipPercentageDiluted" id="fgmc_AccretionAllocatedBasedOnOwnershipPercentageDiluted" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" xbrli:balance="debit" />
  <xsd:element name="BoxablMember" id="fgmc_BoxablMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="true" />
  <xsd:element name="DeferredUnderwritingCommissionPayable" id="fgmc_DeferredUnderwritingCommissionPayable" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="instant" abstract="false" xbrli:balance="credit" />
  <xsd:element name="NonCashOfferingCost" id="fgmc_NonCashOfferingCost" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" xbrli:balance="debit" />
  <xsd:element name="CashWithdrawnFromTrustAccountToPayTaxLiability" id="fgmc_CashWithdrawnFromTrustAccountToPayTaxLiability" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" xbrli:balance="credit" />
  <xsd:element name="ReportingSegmentMember" id="fgmc_ReportingSegmentMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="true" />
  <xsd:element name="WarrantsAndRightInstrumentsPolicyPolicyTextBlock" id="fgmc_WarrantsAndRightInstrumentsPolicyPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="false" />
  <xsd:element name="SignificantAccountingPoliciesTable" id="fgmc_SignificantAccountingPoliciesTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" nillable="true" xbrli:periodType="duration" abstract="true" />
  <xsd:element name="SignificantAccountingPoliciesLineItem" id="fgmc_SignificantAccountingPoliciesLineItem" type="xbrli:stringItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="duration" abstract="true" />
  <xsd:element name="CapitalizedStartUpCosts" id="fgmc_CapitalizedStartUpCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" nillable="true" xbrli:periodType="instant" abstract="false" xbrli:balance="debit" />
</xsd:schema>
