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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock issued and outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Preference Shares Issued and Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred stock, shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MeasurementInputSharePriceMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Measurement Input, Share Price [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Unrecognized compensation expense</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisableNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Equity Instruments Other Than Options Exercisable Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisableNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Number of Warrants, Exercisable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Common stock, shares, issued</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PaymentOfOfferingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Payment of offering costs.</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of Options, Exercisable at June 30, 2026</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingSegmentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Segments [Member]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_GubraAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gubra Agreement [Member]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsOutstandingWeightedAverageRemainingContractualTerms_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Weighted- average remaining contractual term (in years), Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and Equipment, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfOutstandingStockMaximum_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Percentage of Outstanding Stock Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfOutstandingStockMaximum_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of outstanding stock maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">General and Administrative Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">External &#8211; general and administrative</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Statement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_SeriesBConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series B Convertible Preferred Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Forfeited in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Number of Warrants, Forfeited</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_SeriesCConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series C Convertible Preferred Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_OrdinarySharesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Ordinary Shares [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Earnings Per Share, Basic, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss per share, basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Period End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentInformationTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Information [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Expiration Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Share-based compensation expiration period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Purchases of property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Grants in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average exercise price per share, Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Common stock, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Stockholders' Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MeasurementInputExpectedDividendPaymentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Measurement Input, Expected Dividend Payment [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Right-of-Use Asset, after Accumulated Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance leased assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WarrantsAndRightsOutstandingMeasurementInput_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Warrants and Rights Outstanding, Measurement Input</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WarrantsAndRightsOutstandingMeasurementInput_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair value of warrants granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_NovoNordiskMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Novo Nordisk [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_NovoNordiskMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">NovoNordiskMember</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_NovoNordiskMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Novo Nordisk</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Expense and Other Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Requisite Service Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation service period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PreferredShareSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Share, shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PreferredShareSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Preferred share, shares issued.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PreferredShareSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred share, shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Foreign Currency Transactions and Translations Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign Currency</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Net of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other comprehensive income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_EffectOfReorganizationValue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Effect of reorganization, value.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_EffectOfReorganizationValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effect Of Reorganization, Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_EffectOfReorganizationValue_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Effect of Reorganization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate intrinsic value, Outstanding, June 30, 2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalCashFlowElementsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Supplemental Cash Flow Elements [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalCashFlowElementsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Supplemental disclosure of cash flow activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Purchase Price of Common Stock, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchase price of common stock as a percentage of closing price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_Security12bTitle_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title of 12(b) Security</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Value, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred Stock Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Number of Warrants Outstanding, Ending</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Number of Warrants Outstanding, Beginning</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expensed and Capitalized, Amount [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Equity-based Compensation Expense Recorded As Research And Development And General and Administrative Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share based compensation arrangement by share-based payment award, options, grants in period, gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Number of Options, Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_TitleOfIndividualWithRelationshipToEntityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title and Position [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MachineryAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Machinery and Equipment, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MachineryAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Laboratory equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities, Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stockholders' Equity Note, Stock Split, Conversion Ratio</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock split Ratio</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Paid, Excluding Capitalized Interest, Operating Activity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash paid for interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignCorporateDebtSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Security, Corporate, Non-US [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignCorporateDebtSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-U.S. debt securities [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted-Average Remaining Contractual Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average remaining contractual term (in years), Outstanding, June 30, 2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ResearchAndDevelopmentPersonnelExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Research and development personnel expense.</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other comprehensive loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseRightOfUseAssetAccumulatedAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Right-of-Use Asset, Accumulated Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseRightOfUseAssetAccumulatedAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated depreciation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Operating Lease Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Debt Securities, Available-for-Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Purchases of available-for-sale debt securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total stockholders' equity (deficit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_SeriesAConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series A Convertible Preferred Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine2_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Address Line Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Assets, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other non-current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ArrangementsAndNonarrangementTransactionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collaborative Arrangement and Arrangement Other than Collaborative [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PersonnelRelatedCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Personnel related costs.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PersonnelRelatedCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Personnel Related Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PersonnelRelatedCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Personnel-related (excluding equity-based compensation)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net Loss Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestIncomeOther_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Income, Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestIncomeOther_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_WeightedAverageMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Reportable Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of reportable segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stockholders' Equity Note [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_Hmb002Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">HMB 002 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_Hmb002Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">HMB-002 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfStockByClassTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock, Class of Stock [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Accumulated Gross Unrealized Gain, before Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrealized Gains</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_SegmentGeographicalDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Geographical [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SalesTypeLeaseSellingProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sales-type Lease, Selling Profit (Loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SalesTypeLeaseSellingProfitLoss_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Non-cash lease expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Unrealized Loss Position</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityInteractiveDataCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Interactive Data Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_TwoThousandAndTwentySixEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand and Twenty Six Equity Incentive Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_TwoThousandAndTwentySixEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2026 Equity Incentive Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_TwoThousandAndTwentySixEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two Thousand And Twenty Six Equity Incentive Plan Member</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedInPeriodFairValue1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested in Period, Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedInPeriodFairValue1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Grant date fair value of shares underlying warrants/options that vested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_SeriesAConvertiblePreferenceSharesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series A Convertible Preference Shares [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expensed and Capitalized, Amount [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PreferredShareParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred share par or stated value per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PreferredShareParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Share Par Or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PreferredShareParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Preferred share par or stated value per share.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageRemainingContractualTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Outstanding, Weighted Average Remaining Contractual Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingWeightedAverageRemainingContractualTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average remaining contractual term (in years), Vested and expected to vest, June 30, 2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CollaborativeArrangementsAndNoncollaborativeArrangementTransactionsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Value, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stockholders' deficit:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Convertible Preferred Stock and Convertible Preference Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_DeferredOfferingCostsIncludedInAccruedExpensesAndAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Deferred offering costs included in accrued expenses and accounts payable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_DeferredOfferingCostsIncludedInAccruedExpensesAndAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred offering costs included in accrued expenses and accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_DeferredOfferingCostsIncludedInAccruedExpensesAndAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred offering costs included in accrued expenses and accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PreferredShareSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Share, Shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PreferredShareSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Preferred share, shares authorized.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PreferredShareSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred share, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidExpensesOther_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Prepaid Expenses, Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidExpensesOther_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNoncashIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Noncash Income (Expense)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNoncashIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other non-cash items</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockOptionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Option [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockOptionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Option [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Fair Value Assets And Liabilities Measured On Recurring Basis</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ProductOrServiceAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Product and Service [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings (Accumulated Deficit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated deficit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 3 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Significant Unobservable Inputs [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalents, Fair Value Disclosure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Accounts Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total operating expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockConvertibleSharesIssuable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Convertible, Shares Issuable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockConvertibleSharesIssuable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Conversion of convertible preferred stock into common stock upon initial public offering, amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_AgreementAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Agreement [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Measurement Inputs and Valuation Techniques [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Increase (Decrease) in Operating Capital [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Changes in operating assets and liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Vesting period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesIssuedPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares Issued, Price Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesIssuedPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares issued, price per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_UnauditedInterimConsolidatedFinancialInformationTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Unaudited interim consolidated financial information.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_UnauditedInterimConsolidatedFinancialInformationTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unaudited Interim Consolidated Financial Information [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_UnauditedInterimConsolidatedFinancialInformationTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unaudited Interim Consolidated Financial Information</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_SeriesAConvertiblePreferenceSharesAndConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series A Convertible Preference Shares And Convertible Preferred Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, New Issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock issued during period, shares, new issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_NumberOfSharesReservedForIssuanceAnnualIncreasedPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number Of Shares Reserved For Issuance Annual Increased Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_NumberOfSharesReservedForIssuanceAnnualIncreasedPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of shares reserved for issuance annual increased percentage.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_NumberOfSharesReservedForIssuanceAnnualIncreasedPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of annual increase in number of shares reserved for issuance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Warrant or Right, Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class of warrant or right, outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IPOMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">IPO [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PreferredShareLiquidationPreferenceValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Share, Liquidation Preference, Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PreferredShareLiquidationPreferenceValue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Preferred share, liquidation preference, value.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PreferredShareLiquidationPreferenceValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred share, liquidation preference, value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ConvertiblePreferredStockAndConvertiblePreferenceSharesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Convertible Preferred Stock And Convertible Preference Shares [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: accumulated depreciation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Lived Tangible Asset [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FurnitureAndFixturesGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Furniture and Fixtures, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FurnitureAndFixturesGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Furniture and fixtures</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Events [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Events</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effect of Exchange Rate on Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Effect of foreign exchange rate changes on cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfStockIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments of Stock Issuance Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfStockIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpenseExcludingAcquiredInProcessCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Research and Development Expense (Excluding Acquired in Process Cost)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpenseExcludingAcquiredInProcessCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">External research and development costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_IncreaseInCommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase In Common Stock Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_IncreaseInCommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Increase in common stock shares authorized.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_IncreaseInCommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Increase in common stock, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_DeferredOfferingCostsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Offering Costs [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_DeferredOfferingCostsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Deferred offering costs.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_DeferredOfferingCostsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred Offering Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Weighted- average exercise price per share Outstanding, Ending</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Weighted- average exercise price per share Outstanding, Beginning</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities and Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities, convertible preference shares, convertible preferred stock and stockholders' equity (deficit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_UpfrontPayment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Upfront Payment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_UpfrontPayment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">UpfrontPayment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_UpfrontPayment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Upfront Payment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Research and Development Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Research and development</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Research and Development Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalPeriodFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Period Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Expense and Other Assets, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_SeriesCConvertiblePreferenceSharesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series C Convertible Preference Shares [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_TitleOfIndividualAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title and Position [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaid_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Cash paid for income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Paid, before Refund Received</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash paid for income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Exercisable, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average exercise price per share, Exercisable at June 30, 2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Including Exchange Rate Effect and Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net increase (decrease) in cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCurrentReportingStatus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Current Reporting Status</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UseOfEstimates_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Use of Estimates, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UseOfEstimates_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Use of Estimates</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 1 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Quoted Prices in Active Markets [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfStockDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Outstanding Common Stock and Ordinary Share Equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancialInstrumentAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financial Instrument [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Fair Value Disclosure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherNoncurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Other Noncurrent Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherNoncurrentAssets_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other non-current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentTransitionReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Transition Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_AccretionOfDiscountOnAvailableForSaleDebtSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accretion of discount on available for sale debt securities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_AccretionOfDiscountOnAvailableForSaleDebtSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accretion Of Discount On Available For Sale Debt Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_AccretionOfDiscountOnAvailableForSaleDebtSecurities_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Accretion of discount on available-for-sale debt securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity-Based Compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PrepaidExpenseAndOtherCurrentAssetsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Prepaid expense and other current assets.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PrepaidExpenseAndOtherCurrentAssetsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Expense And Other Current Assets [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PrepaidExpenseAndOtherCurrentAssetsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid Expenses and Other Current Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationNonproduction_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation, Nonproduction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationNonproduction_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Depreciation expense</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_DepreciationOnPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Depreciation on property plant and equipment.</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_DepreciationOnPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Depreciation on property plant and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Domain]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Expense, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Lived Assets</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets [Abstract]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Central Index Key</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercisable, Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate intrinsic value, Exercisable at June 30, 2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfStockLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Maturities, Prepayments and Calls of Debt Securities, Available-for-Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maturities of available-for-sale debt securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ConsolidationItemsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Consolidation Items [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current Fiscal Year End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_SeriesBConvertiblePreferenceSharesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series B Convertible Preference Shares [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentQuarterlyReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Quarterly Report</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentOther_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Other, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentOther_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Computer equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 2 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Significant Observable Inputs [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Weighted-average exercise price per share, Outstanding, December 31, 2025</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Weighted-average exercise price per share, Outstanding, June 30, 2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash used in operating activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityIncorporationStateCountryCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Incorporation, State or Country Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodTotalIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangement by share based payment award equity instruments other than options grants in period total intrinsic value.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodTotalIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Equity Instruments Other Than Options Grants In Period Total Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodTotalIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Aggregate intrinsic value (in thousands), Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Earnings Per Share, Diluted, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss per share, diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock, Number of Shares Issued in Transaction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sale of stock, number of shares issued in transaction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, par or stated value per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepositsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deposits [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepositsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Certificates of deposit [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValueOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Value, Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValueOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Carrying Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitments and Contingencies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Aggregate Intrinsic Value, Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Aggregate intrinsic value (in thousands), Outstanding, Ending</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Aggregate intrinsic value (in thousands), Outstanding, Beginning</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Lived Tangible Asset [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total comprehensive loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangement by share based payment award equity instruments other than options vested and expected to vest exercisable weighted average exercise price.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Equity Instruments Other Than Options Vested And Expected To Vest Exercisable Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Weighted- average exercise price per share, Vested and expected to vest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockLiquidationPreferenceValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Liquidation Preference, Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockLiquidationPreferenceValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Liquidation Preference</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockLiquidationPreferenceValue_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Preferred stock, liquidation preference, value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OrganizationConsolidationBasisOfPresentationBusinessDescriptionAndAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Organization, Consolidation, Basis of Presentation, Business Description and Accounting Policies [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OrganizationConsolidationBasisOfPresentationBusinessDescriptionAndAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Description of Business and Liquidity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Components [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash flows from investing activities:</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeBenefitsAndShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee Benefits and Share-Based Compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeBenefitsAndShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredOfferingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Offering Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ScheduleOfConvertiblePreferredStockAndConvertiblePreferenceSharesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule of convertible preferred stock and convertible preference shares.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ScheduleOfConvertiblePreferredStockAndConvertiblePreferenceSharesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Convertible Preferred Stock And Convertible Preference Shares [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ScheduleOfConvertiblePreferredStockAndConvertiblePreferenceSharesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Convertible Preferred Stock And Convertible Preference Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockLiquidationPreference_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Liquidation Preference Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockLiquidationPreference_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, liquidation preference per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Disclosures [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Measurements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation, Depletion and Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Depreciation and amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preference Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Preferred stock, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">OCI, Debt Securities, Available-for-Sale, Unrealized Holding Gain (Loss), before Adjustment, after Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net unrealized (loss) gain on available-for-sale debt securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementClassOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MeasurementInputExpectedTermMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Measurement Input, Expected Term [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_SeriesSeedConvertiblePreferenceSharesAndConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series Seed Convertible Preference Shares And Convertible Preferred Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">AOCI Attributable to Parent [Member]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Options outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Number of Options, Outstanding, June 30, 2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Accumulated Gross Unrealized Loss, before Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Unrealized Losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash flows from operating activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, CODM, Individual Title and Position or Group Name [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities and Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Liabilities, convertible preference shares, convertible preferred stock and stockholders' equity (deficit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Income (Loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Loss from operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MeasurementInputRiskFreeInterestRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Measurement Input, Risk Free Interest Rate [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_AmountOfConversionOfPrincipalPreferredStock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amount of conversion of principal preferred stock.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_AmountOfConversionOfPrincipalPreferredStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amount Of Conversion Of Principal Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_AmountOfConversionOfPrincipalPreferredStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amount of conversion of principal preferred stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFileNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity File Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfIncomeLocationBalanceAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Location, Statement of Income, Balance [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investments in Debt and Marketable Equity Securities (and Certain Trading Assets) Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Available-For-Sale Debt Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangement by share based payment award options grants in period weighted average exercise price.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Options Grants In Period Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share based compensation arrangement by share based payment award options grants in period weighted average exercise price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountingPoliciesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounting Policies [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Selling, General and Administrative Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">General and administrative</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedAndExpectedToVestOutstandingWeightedAverageRemainingContractualTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangement by share based payment award equity instruments other than options vested and expected to vest outstanding weighted average remaining contractual term 1.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedAndExpectedToVestOutstandingWeightedAverageRemainingContractualTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share based Compensation Arrangement By Share based Payment Award Equity Instruments Other Than Options Vested And Expected To Vest Outstanding Weighted Average Remaining Contractual Term 1</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedAndExpectedToVestOutstandingWeightedAverageRemainingContractualTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Weighted- average remaining contractual term (in years), Vested and expected to vest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_AccruedLiabilitiesAndOtherCurrentLiabilitiesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accrued liabilities and other current liabilities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_AccruedLiabilitiesAndOtherCurrentLiabilitiesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Liabilities And Other Current Liabilities Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_AccruedLiabilitiesAndOtherCurrentLiabilitiesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued Expenses and Other Current Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Address Line One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ScheduleOfConvertiblePreferredStockAndConvertiblePreferenceSharesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Convertible Preferred Stock And Convertible Preference Shares [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherReceivables_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Receivables</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherReceivables_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other receivables</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="country_US_lbl" xlink:role="http://www.xbrl.org/2003/role/label">UNITED STATES</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="country_US_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">United States of America [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockVotingRights_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Voting Rights</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockVotingRights_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, voting rights</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Recurring and Nonrecurring [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherOperatingIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Operating Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherOperatingIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total other income, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LossContingenciesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loss Contingencies [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Small Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingAggregateIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Outstanding, Aggregate Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingAggregateIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate intrinsic value, Vested and expected to vest, June 30, 2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Forfeitures, Weighted Average Grant Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted- average exercise price per share, Forfeited</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Significant Accounting Policies [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Significant Accounting Policies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumEmployeeSubscriptionRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Maximum Employee Subscription Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumEmployeeSubscriptionRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maximum common stock purchase allowable as a percentage of compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ConsolidationItemsDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Consolidation Items [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="country_DK_lbl" xlink:role="http://www.xbrl.org/2003/role/label">DENMARK</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="country_DK_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Denmark [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedAndExpectedToVestOutstandingAggregateIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangement by share based payment award equity instruments other than options vested and expected to vest outstanding aggregate intrinsic value.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedAndExpectedToVestOutstandingAggregateIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Equity Instruments Other Than Options Vested And Expected To Vest Outstanding Aggregate Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedAndExpectedToVestOutstandingAggregateIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Aggregate intrinsic value (in thousands), Vested and expected to vest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Stock Option Activity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Option, Activity [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherOperatingIncomeExpenseNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Operating Income (Expense), Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherOperatingIncomeExpenseNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other (expense) income, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherOperatingIncomeExpenseNet_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Other segment (income) expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PaymentForLicensedProduct_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Payment for licensed product.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PaymentForLicensedProduct_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payment For Licensed Product</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PaymentForLicensedProduct_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Payment for licensed product</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ConvertiblePreferredStockAndConvertiblePreferenceSharesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Convertible Preferred Stock And Convertible Preference Shares [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ConvertiblePreferredStockAndConvertiblePreferenceSharesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Convertible preference shares and convertible preferred stock:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongLivedAssetsByGeographicAreasTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Lived Assets by Geographic Areas [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongLivedAssetsByGeographicAreasTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Long-Lived Assets By Geographic Location</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Plan Name [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ProductsAndServicesDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Product and Service [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ConvertiblePreferenceSharesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Convertible Preference Shares [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ConvertiblePreferenceSharesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Convertible preference shares [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash flows from financing activities:</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_TwoThousandAndTwentySixEmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2026 Employee Stock Purchase Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_TwoThousandAndTwentySixEmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two Thousand And Twenty Six Employee Stock Purchase Plan Member</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_SutacimigMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sutacimig [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_SutacimigMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sutacimig [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityTaxIdentificationNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Tax Identification Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, Conversion of Convertible Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock issued during period, shares, conversion of convertible securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_SeriesCConvertiblePreferenceSharesAndConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series C Convertible Preference Shares And Convertible Preferred Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityComponentDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Component [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresInPeriodTotalIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangement by share based payment award equity instruments other than options forfeitures in period total intrinsic value.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresInPeriodTotalIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Equity Instruments Other Than Options Forfeitures In Period Total Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresInPeriodTotalIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Aggregate intrinsic value (in thousands), Forfeited</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, City or Town</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisableIntrinsicValue1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share based Compensation Arrangement By Share based Payment Award Equity Instruments Other Than Options Exercisable Intrinsic Value 1</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisableIntrinsicValue1_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Aggregate intrinsic value (in thousands), Exercisable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenues from External Customers and Long-Lived Assets [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MeasurementInputTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Measurement Input Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock pursuant to initial public offering, net of underwriter's discount and issuance costs of $29.6 million, amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, New Issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investments, Fair Value Disclosure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Common Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_HeldToMaturitySecuritiesDebtMaturities_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Held to maturity securities debt maturities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_HeldToMaturitySecuritiesDebtMaturities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Held To Maturity Securities Debt Maturities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteStockSplit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stockholders' Equity Note, Stock Split</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteStockSplit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock split, Description</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherNoncurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other non-current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ConvertiblePreferredStockAndConvertiblePreferenceSharesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Convertible Preferred Stock And Convertible Preference Shares [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Realized Gain (Loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Debt Securities, Available-for-Sale, Realized Gain (Loss), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net realized gains, on sale of available-for-sale debt securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity-based compensation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Equity-based compensation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Loss before income tax expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Reconciliation of Operating Profit (Loss) from Segments to Consolidated [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReconciliationOfOperatingProfitLossFromSegmentsToConsolidatedTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Reconciliation of Operating Profit (Loss) from Segments to Consolidated</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationAllocationAndClassificationInFinancialStatementsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Recognized Amount [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_InsuredBankDepositsMaximum_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Insured bank deposits, maximum.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_InsuredBankDepositsMaximum_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Insured Bank Deposits, Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityShellCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Shell Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash (used in) provided by investing activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_AccruedContractResearchAndDevelopmentCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accrued contract research and development costs.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_AccruedContractResearchAndDevelopmentCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Contract Research And Development Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_AccruedContractResearchAndDevelopmentCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued contract research and development costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherIncomeAndExpensesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Income and Expenses [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherIncomeAndExpensesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other income (expense), net:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_HMB-003Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">HMB-003 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_HMB-003Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">HMB-003 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_HMB-003Member_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">HMB-003Member</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Maximum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ScheduleOfAssumptionsUsedForDeterminingTheFairValueOfWarrantsGrantedTableTextblock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule of assumptions used for determining the fair value of warrants granted table textblock.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ScheduleOfAssumptionsUsedForDeterminingTheFairValueOfWarrantsGrantedTableTextblock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Assumptions Used for Determining the Fair Value of warrants Granted Table Textblock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ScheduleOfAssumptionsUsedForDeterminingTheFairValueOfWarrantsGrantedTableTextblock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Assumptions Used For Determining The Fair Value of Warrants Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentIncomeInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Income, Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentIncomeInterest_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Interest income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_AmendedAndRestatedAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amended And Restated [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_AmendedAndRestatedAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amended And Restated Axis</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisableWeightedAverageRemainingContractualTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangement by share based payment award equity instruments other than options exercisable weighted average remaining contractual term 1.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisableWeightedAverageRemainingContractualTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share based Compensation Arrangement By Share based Payment Award Equity Instruments Other Than Options Exercisable Weighted Average Remaining Contractual Term 1</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisableWeightedAverageRemainingContractualTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Weighted- average remaining contractual term (in years), Exercisable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConsolidationPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Consolidation, Policy [Policy Text Block]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted- average exercise price per share, granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Weighted- average exercise price per share, Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsNoncashItemsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Noncash Item [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsNoncashItemsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Adjustments to reconcile net loss to net cash used in operating activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current [Abstract]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedAndExpectedToVestOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangement by share based payment award equity instruments other than options vested and expected to vest outstanding number.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedAndExpectedToVestOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Equity Instruments Other Than Options Vested And Expected To Vest Outstanding Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedAndExpectedToVestOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Number of Warrants, Vested and expected to vest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Year Focus</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfCollaborativeArrangementsAndNoncollaborativeArrangementTransactionsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collaborative Arrangement and Arrangement Other than Collaborative [Table]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability, Noncurrent</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_SecurityExchangeName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Security Exchange Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MeasurementInputTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Measurement Input Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PreferredShareSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Share Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PreferredShareSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Preferred share shares outstanding.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PreferredShareSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred share, shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_SeriesAInvestmentAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series A Investment Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Recently Issued Accounting Standards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WarrantMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Warrant [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WarrantMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Warrants to purchase common stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WarrantMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Warrant [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, State or Province</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation arrangement by share-based payment award, number of shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Right-of-Use Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating right-of-use assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LossContingenciesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loss Contingencies [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity-Based Compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expensed and Capitalized, Amount [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_AgreementDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Agreement [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CityAreaCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">City Area Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomePolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomePolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Comprehensive Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from issuance of common stock, net of issuance costs of $29.6 million</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance of Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_PerformanceBasedWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Performance Based Warrants [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpensesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Expenses [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpensesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Operating expenses:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComputerEquipmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Computer Equipment [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_SeriesSeedConvertiblePreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series Seed Convertible Preferred Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_AmendedAndRestatedDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amended And Restated [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_AmendedAndRestatedDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amended And Restated Domain</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_AmountOfConversionOfInterestPreferredStock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amount of conversion of interest preferred stock.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_AmountOfConversionOfInterestPreferredStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amount Of Conversion Of Interest Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_AmountOfConversionOfInterestPreferredStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amount of conversion of interest preferred stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedEmployeeBenefitsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Employee Benefits, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedEmployeeBenefitsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued employee compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, par or stated value per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Common stock, par or stated value per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_EffectOfReorganizationShares_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Effect of reorganization, shares.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_EffectOfReorganizationShares_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effect Of Reorganization, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_EffectOfReorganizationShares_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Effect of Reorganization, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Outstanding, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of Options, Vested and expected to vest, June 30, 2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeBenefitsAndShareBasedCompensationNoncash_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee Benefit and Share-Based Payment Arrangement, Noncash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeBenefitsAndShareBasedCompensationNoncash_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total property and equipment, at cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Cash and cash equivalents at end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Cash and cash equivalents at beginning of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment Reporting</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Available For Sale&#160;Debt Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TypeOfArrangementAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collaborative Arrangement and Arrangement Other than Collaborative [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_TradingSymbol_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Trading Symbol</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_StatementGeographicalAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Geographical [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Property And Equipment, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance of Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from Issuance of Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageRemainingContractualTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Exercisable, Weighted-Average Remaining Contractual Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageRemainingContractualTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average remaining contractual term (in years), Exercisable at June 30, 2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Number of Warrants, Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityEmergingGrowthCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Emerging Growth Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRevenuesFromExternalCustomersAndLongLivedAssetsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Revenues from External Customers and Long-Lived Assets [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid-in Capital [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Costs, Capitalized, Prepaid, and Other Assets Disclosure [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Prepaid Expenses And Other Current Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Plan Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other non-current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Liabilities, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_USTreasurySecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">US Treasury Securities [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_USTreasurySecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">U.S. treasury securities [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_NetProceedsFromInitialPublicOffering_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Net Proceeds from initial public offering.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_NetProceedsFromInitialPublicOffering_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Proceeds From Initial Public Offering</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="coag_NetProceedsFromInitialPublicOffering_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net proceeds from the IPO</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MeasurementInputPriceVolatilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Measurement Input, Price Volatility [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Activity [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of The Company's Warrant Activity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseholdImprovementsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Leasehold Improvements, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseholdImprovementsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Leasehold improvements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Flow, Noncash Investing and Financing Activities Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Supplemental disclosure of non-cash investing and financing activities:</link:label>
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  <xsd:element id="coag_HMB-003Member" name="HMB-003Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
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  <xsd:element id="coag_PreferredShareSharesIssued" name="PreferredShareSharesIssued" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="coag_EffectOfReorganizationValue" name="EffectOfReorganizationValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="coag_DeferredOfferingCostsIncludedInAccruedExpensesAndAccountsPayable" name="DeferredOfferingCostsIncludedInAccruedExpensesAndAccountsPayable" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
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  <xsd:element id="coag_AmendedAndRestatedCertificateOfIncorporationMember" name="AmendedAndRestatedCertificateOfIncorporationMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="coag_UnauditedInterimConsolidatedFinancialInformationTextBlock" name="UnauditedInterimConsolidatedFinancialInformationTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="coag_SeriesCConvertiblePreferenceSharesAndConvertiblePreferredStockMember" name="SeriesCConvertiblePreferenceSharesAndConvertiblePreferredStockMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="coag_DepreciationOnPropertyPlantAndEquipment" name="DepreciationOnPropertyPlantAndEquipment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodTotalIntrinsicValue" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodTotalIntrinsicValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="coag_PersonnelRelatedCosts" name="PersonnelRelatedCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedAndExpectedToVestOutstandingAggregateIntrinsicValue" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedAndExpectedToVestOutstandingAggregateIntrinsicValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="coag_GubraAgreementMember" name="GubraAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="coag_NetProceedsFromInitialPublicOffering" name="NetProceedsFromInitialPublicOffering" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedAndExpectedToVestOutstandingNumber" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedAndExpectedToVestOutstandingNumber" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisableWeightedAverageExercisePrice" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisableWeightedAverageExercisePrice" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="coag_UpfrontPayment" name="UpfrontPayment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
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  <xsd:element id="coag_AccruedContractResearchAndDevelopmentCosts" name="AccruedContractResearchAndDevelopmentCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="coag_NumberOfSharesReservedForIssuanceAnnualIncreasedPercentage" name="NumberOfSharesReservedForIssuanceAnnualIncreasedPercentage" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresInPeriodTotalIntrinsicValue" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresInPeriodTotalIntrinsicValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="coag_AccruedLiabilitiesAndOtherCurrentLiabilitiesDisclosureTextBlock" name="AccruedLiabilitiesAndOtherCurrentLiabilitiesDisclosureTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="coag_TwoThousandAndTwentySixEmployeeStockPurchasePlanMember" name="TwoThousandAndTwentySixEmployeeStockPurchasePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="coag_SeriesAConvertiblePreferredStockMember" name="SeriesAConvertiblePreferredStockMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="coag_SeriesBConvertiblePreferenceSharesMember" name="SeriesBConvertiblePreferenceSharesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="coag_EffectOfReorganizationShares" name="EffectOfReorganizationShares" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisableWeightedAverageRemainingContractualTerm1" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisableWeightedAverageRemainingContractualTerm1" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="coag_AccretionOfDiscountOnAvailableForSaleDebtSecurities" name="AccretionOfDiscountOnAvailableForSaleDebtSecurities" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="coag_ConvertiblePreferredStockAndConvertiblePreferenceSharesTable" name="ConvertiblePreferredStockAndConvertiblePreferenceSharesTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="coag_PreferredShareLiquidationPreferenceValue" name="PreferredShareLiquidationPreferenceValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="coag_SeriesSeedConvertiblePreferenceSharesMember" name="SeriesSeedConvertiblePreferenceSharesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="coag_PaymentOfOfferingCosts" name="PaymentOfOfferingCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="coag_Hmb002Member" name="Hmb002Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="coag_AmountOfConversionOfPrincipalPreferredStock" name="AmountOfConversionOfPrincipalPreferredStock" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="coag_ConvertiblePreferredStockAndConvertiblePreferenceSharesAbstract" name="ConvertiblePreferredStockAndConvertiblePreferenceSharesAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="coag_AmountOfConversionOfInterestPreferredStock" name="AmountOfConversionOfInterestPreferredStock" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="coag_ScheduleOfConvertiblePreferredStockAndConvertiblePreferenceSharesTableTextBlock" name="ScheduleOfConvertiblePreferredStockAndConvertiblePreferenceSharesTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="coag_AmendedAndRestatedAxis" name="AmendedAndRestatedAxis" type="xbrli:stringItemType" substitutionGroup="xbrldt:dimensionItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="coag_SutacimigMember" name="SutacimigMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="coag_InsuredBankDepositsMaximum" name="InsuredBankDepositsMaximum" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="coag_PrepaidExpenseAndOtherCurrentAssetsTextBlock" name="PrepaidExpenseAndOtherCurrentAssetsTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedAndExpectedToVestOutstandingWeightedAverageRemainingContractualTerm1" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedAndExpectedToVestOutstandingWeightedAverageRemainingContractualTerm1" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="coag_AmendedAndRestatedDomain" name="AmendedAndRestatedDomain" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="coag_ConvertiblePreferenceSharesMember" name="ConvertiblePreferenceSharesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="coag_SeriesCConvertiblePreferenceSharesMember" name="SeriesCConvertiblePreferenceSharesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="coag_ExternalDiscoveryAndOtherExpense" name="ExternalDiscoveryAndOtherExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="coag_ResearchAndDevelopmentPersonnelExpense" name="ResearchAndDevelopmentPersonnelExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="coag_PreferredShareSharesAuthorized" name="PreferredShareSharesAuthorized" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="coag_CashAndCashEquivalentsAndMarketableSecurities" name="CashAndCashEquivalentsAndMarketableSecurities" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="coag_SeriesAInvestmentAgreementMember" name="SeriesAInvestmentAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="coag_PreferredShareParOrStatedValuePerShare" name="PreferredShareParOrStatedValuePerShare" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="coag_TwoThousandAndTwentySixEquityIncentivePlanMember" name="TwoThousandAndTwentySixEquityIncentivePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisableIntrinsicValue1" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisableIntrinsicValue1" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="coag_SeriesSeedConvertiblePreferenceSharesAndConvertiblePreferredStockMember" name="SeriesSeedConvertiblePreferenceSharesAndConvertiblePreferredStockMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="coag_ScheduleOfAccruedLiabilitiesAndOtherCurrentLiabilitiesTableTextBlock" name="ScheduleOfAccruedLiabilitiesAndOtherCurrentLiabilitiesTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="coag_PreferredShareSharesOutstanding" name="PreferredShareSharesOutstanding" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="coag_SeriesAConvertiblePreferenceSharesAndConvertiblePreferredStockMember" name="SeriesAConvertiblePreferenceSharesAndConvertiblePreferredStockMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisableNumber" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisableNumber" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="coag_AgreementDomain" name="AgreementDomain" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="coag_NovoNordiskMember" name="NovoNordiskMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="coag_OrdinarySharesMember" name="OrdinarySharesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="coag_SeriesBConvertiblePreferenceSharesAndConvertiblePreferredStockMember" name="SeriesBConvertiblePreferenceSharesAndConvertiblePreferredStockMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="coag_DeferredOfferingCostsPolicyTextBlock" name="DeferredOfferingCostsPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="coag_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
</xsd:schema>
