<?xml version="1.0" encoding="US-ASCII"?>
<!-- Generated by Broadridge Transform (tm) - http://www.broadridge.com -->
<!-- Created: Tue Aug 18 15:25:39 UTC 2026 -->
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementClassOfStockAxis_lbl" xml:lang="en-US">Class of Stock [Axis]</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_AssetsCurrent_lbl" xml:lang="en-US">Total Current Assets</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_Assets_lbl" xml:lang="en-US">Total Assets</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xml:lang="en-US">Total Current Liabilities</label>
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    <loc xlink:type="locator" xlink:label="us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquity"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_StockholdersEquity_lbl" xml:lang="en-US">Total Shareholder&#8217;s (Deficit) Equity</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_StockholdersEquity_lbl0" xml:lang="en-US">Balance</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xml:lang="en-US">Total Liabilities and Shareholder&#8217;s (Deficit) Equity</label>
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    <loc xlink:type="locator" xlink:label="us-gaap_ProfitLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProfitLoss"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_ProfitLoss_lbl" xml:lang="en-US">Net loss</label>
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    <loc xlink:type="locator" xlink:label="us-gaap_SharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharesIssued"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_SharesIssued_lbl" xml:lang="en-US">Balance (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharesIssued" xlink:to="us-gaap_SharesIssued_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_SharesIssued_lbl0" xml:lang="en-US">Balance (in Shares)</label>
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    <loc xlink:type="locator" xlink:label="us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xml:lang="en-US">Equity Components [Axis]</label>
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    <loc xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xml:lang="en-US">Net cash used in operating activities</label>
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    <loc xlink:type="locator" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect_lbl" xml:lang="en-US">Net change in cash</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xlink:to="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US">Cash, beginning of the period</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl0" xml:lang="en-US">Cash, end of the period</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_lbl" xml:lang="en-US">Organization and Business Operations [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_DocumentType" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentType"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_DocumentType_lbl" xml:lang="en-US">Document Type</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentType" xlink:to="dei_DocumentType_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_DocumentQuarterlyReport" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentQuarterlyReport"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_DocumentQuarterlyReport_lbl" xml:lang="en-US">Document Quarterly Report</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentQuarterlyReport" xlink:to="dei_DocumentQuarterlyReport_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_DocumentPeriodEndDate" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentPeriodEndDate"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_DocumentPeriodEndDate_lbl" xml:lang="en-US">Document Period End Date</label>
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    <loc xlink:type="locator" xlink:label="dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalYearFocus"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_DocumentFiscalYearFocus_lbl" xml:lang="en-US">Document Fiscal Year Focus</label>
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    <loc xlink:type="locator" xlink:label="dei_DocumentTransitionReport" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentTransitionReport"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_DocumentTransitionReport_lbl" xml:lang="en-US">Document Transition Report</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentTransitionReport" xlink:to="dei_DocumentTransitionReport_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityFileNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFileNumber"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityFileNumber_lbl" xml:lang="en-US">Entity File Number</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityFileNumber" xlink:to="dei_EntityFileNumber_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityRegistrantName"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityRegistrantName_lbl" xml:lang="en-US">Entity Registrant Name</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityRegistrantName" xlink:to="dei_EntityRegistrantName_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityIncorporationStateCountryCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityIncorporationStateCountryCode"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityIncorporationStateCountryCode_lbl" xml:lang="en-US">Entity Incorporation, State or Country Code</label>
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    <loc xlink:type="locator" xlink:label="dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityTaxIdentificationNumber"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityTaxIdentificationNumber_lbl" xml:lang="en-US">Entity Tax Identification Number</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityTaxIdentificationNumber" xlink:to="dei_EntityTaxIdentificationNumber_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityAddressAddressLine1_lbl" xml:lang="en-US">Entity Address, Address Line One</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressAddressLine1" xlink:to="dei_EntityAddressAddressLine1_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressCityOrTown"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityAddressCityOrTown_lbl" xml:lang="en-US">Entity Address, City or Town</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressCityOrTown" xlink:to="dei_EntityAddressCityOrTown_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressStateOrProvince"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityAddressStateOrProvince_lbl" xml:lang="en-US">Entity Address, State or Province</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressStateOrProvince" xlink:to="dei_EntityAddressStateOrProvince_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressPostalZipCode"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityAddressPostalZipCode_lbl" xml:lang="en-US">Entity Address, Postal Zip Code</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressPostalZipCode" xlink:to="dei_EntityAddressPostalZipCode_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CityAreaCode"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_CityAreaCode_lbl" xml:lang="en-US">City Area Code</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_CityAreaCode" xlink:to="dei_CityAreaCode_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LocalPhoneNumber"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_LocalPhoneNumber_lbl" xml:lang="en-US">Local Phone Number</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_LocalPhoneNumber" xlink:to="dei_LocalPhoneNumber_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_Security12bTitle"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_Security12bTitle_lbl" xml:lang="en-US">Title of 12(b) Security</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_Security12bTitle" xlink:to="dei_Security12bTitle_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_TradingSymbol"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_TradingSymbol_lbl" xml:lang="en-US">Trading Symbol</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_TradingSymbol" xlink:to="dei_TradingSymbol_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_SecurityExchangeName"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_SecurityExchangeName_lbl" xml:lang="en-US">Security Exchange Name</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_SecurityExchangeName" xlink:to="dei_SecurityExchangeName_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityCurrentReportingStatus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCurrentReportingStatus"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityCurrentReportingStatus_lbl" xml:lang="en-US">Entity Current Reporting Status</label>
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    <loc xlink:type="locator" xlink:label="dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityInteractiveDataCurrent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityInteractiveDataCurrent_lbl" xml:lang="en-US">Entity Interactive Data Current</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityInteractiveDataCurrent" xlink:to="dei_EntityInteractiveDataCurrent_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFilerCategory"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityFilerCategory_lbl" xml:lang="en-US">Entity Filer Category</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityFilerCategory" xlink:to="dei_EntityFilerCategory_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntitySmallBusiness" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntitySmallBusiness"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntitySmallBusiness_lbl" xml:lang="en-US">Entity Small Business</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntitySmallBusiness" xlink:to="dei_EntitySmallBusiness_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityEmergingGrowthCompany"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityEmergingGrowthCompany_lbl" xml:lang="en-US">Entity Emerging Growth Company</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityEmergingGrowthCompany" xlink:to="dei_EntityEmergingGrowthCompany_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityExTransitionPeriod" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityExTransitionPeriod"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityExTransitionPeriod_lbl" xml:lang="en-US">Entity Ex Transition Period</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityExTransitionPeriod" xlink:to="dei_EntityExTransitionPeriod_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityShellCompany" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityShellCompany"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityShellCompany_lbl" xml:lang="en-US">Entity Shell Company</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityShellCompany" xlink:to="dei_EntityShellCompany_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xml:lang="en-US">Entity Common Stock, Shares Outstanding</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityCommonStockSharesOutstanding" xlink:to="dei_EntityCommonStockSharesOutstanding_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCentralIndexKey"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityCentralIndexKey_lbl" xml:lang="en-US">Entity Central Index Key</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityCentralIndexKey" xlink:to="dei_EntityCentralIndexKey_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_AmendmentFlag" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_AmendmentFlag"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_AmendmentFlag_lbl" xml:lang="en-US">Amendment Flag</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_AmendmentFlag" xlink:to="dei_AmendmentFlag_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_DocumentFiscalPeriodFocus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalPeriodFocus"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_DocumentFiscalPeriodFocus_lbl" xml:lang="en-US">Document Fiscal Period Focus</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentFiscalPeriodFocus" xlink:to="dei_DocumentFiscalPeriodFocus_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CurrentFiscalYearEndDate"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xml:lang="en-US">Current Fiscal Year End Date</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_CurrentFiscalYearEndDate" xlink:to="dei_CurrentFiscalYearEndDate_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetsAbstract_lbl" xml:lang="en-US">Assets:</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsAbstract" xlink:to="us-gaap_AssetsAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AssetsCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsCurrentAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xml:lang="en-US">Current Assets</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsCurrentAbstract" xlink:to="us-gaap_AssetsCurrentAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PrepaidExpenseCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrepaidExpenseCurrent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PrepaidExpenseCurrent_lbl" xml:lang="en-US">Prepaid expenses</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PrepaidExpenseCurrent" xlink:to="us-gaap_PrepaidExpenseCurrent_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DeferredCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredCosts"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DeferredCosts_lbl" xml:lang="en-US">Deferred offering costs</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredCosts" xlink:to="us-gaap_DeferredCosts_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_LiabilitiesAndShareholderSDeficitEquityAbstract" xlink:href="cmiii-20260630.xsd#cmiii_LiabilitiesAndShareholderSDeficitEquityAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_LiabilitiesAndShareholderSDeficitEquityAbstract_lbl" xml:lang="en-US">Liabilities and Shareholder&#8217;s (Deficit) Equity:</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_LiabilitiesAndShareholderSDeficitEquityAbstract" xlink:to="cmiii_LiabilitiesAndShareholderSDeficitEquityAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LiabilitiesCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesCurrentAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xml:lang="en-US">Current Liabilities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesCurrentAbstract" xlink:to="us-gaap_LiabilitiesCurrentAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AccruedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedLiabilitiesCurrent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xml:lang="en-US">Accrued expenses</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccruedLiabilitiesCurrent" xlink:to="us-gaap_AccruedLiabilitiesCurrent_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_AccruedOfferingCostsCurrent" xlink:href="cmiii-20260630.xsd#cmiii_AccruedOfferingCostsCurrent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_AccruedOfferingCostsCurrent_lbl" xml:lang="en-US">Accrued offering costs</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_AccruedOfferingCostsCurrent" xlink:to="cmiii_AccruedOfferingCostsCurrent_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NotesPayableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NotesPayableCurrent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NotesPayableCurrent_lbl" xml:lang="en-US">IPO Promissory Note</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NotesPayableCurrent" xlink:to="us-gaap_NotesPayableCurrent_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_NotesPayableCurrent_lbl0" xml:lang="en-US">Borrowed amount</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NotesPayableCurrent" xlink:to="us-gaap_NotesPayableCurrent_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CommitmentsAndContingencies" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingencies"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xml:lang="en-US">Commitments and Contingencies (Note 6)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommitmentsAndContingencies" xlink:to="us-gaap_CommitmentsAndContingencies_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_StockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xml:lang="en-US">Shareholder&#8217;s (Deficit) Equity</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityAbstract" xlink:to="us-gaap_StockholdersEquityAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PreferredStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockValue"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PreferredStockValue_lbl" xml:lang="en-US">Preferred shares, $0.0001 par value; 5,000,000 shares authorized; none issued or outstanding as of June 30, 2026 and December 31, 2025</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockValue" xlink:to="us-gaap_PreferredStockValue_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockParOrStatedValuePerShare"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xml:lang="en-US">Preferred shares, par value (in Dollars per share)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockParOrStatedValuePerShare" xlink:to="us-gaap_PreferredStockParOrStatedValuePerShare_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PreferredStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockSharesAuthorized"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xml:lang="en-US">Preferred shares, authorized (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockSharesAuthorized" xlink:to="us-gaap_PreferredStockSharesAuthorized_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl0" xml:lang="en-US">Preferred shares, authorized</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockSharesAuthorized" xlink:to="us-gaap_PreferredStockSharesAuthorized_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PreferredStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockSharesIssued"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PreferredStockSharesIssued_lbl" xml:lang="en-US">Preferred shares, issued (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockSharesIssued" xlink:to="us-gaap_PreferredStockSharesIssued_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PreferredStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockSharesOutstanding"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xml:lang="en-US">Preferred shares, outstanding (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockSharesOutstanding" xlink:to="us-gaap_PreferredStockSharesOutstanding_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockValue"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockValue_lbl" xml:lang="en-US">Common stock, value</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockValue" xlink:to="us-gaap_CommonStockValue_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xml:lang="en-US">Ordinary shares, par value (in Dollars per share)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockParOrStatedValuePerShare" xlink:to="us-gaap_CommonStockParOrStatedValuePerShare_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CommonStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xml:lang="en-US">Ordinary shares, shares authorized (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesAuthorized" xlink:to="us-gaap_CommonStockSharesAuthorized_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl0" xml:lang="en-US">Ordinary shares, authorized</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesAuthorized" xlink:to="us-gaap_CommonStockSharesAuthorized_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CommonStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesIssued"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xml:lang="en-US">Ordinary shares, shares issued (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesIssued" xlink:to="us-gaap_CommonStockSharesIssued_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xml:lang="en-US">Ordinary shares, shares outstanding (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesOutstanding" xlink:to="us-gaap_CommonStockSharesOutstanding_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AdditionalPaidInCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapital"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xml:lang="en-US">Additional paid-in capital</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdditionalPaidInCapital" xlink:to="us-gaap_AdditionalPaidInCapital_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xml:lang="en-US">Accumulated deficit</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="us-gaap_RetainedEarningsAccumulatedDeficit_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_GeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xml:lang="en-US">General and administrative costs</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GeneralAndAdministrativeExpense" xlink:to="us-gaap_GeneralAndAdministrativeExpense_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xml:lang="en-US">Basic and diluted weighted average Class B ordinary shares outstanding (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xml:lang="en-US">Basic and diluted weighted average Class B ordinary shares outstanding (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_EarningsPerShareBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareBasic"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xml:lang="en-US">Basic and diluted net loss per Class B ordinary share (in Dollars per share)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerShareBasic" xlink:to="us-gaap_EarningsPerShareBasic_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_EarningsPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareDiluted"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xml:lang="en-US">Basic and diluted net loss per Class B ordinary share (in Dollars per share)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerShareDiluted" xlink:to="us-gaap_EarningsPerShareDiluted_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLoss"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetIncomeLoss_lbl" xml:lang="en-US">Net loss</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_NetIncomeLoss_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xml:lang="en-US">Cash flows from operating activities:</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xml:lang="en-US">Adjustments to reconcile net loss to net cash used in operating activities:</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_GeneralAndAdministrativeCostsPaidThroughIPOPromissoryNote" xlink:href="cmiii-20260630.xsd#cmiii_GeneralAndAdministrativeCostsPaidThroughIPOPromissoryNote"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_GeneralAndAdministrativeCostsPaidThroughIPOPromissoryNote_lbl" xml:lang="en-US">General and administrative costs paid through IPO Promissory Note</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_GeneralAndAdministrativeCostsPaidThroughIPOPromissoryNote" xlink:to="cmiii_GeneralAndAdministrativeCostsPaidThroughIPOPromissoryNote_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOperatingCapitalAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xml:lang="en-US">Changes in operating assets and liabilities:</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:to="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccruedLiabilities"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilities_lbl" xml:lang="en-US">Accrued expenses</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:to="us-gaap_IncreaseDecreaseInAccruedLiabilities_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_lbl" xml:lang="en-US">Noncash investing and financing activities:</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:to="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_DeferredOfferingCostsIncludedInAccruedOfferingCosts" xlink:href="cmiii-20260630.xsd#cmiii_DeferredOfferingCostsIncludedInAccruedOfferingCosts"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_DeferredOfferingCostsIncludedInAccruedOfferingCosts_lbl" xml:lang="en-US">Deferred offering costs included in accrued offering costs</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_DeferredOfferingCostsIncludedInAccruedOfferingCosts" xlink:to="cmiii_DeferredOfferingCostsIncludedInAccruedOfferingCosts_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_DeferredOfferingCostsPaidThroughIPOPromissoryNote" xlink:href="cmiii-20260630.xsd#cmiii_DeferredOfferingCostsPaidThroughIPOPromissoryNote"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_DeferredOfferingCostsPaidThroughIPOPromissoryNote_lbl" xml:lang="en-US">Deferred offering costs paid through IPO Promissory Note</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_DeferredOfferingCostsPaidThroughIPOPromissoryNote" xlink:to="cmiii_DeferredOfferingCostsPaidThroughIPOPromissoryNote_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_DeferredOfferingCostsPaidThroughPrepaidExpenses" xlink:href="cmiii-20260630.xsd#cmiii_DeferredOfferingCostsPaidThroughPrepaidExpenses"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_DeferredOfferingCostsPaidThroughPrepaidExpenses_lbl" xml:lang="en-US">Deferred offering costs paid through prepaid expenses</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_DeferredOfferingCostsPaidThroughPrepaidExpenses" xlink:to="cmiii_DeferredOfferingCostsPaidThroughPrepaidExpenses_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_PrepaidServicesPaidThroughIPOPromissoryNote" xlink:href="cmiii-20260630.xsd#cmiii_PrepaidServicesPaidThroughIPOPromissoryNote"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_PrepaidServicesPaidThroughIPOPromissoryNote_lbl" xml:lang="en-US">Prepaid services paid through IPO Promissory Note</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_PrepaidServicesPaidThroughIPOPromissoryNote" xlink:to="cmiii_PrepaidServicesPaidThroughIPOPromissoryNote_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_UnitsEachConsistingOfOneClassAOrdinaryShareAndOnethirdOfOneRedeemableWarrantMember" xlink:href="cmiii-20260630.xsd#cmiii_UnitsEachConsistingOfOneClassAOrdinaryShareAndOnethirdOfOneRedeemableWarrantMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_UnitsEachConsistingOfOneClassAOrdinaryShareAndOnethirdOfOneRedeemableWarrantMember_lbl" xml:lang="en-US">Units, each consisting of one Class A Ordinary Share and one-third of one redeemable Warrant</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_UnitsEachConsistingOfOneClassAOrdinaryShareAndOnethirdOfOneRedeemableWarrantMember" xlink:to="cmiii_UnitsEachConsistingOfOneClassAOrdinaryShareAndOnethirdOfOneRedeemableWarrantMember_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_ClassAOrdinarySharesParValue00001PerShareMember" xlink:href="cmiii-20260630.xsd#cmiii_ClassAOrdinarySharesParValue00001PerShareMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_ClassAOrdinarySharesParValue00001PerShareMember_lbl" xml:lang="en-US">Class A Ordinary Shares, par value $0.0001 per share</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ClassAOrdinarySharesParValue00001PerShareMember" xlink:to="cmiii_ClassAOrdinarySharesParValue00001PerShareMember_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_RedeemableWarrantsEachWholeWarrantExercisableForOneClassAOrdinaryShareAtAnExercisePriceOf1150PerShareMember" xlink:href="cmiii-20260630.xsd#cmiii_RedeemableWarrantsEachWholeWarrantExercisableForOneClassAOrdinaryShareAtAnExercisePriceOf1150PerShareMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_RedeemableWarrantsEachWholeWarrantExercisableForOneClassAOrdinaryShareAtAnExercisePriceOf1150PerShareMember_lbl" xml:lang="en-US">Redeemable Warrants, each whole Warrant exercisable for one Class A Ordinary Share at an exercise price of $11.50 per share</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_RedeemableWarrantsEachWholeWarrantExercisableForOneClassAOrdinaryShareAtAnExercisePriceOf1150PerShareMember" xlink:to="cmiii_RedeemableWarrantsEachWholeWarrantExercisableForOneClassAOrdinaryShareAtAnExercisePriceOf1150PerShareMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CommonClassAMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassAMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonClassAMember_lbl" xml:lang="en-US">Class A Ordinary Shares</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonClassAMember" xlink:to="us-gaap_CommonClassAMember_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CommonClassAMember_lbl0" xml:lang="en-US">Class A ordinary share [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonClassAMember" xlink:to="us-gaap_CommonClassAMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:label="us-gaap_CommonClassAMember_lbl1" xml:lang="en-US">Class A Ordinary Shares [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonClassAMember" xlink:to="us-gaap_CommonClassAMember_lbl1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CommonClassBMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassBMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonClassBMember_lbl" xml:lang="en-US">Class B Ordinary Shares</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonClassBMember" xlink:to="us-gaap_CommonClassBMember_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CommonClassBMember_lbl0" xml:lang="en-US">Class B</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonClassBMember" xlink:to="us-gaap_CommonClassBMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:label="us-gaap_CommonClassBMember_lbl1" xml:lang="en-US">Class B Ordinary Shares [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonClassBMember" xlink:to="us-gaap_CommonClassBMember_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonClassBMember_lbl2" xml:lang="en-US">Common Class B [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonClassBMember" xlink:to="us-gaap_CommonClassBMember_lbl2"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CommonStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockMember_lbl" xml:lang="en-US">Ordinary shares</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockMember" xlink:to="us-gaap_CommonStockMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AdditionalPaidInCapitalMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xml:lang="en-US">Additional Paid-In Capital</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdditionalPaidInCapitalMember" xlink:to="us-gaap_AdditionalPaidInCapitalMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RetainedEarningsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RetainedEarningsMember_lbl" xml:lang="en-US">Accumulated Deficit</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RetainedEarningsMember" xlink:to="us-gaap_RetainedEarningsMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NatureOfOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NatureOfOperations"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NatureOfOperations_lbl" xml:lang="en-US">Organization and Business Operations</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NatureOfOperations" xlink:to="us-gaap_NatureOfOperations_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SignificantAccountingPoliciesTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xml:lang="en-US">Significant Accounting Policies</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="us-gaap_SignificantAccountingPoliciesTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_InitialPublicOfferingTextBlock" xlink:href="cmiii-20260630.xsd#cmiii_InitialPublicOfferingTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_InitialPublicOfferingTextBlock_lbl" xml:lang="en-US">Initial Public Offering</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_InitialPublicOfferingTextBlock" xlink:to="cmiii_InitialPublicOfferingTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_PrivatePlacementTextBlock" xlink:href="cmiii-20260630.xsd#cmiii_PrivatePlacementTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_PrivatePlacementTextBlock_lbl" xml:lang="en-US">Private Placement</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_PrivatePlacementTextBlock" xlink:to="cmiii_PrivatePlacementTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsDisclosureTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_lbl" xml:lang="en-US">Related Party Transactions</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:to="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl" xml:lang="en-US">Commitments and Contingencies</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:to="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl" xml:lang="en-US">Shareholder&#8217;s (Deficit) Equity</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingDisclosureTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xml:lang="en-US">Segment Information</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingDisclosureTextBlock" xlink:to="us-gaap_SegmentReportingDisclosureTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xml:lang="en-US">Schedule of Company Performance And Making Key Decisions</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:to="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DeferredOfferingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredOfferingCosts"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DeferredOfferingCosts_lbl" xml:lang="en-US">Deferred offering costs</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredOfferingCosts" xlink:to="us-gaap_DeferredOfferingCosts_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SubsequentEventsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventsTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xml:lang="en-US">Subsequent Events</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventsTextBlock" xlink:to="us-gaap_SubsequentEventsTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl" xml:lang="en-US">Related and Nonrelated Parties [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SubsequentEventTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTypeAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventTypeAxis_lbl" xml:lang="en-US">Subsequent Event Type [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventTypeAxis" xlink:to="us-gaap_SubsequentEventTypeAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SubsidiarySaleOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsidiarySaleOfStockAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xml:lang="en-US">Sale of Stock [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsidiarySaleOfStockAxis" xlink:to="us-gaap_SubsidiarySaleOfStockAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ClassOfWarrantOrRightAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfWarrantOrRightAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ClassOfWarrantOrRightAxis_lbl" xml:lang="en-US">Class of Warrant or Right [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ClassOfWarrantOrRightAxis" xlink:to="us-gaap_ClassOfWarrantOrRightAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RelatedPartyTransactionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionAxis_lbl" xml:lang="en-US">Related Party Transaction [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionAxis" xlink:to="us-gaap_RelatedPartyTransactionAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="srt_TitleOfIndividualAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_TitleOfIndividualAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_TitleOfIndividualAxis_lbl" xml:lang="en-US">Title and Position [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_TitleOfIndividualAxis" xlink:to="srt_TitleOfIndividualAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentAxis_lbl" xml:lang="en-US">Debt Instrument [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentAxis" xlink:to="us-gaap_DebtInstrumentAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AccountingPoliciesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountingPoliciesAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountingPoliciesAbstract_lbl" xml:lang="en-US">Accounting Policies [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountingPoliciesAbstract" xlink:to="us-gaap_AccountingPoliciesAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="ecd_Rule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Rule10b51ArrAdoptedFlag"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="ecd_Rule10b51ArrAdoptedFlag_lbl" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted [Flag]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ecd_Rule10b51ArrAdoptedFlag" xlink:to="ecd_Rule10b51ArrAdoptedFlag_lbl"/>
    <loc xlink:type="locator" xlink:label="ecd_Rule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Rule10b51ArrTrmntdFlag"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="ecd_Rule10b51ArrTrmntdFlag_lbl" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated [Flag]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ecd_Rule10b51ArrTrmntdFlag" xlink:to="ecd_Rule10b51ArrTrmntdFlag_lbl"/>
    <loc xlink:type="locator" xlink:label="ecd_NonRule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonRule10b51ArrTrmntdFlag"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="ecd_NonRule10b51ArrTrmntdFlag_lbl" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated [Flag]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ecd_NonRule10b51ArrTrmntdFlag" xlink:to="ecd_NonRule10b51ArrTrmntdFlag_lbl"/>
    <loc xlink:type="locator" xlink:label="ecd_NonRule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonRule10b51ArrAdoptedFlag"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="ecd_NonRule10b51ArrAdoptedFlag_lbl" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted [Flag]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ecd_NonRule10b51ArrAdoptedFlag" xlink:to="ecd_NonRule10b51ArrAdoptedFlag_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_YearOfInception" xlink:href="cmiii-20260630.xsd#cmiii_YearOfInception"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_YearOfInception_lbl" xml:lang="en-US">Year of inception</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_YearOfInception" xlink:to="cmiii_YearOfInception_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_UnitsIssuedDuringPeriodSharesNewIssues" xlink:href="cmiii-20260630.xsd#cmiii_UnitsIssuedDuringPeriodSharesNewIssues"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_UnitsIssuedDuringPeriodSharesNewIssues_lbl" xml:lang="en-US">Number of units issued</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_UnitsIssuedDuringPeriodSharesNewIssues" xlink:to="cmiii_UnitsIssuedDuringPeriodSharesNewIssues_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cmiii_UnitsIssuedDuringPeriodSharesNewIssues_lbl0" xml:lang="en-US">Number of units issued (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_UnitsIssuedDuringPeriodSharesNewIssues" xlink:to="cmiii_UnitsIssuedDuringPeriodSharesNewIssues_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:label="cmiii_UnitsIssuedDuringPeriodSharesNewIssues_lbl1" xml:lang="en-US">Units purchase an additional (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_UnitsIssuedDuringPeriodSharesNewIssues" xlink:to="cmiii_UnitsIssuedDuringPeriodSharesNewIssues_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_UnitsIssuedDuringPeriodSharesNewIssues_lbl2" xml:lang="en-US">Number of units issued (in Shares) (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_UnitsIssuedDuringPeriodSharesNewIssues" xlink:to="cmiii_UnitsIssuedDuringPeriodSharesNewIssues_lbl2"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SharesIssuedPricePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharesIssuedPricePerShare"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SharesIssuedPricePerShare_lbl" xml:lang="en-US">Price per share (in Dollars per share)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharesIssuedPricePerShare" xlink:to="us-gaap_SharesIssuedPricePerShare_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_SharesIssuedPricePerShare_lbl0" xml:lang="en-US">Purchase price</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharesIssuedPricePerShare" xlink:to="us-gaap_SharesIssuedPricePerShare_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:label="us-gaap_SharesIssuedPricePerShare_lbl1" xml:lang="en-US">Price per unit issued (in Dollars per share)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharesIssuedPricePerShare" xlink:to="us-gaap_SharesIssuedPricePerShare_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SharesIssuedPricePerShare_lbl2" xml:lang="en-US">Price per share (in Dollars per share) (in Dollars per share)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharesIssuedPricePerShare" xlink:to="us-gaap_SharesIssuedPricePerShare_lbl2"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ProceedsFromIssuanceInitialPublicOffering" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromIssuanceInitialPublicOffering"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromIssuanceInitialPublicOffering_lbl" xml:lang="en-US">Gross proceeds (in Dollars)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromIssuanceInitialPublicOffering" xlink:to="us-gaap_ProceedsFromIssuanceInitialPublicOffering_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ProceedsFromIssuanceInitialPublicOffering_lbl0" xml:lang="en-US">Generating gross proceeds</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromIssuanceInitialPublicOffering" xlink:to="us-gaap_ProceedsFromIssuanceInitialPublicOffering_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:label="us-gaap_ProceedsFromIssuanceInitialPublicOffering_lbl1" xml:lang="en-US">Generating gross proceed</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromIssuanceInitialPublicOffering" xlink:to="us-gaap_ProceedsFromIssuanceInitialPublicOffering_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromIssuanceInitialPublicOffering_lbl2" xml:lang="en-US">Proceeds from Issuance Initial Public Offering</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromIssuanceInitialPublicOffering" xlink:to="us-gaap_ProceedsFromIssuanceInitialPublicOffering_lbl2"/>
    <loc xlink:type="locator" xlink:label="cmiii_UnitsIssuedDuringPeriodNewIssues" xlink:href="cmiii-20260630.xsd#cmiii_UnitsIssuedDuringPeriodNewIssues"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_UnitsIssuedDuringPeriodNewIssues_lbl" xml:lang="en-US">Private placement units issued</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_UnitsIssuedDuringPeriodNewIssues" xlink:to="cmiii_UnitsIssuedDuringPeriodNewIssues_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_TransactionCosts" xlink:href="cmiii-20260630.xsd#cmiii_TransactionCosts"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_TransactionCosts_lbl" xml:lang="en-US">Transaction costs (in Dollars)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_TransactionCosts" xlink:to="cmiii_TransactionCosts_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PaymentsForUnderwritingExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsForUnderwritingExpense"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PaymentsForUnderwritingExpense_lbl" xml:lang="en-US">Cash underwriting fee (in Dollars)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsForUnderwritingExpense" xlink:to="us-gaap_PaymentsForUnderwritingExpense_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_OtherOfferingCosts" xlink:href="cmiii-20260630.xsd#cmiii_OtherOfferingCosts"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_OtherOfferingCosts_lbl" xml:lang="en-US">Other offering costs (in Dollars)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_OtherOfferingCosts" xlink:to="cmiii_OtherOfferingCosts_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_ThresholdFairMarketValueOfTargetBusinessAsPercentOfNetBalanceInTrustAccount" xlink:href="cmiii-20260630.xsd#cmiii_ThresholdFairMarketValueOfTargetBusinessAsPercentOfNetBalanceInTrustAccount"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_ThresholdFairMarketValueOfTargetBusinessAsPercentOfNetBalanceInTrustAccount_lbl" xml:lang="en-US">Percent of fair market value of target businesse</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ThresholdFairMarketValueOfTargetBusinessAsPercentOfNetBalanceInTrustAccount" xlink:to="cmiii_ThresholdFairMarketValueOfTargetBusinessAsPercentOfNetBalanceInTrustAccount_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_ThresholdOwnershipPercentageInTargetCompany" xlink:href="cmiii-20260630.xsd#cmiii_ThresholdOwnershipPercentageInTargetCompany"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_ThresholdOwnershipPercentageInTargetCompany_lbl" xml:lang="en-US">Percentage of ownership interest to be acquired</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ThresholdOwnershipPercentageInTargetCompany" xlink:to="cmiii_ThresholdOwnershipPercentageInTargetCompany_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_NetProceedsFromIssuanceInitialPublicOffering" xlink:href="cmiii-20260630.xsd#cmiii_NetProceedsFromIssuanceInitialPublicOffering"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_NetProceedsFromIssuanceInitialPublicOffering_lbl" xml:lang="en-US">Net proceeds (in Dollars)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_NetProceedsFromIssuanceInitialPublicOffering" xlink:to="cmiii_NetProceedsFromIssuanceInitialPublicOffering_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cmiii_NetProceedsFromIssuanceInitialPublicOffering_lbl0" xml:lang="en-US">Net proceeds of sale</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_NetProceedsFromIssuanceInitialPublicOffering" xlink:to="cmiii_NetProceedsFromIssuanceInitialPublicOffering_lbl0"/>
    <loc xlink:type="locator" xlink:label="cmiii_MaximumPeriodToCompleteTheInitialBusinessCombinationAfterInitialPublicOffering" xlink:href="cmiii-20260630.xsd#cmiii_MaximumPeriodToCompleteTheInitialBusinessCombinationAfterInitialPublicOffering"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_MaximumPeriodToCompleteTheInitialBusinessCombinationAfterInitialPublicOffering_lbl" xml:lang="en-US">Maximum period to complete the business combination</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_MaximumPeriodToCompleteTheInitialBusinessCombinationAfterInitialPublicOffering" xlink:to="cmiii_MaximumPeriodToCompleteTheInitialBusinessCombinationAfterInitialPublicOffering_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_PercentOfPublicSharesToBeRedeemedIfBusinessCombinationNotCompleted" xlink:href="cmiii-20260630.xsd#cmiii_PercentOfPublicSharesToBeRedeemedIfBusinessCombinationNotCompleted"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_PercentOfPublicSharesToBeRedeemedIfBusinessCombinationNotCompleted_lbl" xml:lang="en-US">Redemption percentage of shares if business combination not completed</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_PercentOfPublicSharesToBeRedeemedIfBusinessCombinationNotCompleted" xlink:to="cmiii_PercentOfPublicSharesToBeRedeemedIfBusinessCombinationNotCompleted_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SharePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharePrice"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SharePrice_lbl" xml:lang="en-US">Share price (in Dollars per share)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharePrice" xlink:to="us-gaap_SharePrice_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_MaximumInterestEarnedFromTrustAccountUsedForDissolution" xlink:href="cmiii-20260630.xsd#cmiii_MaximumInterestEarnedFromTrustAccountUsedForDissolution"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_MaximumInterestEarnedFromTrustAccountUsedForDissolution_lbl" xml:lang="en-US">Dissolution expense (in Dollars)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_MaximumInterestEarnedFromTrustAccountUsedForDissolution" xlink:to="cmiii_MaximumInterestEarnedFromTrustAccountUsedForDissolution_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_TrustValueActualPerShare" xlink:href="cmiii-20260630.xsd#cmiii_TrustValueActualPerShare"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_TrustValueActualPerShare_lbl" xml:lang="en-US">Triggering event per share (in Dollars per share)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_TrustValueActualPerShare" xlink:to="cmiii_TrustValueActualPerShare_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SecuredDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SecuredDebt"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SecuredDebt_lbl" xml:lang="en-US">Loan amount</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SecuredDebt" xlink:to="us-gaap_SecuredDebt_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_Cash" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Cash"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_Cash_lbl" xml:lang="en-US">Cash</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Cash" xlink:to="us-gaap_Cash_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_WorkingCapitalDeficit" xlink:href="cmiii-20260630.xsd#cmiii_WorkingCapitalDeficit"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_WorkingCapitalDeficit_lbl" xml:lang="en-US">Working capital deficit</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_WorkingCapitalDeficit" xlink:to="cmiii_WorkingCapitalDeficit_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SaleOfStockPricePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockPricePerShare"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl" xml:lang="en-US">Price per unit (in Dollars per share)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SaleOfStockPricePerShare" xlink:to="us-gaap_SaleOfStockPricePerShare_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl" xml:lang="en-US">Consummated sale (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:to="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl0" xml:lang="en-US">Sale of shares</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:to="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ProceedsFromIssuanceOfPrivatePlacement" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromIssuanceOfPrivatePlacement"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromIssuanceOfPrivatePlacement_lbl" xml:lang="en-US">Generating gross proceeds</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromIssuanceOfPrivatePlacement" xlink:to="us-gaap_ProceedsFromIssuanceOfPrivatePlacement_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_WorkingCapitalLoans" xlink:href="cmiii-20260630.xsd#cmiii_WorkingCapitalLoans"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_WorkingCapitalLoans_lbl" xml:lang="en-US">Working capital loans</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_WorkingCapitalLoans" xlink:to="cmiii_WorkingCapitalLoans_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_EntityPricePerUnit" xlink:href="cmiii-20260630.xsd#cmiii_EntityPricePerUnit"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_EntityPricePerUnit_lbl" xml:lang="en-US">Entity price per unit (in Dollars per share) (in Dollars per share)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_EntityPricePerUnit" xlink:to="cmiii_EntityPricePerUnit_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensationForfeited" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensationForfeited"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensationForfeited_lbl" xml:lang="en-US">Aggregate shares subject to forfeiture (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensationForfeited" xlink:to="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensationForfeited_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xml:lang="en-US">Number of units (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:to="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl0" xml:lang="en-US">Number of shares issued (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:to="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl0"/>
    <loc xlink:type="locator" xlink:label="cmiii_NumberOfWarrants" xlink:href="cmiii-20260630.xsd#cmiii_NumberOfWarrants"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_NumberOfWarrants_lbl" xml:lang="en-US">Number of warrants</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_NumberOfWarrants" xlink:to="cmiii_NumberOfWarrants_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight_lbl" xml:lang="en-US">Number of shares issued per warrant</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:to="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_lbl" xml:lang="en-US">Warrant exercise price</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:to="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_ThresholdNumberOfDaysForRestrictionToExerciseWarrantsFromCompletionOfInitialBusinessCombination" xlink:href="cmiii-20260630.xsd#cmiii_ThresholdNumberOfDaysForRestrictionToExerciseWarrantsFromCompletionOfInitialBusinessCombination"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_ThresholdNumberOfDaysForRestrictionToExerciseWarrantsFromCompletionOfInitialBusinessCombination_lbl" xml:lang="en-US">Warrants exercisable term</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ThresholdNumberOfDaysForRestrictionToExerciseWarrantsFromCompletionOfInitialBusinessCombination" xlink:to="cmiii_ThresholdNumberOfDaysForRestrictionToExerciseWarrantsFromCompletionOfInitialBusinessCombination_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_WarrantsAndRightsOutstandingTerm" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WarrantsAndRightsOutstandingTerm"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_WarrantsAndRightsOutstandingTerm_lbl" xml:lang="en-US">Warrants expiry term</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WarrantsAndRightsOutstandingTerm" xlink:to="us-gaap_WarrantsAndRightsOutstandingTerm_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_ThresholdNumberOfDaysForFilingRegistrationStatementAfterBusinessCombinationClosing" xlink:href="cmiii-20260630.xsd#cmiii_ThresholdNumberOfDaysForFilingRegistrationStatementAfterBusinessCombinationClosing"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_ThresholdNumberOfDaysForFilingRegistrationStatementAfterBusinessCombinationClosing_lbl" xml:lang="en-US">Number of days</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ThresholdNumberOfDaysForFilingRegistrationStatementAfterBusinessCombinationClosing" xlink:to="cmiii_ThresholdNumberOfDaysForFilingRegistrationStatementAfterBusinessCombinationClosing_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_ThresholdPeriodForMakingRegistrationStatementEffectiveAfterBusinessCombinationClosing" xlink:href="cmiii-20260630.xsd#cmiii_ThresholdPeriodForMakingRegistrationStatementEffectiveAfterBusinessCombinationClosing"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_ThresholdPeriodForMakingRegistrationStatementEffectiveAfterBusinessCombinationClosing_lbl" xml:lang="en-US">Threshold period for making the registration statement effective</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ThresholdPeriodForMakingRegistrationStatementEffectiveAfterBusinessCombinationClosing" xlink:to="cmiii_ThresholdPeriodForMakingRegistrationStatementEffectiveAfterBusinessCombinationClosing_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_TradingDaysForComputationOfFairMarketValue" xlink:href="cmiii-20260630.xsd#cmiii_TradingDaysForComputationOfFairMarketValue"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_TradingDaysForComputationOfFairMarketValue_lbl" xml:lang="en-US">Trading days for computation of fair market value</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_TradingDaysForComputationOfFairMarketValue" xlink:to="cmiii_TradingDaysForComputationOfFairMarketValue_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightStockPriceTrigger" xlink:href="cmiii-20260630.xsd#cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightStockPriceTrigger"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightStockPriceTrigger_lbl" xml:lang="en-US">Stock price trigger for redemption of warrants</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightStockPriceTrigger" xlink:to="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightStockPriceTrigger_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_ClassOfWarrantRightThresholdPriorWrittenNoticePeriodForRedemptionOfWarrants" xlink:href="cmiii-20260630.xsd#cmiii_ClassOfWarrantRightThresholdPriorWrittenNoticePeriodForRedemptionOfWarrants"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_ClassOfWarrantRightThresholdPriorWrittenNoticePeriodForRedemptionOfWarrants_lbl" xml:lang="en-US">Threshold prior written notice period for redemption of warrants</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ClassOfWarrantRightThresholdPriorWrittenNoticePeriodForRedemptionOfWarrants" xlink:to="cmiii_ClassOfWarrantRightThresholdPriorWrittenNoticePeriodForRedemptionOfWarrants_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_ClassOfWarrantOrRightRedemptionWarrantOrRightThresholdTradingDays" xlink:href="cmiii-20260630.xsd#cmiii_ClassOfWarrantOrRightRedemptionWarrantOrRightThresholdTradingDays"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_ClassOfWarrantOrRightRedemptionWarrantOrRightThresholdTradingDays_lbl" xml:lang="en-US">Threshold trading days for redemption of warrants</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ClassOfWarrantOrRightRedemptionWarrantOrRightThresholdTradingDays" xlink:to="cmiii_ClassOfWarrantOrRightRedemptionWarrantOrRightThresholdTradingDays_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightThresholdConsecutiveTradingDays" xlink:href="cmiii-20260630.xsd#cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightThresholdConsecutiveTradingDays"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightThresholdConsecutiveTradingDays_lbl" xml:lang="en-US">Threshold consecutive trading days for redemption of warrants</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightThresholdConsecutiveTradingDays" xlink:to="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightThresholdConsecutiveTradingDays_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightThresholdCommencementPeriodAfterInitialBusinessCombinationClosing" xlink:href="cmiii-20260630.xsd#cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightThresholdCommencementPeriodAfterInitialBusinessCombinationClosing"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightThresholdCommencementPeriodAfterInitialBusinessCombinationClosing_lbl" xml:lang="en-US">Threshold period for commencing redemption of warrants</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightThresholdCommencementPeriodAfterInitialBusinessCombinationClosing" xlink:to="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightThresholdCommencementPeriodAfterInitialBusinessCombinationClosing_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_NumberOfOrdinaryShares" xlink:href="cmiii-20260630.xsd#cmiii_NumberOfOrdinaryShares"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_NumberOfOrdinaryShares_lbl" xml:lang="en-US">Number of ordinary shares</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_NumberOfOrdinaryShares" xlink:to="cmiii_NumberOfOrdinaryShares_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_ExercisableAfterTheCompletionOfTheInitialBusinessCombination" xlink:href="cmiii-20260630.xsd#cmiii_ExercisableAfterTheCompletionOfTheInitialBusinessCombination"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_ExercisableAfterTheCompletionOfTheInitialBusinessCombination_lbl" xml:lang="en-US">Initial business combination period</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ExercisableAfterTheCompletionOfTheInitialBusinessCombination" xlink:to="cmiii_ExercisableAfterTheCompletionOfTheInitialBusinessCombination_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_InitialBusinessCombinationExercisableCompletionTerm" xlink:href="cmiii-20260630.xsd#cmiii_InitialBusinessCombinationExercisableCompletionTerm"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_InitialBusinessCombinationExercisableCompletionTerm_lbl" xml:lang="en-US">Initial business combination exercisable completion term</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_InitialBusinessCombinationExercisableCompletionTerm" xlink:to="cmiii_InitialBusinessCombinationExercisableCompletionTerm_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_InitialBusinessCombinationExercisableTerm" xlink:href="cmiii-20260630.xsd#cmiii_InitialBusinessCombinationExercisableTerm"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_InitialBusinessCombinationExercisableTerm_lbl" xml:lang="en-US">Initial business combination exercisable term</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_InitialBusinessCombinationExercisableTerm" xlink:to="cmiii_InitialBusinessCombinationExercisableTerm_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xml:lang="en-US">Capital contribution</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:to="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl0" xml:lang="en-US">Aggregate amount</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:to="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_StockRepurchasedDuringPeriodShares" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockRepurchasedDuringPeriodShares"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockRepurchasedDuringPeriodShares_lbl" xml:lang="en-US">Shares surrendered (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockRepurchasedDuringPeriodShares" xlink:to="us-gaap_StockRepurchasedDuringPeriodShares_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_MaximumNumberOfSharesSubjectToForfeiture" xlink:href="cmiii-20260630.xsd#cmiii_MaximumNumberOfSharesSubjectToForfeiture"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_MaximumNumberOfSharesSubjectToForfeiture_lbl" xml:lang="en-US">Maximum number of shares subject to forfeiture (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_MaximumNumberOfSharesSubjectToForfeiture" xlink:to="cmiii_MaximumNumberOfSharesSubjectToForfeiture_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_InterestEquivalentAggregateShares" xlink:href="cmiii-20260630.xsd#cmiii_InterestEquivalentAggregateShares"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_InterestEquivalentAggregateShares_lbl" xml:lang="en-US">Interest equivalent aggregate shares (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_InterestEquivalentAggregateShares" xlink:to="cmiii_InterestEquivalentAggregateShares_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod_lbl" xml:lang="en-US">Granted shares (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_FairValueAmountIssued" xlink:href="cmiii-20260630.xsd#cmiii_FairValueAmountIssued"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_FairValueAmountIssued_lbl" xml:lang="en-US">Fair value amount issued</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_FairValueAmountIssued" xlink:to="cmiii_FairValueAmountIssued_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_MarketableValuePerShare" xlink:href="cmiii-20260630.xsd#cmiii_MarketableValuePerShare"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_MarketableValuePerShare_lbl" xml:lang="en-US">Marketable value per share (in Dollars per share)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_MarketableValuePerShare" xlink:to="cmiii_MarketableValuePerShare_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_InitialBusinessCombination" xlink:href="cmiii-20260630.xsd#cmiii_InitialBusinessCombination"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_InitialBusinessCombination_lbl" xml:lang="en-US">Initial business combination percentage</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_InitialBusinessCombination" xlink:to="cmiii_InitialBusinessCombination_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_RedeemPublicSharesPercentage" xlink:href="cmiii-20260630.xsd#cmiii_RedeemPublicSharesPercentage"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_RedeemPublicSharesPercentage_lbl" xml:lang="en-US">Redeem public shares percentage</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_RedeemPublicSharesPercentage" xlink:to="cmiii_RedeemPublicSharesPercentage_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtInstrumentFaceAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentFaceAmount"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xml:lang="en-US">Expenses of the proposed public offering.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentFaceAmount" xlink:to="us-gaap_DebtInstrumentFaceAmount_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_RelatedPartyTransactionMonthlyAdministrativeExpenses" xlink:href="cmiii-20260630.xsd#cmiii_RelatedPartyTransactionMonthlyAdministrativeExpenses"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_RelatedPartyTransactionMonthlyAdministrativeExpenses_lbl" xml:lang="en-US">Monthly administrative expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_RelatedPartyTransactionMonthlyAdministrativeExpenses" xlink:to="cmiii_RelatedPartyTransactionMonthlyAdministrativeExpenses_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtConversionOriginalDebtAmount1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtConversionOriginalDebtAmount1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtConversionOriginalDebtAmount1_lbl" xml:lang="en-US">Loan amount converted into warrants</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtConversionOriginalDebtAmount1" xlink:to="us-gaap_DebtConversionOriginalDebtAmount1_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtInstrumentConvertibleConversionPrice1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentConvertibleConversionPrice1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentConvertibleConversionPrice1_lbl" xml:lang="en-US">Conversion price (in Dollars per share)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentConvertibleConversionPrice1" xlink:to="us-gaap_DebtInstrumentConvertibleConversionPrice1_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_OverAllotmentPeriod" xlink:href="cmiii-20260630.xsd#cmiii_OverAllotmentPeriod"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_OverAllotmentPeriod_lbl" xml:lang="en-US">Over allotment period</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_OverAllotmentPeriod" xlink:to="cmiii_OverAllotmentPeriod_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_MaximumNumberOfAdditionalUnitsOfferedForPurchase" xlink:href="cmiii-20260630.xsd#cmiii_MaximumNumberOfAdditionalUnitsOfferedForPurchase"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_MaximumNumberOfAdditionalUnitsOfferedForPurchase_lbl" xml:lang="en-US">Maximum number of additional units offered for purchase</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_MaximumNumberOfAdditionalUnitsOfferedForPurchase" xlink:to="cmiii_MaximumNumberOfAdditionalUnitsOfferedForPurchase_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_CashUnderwritingDiscountPercent" xlink:href="cmiii-20260630.xsd#cmiii_CashUnderwritingDiscountPercent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_CashUnderwritingDiscountPercent_lbl" xml:lang="en-US">Cash underwriting discount percent</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_CashUnderwritingDiscountPercent" xlink:to="cmiii_CashUnderwritingDiscountPercent_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="cmiii_CashUnderwritingDiscountPercent_lbl0" xml:lang="en-US">Underwriting discount percent</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_CashUnderwritingDiscountPercent" xlink:to="cmiii_CashUnderwritingDiscountPercent_lbl0"/>
    <loc xlink:type="locator" xlink:label="cmiii_CashUnderwritingDiscountGrossProceeds" xlink:href="cmiii-20260630.xsd#cmiii_CashUnderwritingDiscountGrossProceeds"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_CashUnderwritingDiscountGrossProceeds_lbl" xml:lang="en-US">Cash underwriting discount gross proceeds</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_CashUnderwritingDiscountGrossProceeds" xlink:to="cmiii_CashUnderwritingDiscountGrossProceeds_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_lbl" xml:lang="en-US">Shares subject forfeiture</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:to="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NumberOfReportableSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NumberOfReportableSegments"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xml:lang="en-US">Number of reportable segment</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NumberOfReportableSegments" xlink:to="us-gaap_NumberOfReportableSegments_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PaymentsForRent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsForRent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PaymentsForRent_lbl" xml:lang="en-US">Payments for Rent</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsForRent" xlink:to="us-gaap_PaymentsForRent_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LongTermDebtAverageAmountOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtAverageAmountOutstanding"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermDebtAverageAmountOutstanding_lbl" xml:lang="en-US">Repaid outstanding amount</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtAverageAmountOutstanding" xlink:to="us-gaap_LongTermDebtAverageAmountOutstanding_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BasisOfAccountingPolicyPolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl" xml:lang="en-US">Basis of Presentation</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:to="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_LiquidityAndCapitalResourcesPolicyPolicyTextBlock" xlink:href="cmiii-20260630.xsd#cmiii_LiquidityAndCapitalResourcesPolicyPolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_LiquidityAndCapitalResourcesPolicyPolicyTextBlock_lbl" xml:lang="en-US">Liquidity and Capital Resources</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_LiquidityAndCapitalResourcesPolicyPolicyTextBlock" xlink:to="cmiii_LiquidityAndCapitalResourcesPolicyPolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_EmergingGrowthCompanyPolicyTextBlock" xlink:href="cmiii-20260630.xsd#cmiii_EmergingGrowthCompanyPolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_EmergingGrowthCompanyPolicyTextBlock_lbl" xml:lang="en-US">Emerging Growth Company Status</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_EmergingGrowthCompanyPolicyTextBlock" xlink:to="cmiii_EmergingGrowthCompanyPolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_UseOfEstimates" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UseOfEstimates"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_UseOfEstimates_lbl" xml:lang="en-US">Use of Estimates</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_UseOfEstimates" xlink:to="us-gaap_UseOfEstimates_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DeferredChargesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredChargesPolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DeferredChargesPolicyTextBlock_lbl" xml:lang="en-US">Deferred Offering Costs</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredChargesPolicyTextBlock" xlink:to="us-gaap_DeferredChargesPolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueOfFinancialInstrumentsPolicy"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueOfFinancialInstrumentsPolicy_lbl" xml:lang="en-US">Fair Value of Financial Instruments</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:to="us-gaap_FairValueOfFinancialInstrumentsPolicy_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_EarningsPerSharePolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerSharePolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EarningsPerSharePolicyTextBlock_lbl" xml:lang="en-US">Net Loss per Class B Ordinary Share</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerSharePolicyTextBlock" xlink:to="us-gaap_EarningsPerSharePolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncomeTaxPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxPolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeTaxPolicyTextBlock_lbl" xml:lang="en-US">Income Taxes</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxPolicyTextBlock" xlink:to="us-gaap_IncomeTaxPolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_lbl" xml:lang="en-US">Share-Based Compensation</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:to="us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_WarrantInstrumentsPolicyPolicyTextBlock" xlink:href="cmiii-20260630.xsd#cmiii_WarrantInstrumentsPolicyPolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_WarrantInstrumentsPolicyPolicyTextBlock_lbl" xml:lang="en-US">Warrant Instruments</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_WarrantInstrumentsPolicyPolicyTextBlock" xlink:to="cmiii_WarrantInstrumentsPolicyPolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xml:lang="en-US">Recent Accounting Pronouncements</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_SponsorMember" xlink:href="cmiii-20260630.xsd#cmiii_SponsorMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_SponsorMember_lbl" xml:lang="en-US">Sponsor [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_SponsorMember" xlink:to="cmiii_SponsorMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SubsequentEventMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SubsequentEventMember_lbl" xml:lang="en-US">Subsequent Event [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventMember" xlink:to="us-gaap_SubsequentEventMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IPOMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IPOMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IPOMember_lbl" xml:lang="en-US">IPO [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IPOMember" xlink:to="us-gaap_IPOMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OverAllotmentOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OverAllotmentOptionMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OverAllotmentOptionMember_lbl" xml:lang="en-US">Over-Allotment Option [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OverAllotmentOptionMember" xlink:to="us-gaap_OverAllotmentOptionMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PrivatePlacementMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrivatePlacementMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PrivatePlacementMember_lbl" xml:lang="en-US">Private Placement [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PrivatePlacementMember" xlink:to="us-gaap_PrivatePlacementMember_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_RepresentativesMember" xlink:href="cmiii-20260630.xsd#cmiii_RepresentativesMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_RepresentativesMember_lbl" xml:lang="en-US">Representatives [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_RepresentativesMember" xlink:to="cmiii_RepresentativesMember_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_PublicWarrantsMember" xlink:href="cmiii-20260630.xsd#cmiii_PublicWarrantsMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_PublicWarrantsMember_lbl" xml:lang="en-US">Public Warrants [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_PublicWarrantsMember" xlink:to="cmiii_PublicWarrantsMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_WarrantMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WarrantMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_WarrantMember_lbl" xml:lang="en-US">Warrant [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WarrantMember" xlink:to="us-gaap_WarrantMember_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_PrivatePlacementUnitsMember" xlink:href="cmiii-20260630.xsd#cmiii_PrivatePlacementUnitsMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_PrivatePlacementUnitsMember_lbl" xml:lang="en-US">Private Placement Units [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_PrivatePlacementUnitsMember" xlink:to="cmiii_PrivatePlacementUnitsMember_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_PrivatePlacementWarrantsMember" xlink:href="cmiii-20260630.xsd#cmiii_PrivatePlacementWarrantsMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_PrivatePlacementWarrantsMember_lbl" xml:lang="en-US">Private Placement Warrants [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_PrivatePlacementWarrantsMember" xlink:to="cmiii_PrivatePlacementWarrantsMember_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_FounderShareMember" xlink:href="cmiii-20260630.xsd#cmiii_FounderShareMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_FounderShareMember_lbl" xml:lang="en-US">Founder Shares [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_FounderShareMember" xlink:to="cmiii_FounderShareMember_lbl"/>
    <loc xlink:type="locator" xlink:label="srt_DirectorMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_DirectorMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_DirectorMember_lbl" xml:lang="en-US">Director [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_DirectorMember" xlink:to="srt_DirectorMember_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_RelatedPartyPromissoryNoteLoanMember" xlink:href="cmiii-20260630.xsd#cmiii_RelatedPartyPromissoryNoteLoanMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_RelatedPartyPromissoryNoteLoanMember_lbl" xml:lang="en-US">Related Party Promissory Note Loan [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_RelatedPartyPromissoryNoteLoanMember" xlink:to="cmiii_RelatedPartyPromissoryNoteLoanMember_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_PromissoryNoteMember" xlink:href="cmiii-20260630.xsd#cmiii_PromissoryNoteMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_PromissoryNoteMember_lbl" xml:lang="en-US">Promissory Note [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_PromissoryNoteMember" xlink:to="cmiii_PromissoryNoteMember_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_AdministrativeServicesAgreementMember" xlink:href="cmiii-20260630.xsd#cmiii_AdministrativeServicesAgreementMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_AdministrativeServicesAgreementMember_lbl" xml:lang="en-US">Administrative Services Agreement [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_AdministrativeServicesAgreementMember" xlink:to="cmiii_AdministrativeServicesAgreementMember_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_WorkingCapitalLoansMember" xlink:href="cmiii-20260630.xsd#cmiii_WorkingCapitalLoansMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="cmiii_WorkingCapitalLoansMember_lbl" xml:lang="en-US">Working Capital Loans [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_WorkingCapitalLoansMember" xlink:to="cmiii_WorkingCapitalLoansMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RelatedPartyMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RelatedPartyMember_lbl" xml:lang="en-US">Related Party [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyMember" xlink:to="us-gaap_RelatedPartyMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ClassOfStockDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ClassOfStockDomain_lbl" xml:lang="en-US">Class of Stock [Domain]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="us-gaap_ClassOfStockDomain_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementTable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementTable_lbl" xml:lang="en-US">Statement [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementTable" xlink:to="us-gaap_StatementTable_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_StatementLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementLineItems"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementLineItems_lbl" xml:lang="en-US">Statement [Line Items]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_StatementLineItems_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_EquityComponentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityComponentDomain"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityComponentDomain_lbl" xml:lang="en-US">Equity Component [Domain]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityComponentDomain" xlink:to="us-gaap_EquityComponentDomain_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockNameOfTransactionDomain"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xml:lang="en-US">Sale of Stock [Domain]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="us-gaap_SaleOfStockNameOfTransactionDomain_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RelatedPartyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyDomain"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyDomain_lbl" xml:lang="en-US">Related and Nonrelated Parties [Domain]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="us-gaap_RelatedPartyDomain_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SubsequentEventTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventTypeDomain"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventTypeDomain_lbl" xml:lang="en-US">Subsequent Event Type [Domain]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventTypeDomain" xlink:to="us-gaap_SubsequentEventTypeDomain_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_OrganizationandBusinessOperationsDetailsTable" xlink:href="cmiii-20260630.xsd#cmiii_OrganizationandBusinessOperationsDetailsTable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_OrganizationandBusinessOperationsDetailsTable_lbl" xml:lang="en-US">Organization and Business Operations (Details) [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_OrganizationandBusinessOperationsDetailsTable" xlink:to="cmiii_OrganizationandBusinessOperationsDetailsTable_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_OrganizationandBusinessOperationsDetailsLineItems" xlink:href="cmiii-20260630.xsd#cmiii_OrganizationandBusinessOperationsDetailsLineItems"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_OrganizationandBusinessOperationsDetailsLineItems_lbl" xml:lang="en-US">Organization and Business Operations (Details) [Line Items]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_OrganizationandBusinessOperationsDetailsLineItems" xlink:to="cmiii_OrganizationandBusinessOperationsDetailsLineItems_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_SignificantAccountingPoliciesDetailsTable" xlink:href="cmiii-20260630.xsd#cmiii_SignificantAccountingPoliciesDetailsTable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_SignificantAccountingPoliciesDetailsTable_lbl" xml:lang="en-US">Significant Accounting Policies (Details) [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_SignificantAccountingPoliciesDetailsTable" xlink:to="cmiii_SignificantAccountingPoliciesDetailsTable_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_SignificantAccountingPoliciesDetailsLineItems" xlink:href="cmiii-20260630.xsd#cmiii_SignificantAccountingPoliciesDetailsLineItems"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_SignificantAccountingPoliciesDetailsLineItems_lbl" xml:lang="en-US">Significant Accounting Policies (Details) [Line Items]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_SignificantAccountingPoliciesDetailsLineItems" xlink:to="cmiii_SignificantAccountingPoliciesDetailsLineItems_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ClassOfWarrantOrRightDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfWarrantOrRightDomain"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ClassOfWarrantOrRightDomain_lbl" xml:lang="en-US">Class of Warrant or Right [Domain]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ClassOfWarrantOrRightDomain" xlink:to="us-gaap_ClassOfWarrantOrRightDomain_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_InitialPublicOfferingDetailsTable" xlink:href="cmiii-20260630.xsd#cmiii_InitialPublicOfferingDetailsTable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_InitialPublicOfferingDetailsTable_lbl" xml:lang="en-US">Initial Public Offering (Details) [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_InitialPublicOfferingDetailsTable" xlink:to="cmiii_InitialPublicOfferingDetailsTable_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_InitialPublicOfferingDetailsLineItems" xlink:href="cmiii-20260630.xsd#cmiii_InitialPublicOfferingDetailsLineItems"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_InitialPublicOfferingDetailsLineItems_lbl" xml:lang="en-US">Initial Public Offering (Details) [Line Items]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_InitialPublicOfferingDetailsLineItems" xlink:to="cmiii_InitialPublicOfferingDetailsLineItems_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_PrivatePlacementDetailsTable" xlink:href="cmiii-20260630.xsd#cmiii_PrivatePlacementDetailsTable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_PrivatePlacementDetailsTable_lbl" xml:lang="en-US">Private Placement (Details) [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_PrivatePlacementDetailsTable" xlink:to="cmiii_PrivatePlacementDetailsTable_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_PrivatePlacementDetailsLineItems" xlink:href="cmiii-20260630.xsd#cmiii_PrivatePlacementDetailsLineItems"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_PrivatePlacementDetailsLineItems_lbl" xml:lang="en-US">Private Placement (Details) [Line Items]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_PrivatePlacementDetailsLineItems" xlink:to="cmiii_PrivatePlacementDetailsLineItems_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RelatedPartyTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionDomain"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionDomain_lbl" xml:lang="en-US">Related Party Transaction [Domain]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionDomain" xlink:to="us-gaap_RelatedPartyTransactionDomain_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentNameDomain_lbl" xml:lang="en-US">Debt Instrument, Name [Domain]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentNameDomain" xlink:to="us-gaap_DebtInstrumentNameDomain_lbl"/>
    <loc xlink:type="locator" xlink:label="srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_TitleOfIndividualWithRelationshipToEntityDomain"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_TitleOfIndividualWithRelationshipToEntityDomain_lbl" xml:lang="en-US">Title and Position [Domain]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:to="srt_TitleOfIndividualWithRelationshipToEntityDomain_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_RelatedPartyTransactionsDetailsTable" xlink:href="cmiii-20260630.xsd#cmiii_RelatedPartyTransactionsDetailsTable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_RelatedPartyTransactionsDetailsTable_lbl" xml:lang="en-US">Related Party Transactions (Details) [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_RelatedPartyTransactionsDetailsTable" xlink:to="cmiii_RelatedPartyTransactionsDetailsTable_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_RelatedPartyTransactionsDetailsLineItems" xlink:href="cmiii-20260630.xsd#cmiii_RelatedPartyTransactionsDetailsLineItems"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_RelatedPartyTransactionsDetailsLineItems_lbl" xml:lang="en-US">Related Party Transactions (Details) [Line Items]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_RelatedPartyTransactionsDetailsLineItems" xlink:to="cmiii_RelatedPartyTransactionsDetailsLineItems_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_CommitmentsandContingenciesDetailsTable" xlink:href="cmiii-20260630.xsd#cmiii_CommitmentsandContingenciesDetailsTable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_CommitmentsandContingenciesDetailsTable_lbl" xml:lang="en-US">Commitments and Contingencies (Details) [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_CommitmentsandContingenciesDetailsTable" xlink:to="cmiii_CommitmentsandContingenciesDetailsTable_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_CommitmentsandContingenciesDetailsLineItems" xlink:href="cmiii-20260630.xsd#cmiii_CommitmentsandContingenciesDetailsLineItems"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_CommitmentsandContingenciesDetailsLineItems_lbl" xml:lang="en-US">Commitments and Contingencies (Details) [Line Items]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_CommitmentsandContingenciesDetailsLineItems" xlink:to="cmiii_CommitmentsandContingenciesDetailsLineItems_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_ShareholdersDeficitEquityDetailsTable" xlink:href="cmiii-20260630.xsd#cmiii_ShareholdersDeficitEquityDetailsTable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_ShareholdersDeficitEquityDetailsTable_lbl" xml:lang="en-US">Shareholder&#8217;s (Deficit) Equity (Details) [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ShareholdersDeficitEquityDetailsTable" xlink:to="cmiii_ShareholdersDeficitEquityDetailsTable_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_ShareholdersDeficitEquityDetailsLineItems" xlink:href="cmiii-20260630.xsd#cmiii_ShareholdersDeficitEquityDetailsLineItems"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_ShareholdersDeficitEquityDetailsLineItems_lbl" xml:lang="en-US">Shareholder&#8217;s (Deficit) Equity (Details) [Line Items]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ShareholdersDeficitEquityDetailsLineItems" xlink:to="cmiii_ShareholdersDeficitEquityDetailsLineItems_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_SubsequentEventsDetailsTable" xlink:href="cmiii-20260630.xsd#cmiii_SubsequentEventsDetailsTable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_SubsequentEventsDetailsTable_lbl" xml:lang="en-US">Subsequent Events (Details) [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_SubsequentEventsDetailsTable" xlink:to="cmiii_SubsequentEventsDetailsTable_lbl"/>
    <loc xlink:type="locator" xlink:label="cmiii_SubsequentEventsDetailsLineItems" xlink:href="cmiii-20260630.xsd#cmiii_SubsequentEventsDetailsLineItems"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_SubsequentEventsDetailsLineItems_lbl" xml:lang="en-US">Subsequent Events (Details) [Line Items]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_SubsequentEventsDetailsLineItems" xlink:to="cmiii_SubsequentEventsDetailsLineItems_lbl"/>
    <loc xlink:type="locator" xlink:label="ecd_TradingArrByIndTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TradingArrByIndTable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="ecd_TradingArrByIndTable_lbl" xml:lang="en-US">Trading Arrangements, by Individual [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ecd_TradingArrByIndTable" xlink:to="ecd_TradingArrByIndTable_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_AccruedOfferingCostsCurrent_lbl0" xml:lang="en-US">Accrued offering costs.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_AccruedOfferingCostsCurrent" xlink:to="cmiii_AccruedOfferingCostsCurrent_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_CashUnderwritingDiscountGrossProceeds_lbl0" xml:lang="en-US">Represent the amount of cash underwriting discount gross proceeds.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_CashUnderwritingDiscountGrossProceeds" xlink:to="cmiii_CashUnderwritingDiscountGrossProceeds_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_CashUnderwritingDiscountPercent_lbl1" xml:lang="en-US">Cash underwriting discount percent.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_CashUnderwritingDiscountPercent" xlink:to="cmiii_CashUnderwritingDiscountPercent_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightStockPriceTrigger_lbl0" xml:lang="en-US">Price of the entity&apos;s common stock which would be required to be attained to trigger the redemption of warrants.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightStockPriceTrigger" xlink:to="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightStockPriceTrigger_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightThresholdCommencementPeriodAfterInitialBusinessCombinationClosing_lbl0" xml:lang="en-US">Threshold period for commencing redemption of warrants after completion of business combination.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightThresholdCommencementPeriodAfterInitialBusinessCombinationClosing" xlink:to="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightThresholdCommencementPeriodAfterInitialBusinessCombinationClosing_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightThresholdConsecutiveTradingDays_lbl0" xml:lang="en-US">Threshold number of specified consecutive trading days for stock price trigger considered for redemption of warrants.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightThresholdConsecutiveTradingDays" xlink:to="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightThresholdConsecutiveTradingDays_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_ClassOfWarrantOrRightRedemptionWarrantOrRightThresholdTradingDays_lbl0" xml:lang="en-US">Threshold number of specified trading days for stock price trigger considered for redemption of warrants.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ClassOfWarrantOrRightRedemptionWarrantOrRightThresholdTradingDays" xlink:to="cmiii_ClassOfWarrantOrRightRedemptionWarrantOrRightThresholdTradingDays_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_ClassOfWarrantRightThresholdPriorWrittenNoticePeriodForRedemptionOfWarrants_lbl0" xml:lang="en-US">Threshold number of days of prior written notice required for redemption of warrants.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ClassOfWarrantRightThresholdPriorWrittenNoticePeriodForRedemptionOfWarrants" xlink:to="cmiii_ClassOfWarrantRightThresholdPriorWrittenNoticePeriodForRedemptionOfWarrants_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_DeferredOfferingCostsIncludedInAccruedOfferingCosts_lbl0" xml:lang="en-US">The amount of deferred offering costs included in accrued offering costs.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_DeferredOfferingCostsIncludedInAccruedOfferingCosts" xlink:to="cmiii_DeferredOfferingCostsIncludedInAccruedOfferingCosts_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_DeferredOfferingCostsPaidThroughIPOPromissoryNote_lbl0" xml:lang="en-US">The amount of deferred offering costs paid through IPO promissory note.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_DeferredOfferingCostsPaidThroughIPOPromissoryNote" xlink:to="cmiii_DeferredOfferingCostsPaidThroughIPOPromissoryNote_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_DeferredOfferingCostsPaidThroughPrepaidExpenses_lbl0" xml:lang="en-US">The amount of deferred offering costs paid through prepaid expenses.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_DeferredOfferingCostsPaidThroughPrepaidExpenses" xlink:to="cmiii_DeferredOfferingCostsPaidThroughPrepaidExpenses_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_EmergingGrowthCompanyPolicyTextBlock_lbl0" xml:lang="en-US">Disclosure of accounting policy for emerging growth company.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_EmergingGrowthCompanyPolicyTextBlock" xlink:to="cmiii_EmergingGrowthCompanyPolicyTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_EntityPricePerUnit_lbl0" xml:lang="en-US">Amount of entity per unit.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_EntityPricePerUnit" xlink:to="cmiii_EntityPricePerUnit_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_ExercisableAfterTheCompletionOfTheInitialBusinessCombination_lbl0" xml:lang="en-US">Exercisable after the completion of the initial business combination.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ExercisableAfterTheCompletionOfTheInitialBusinessCombination" xlink:to="cmiii_ExercisableAfterTheCompletionOfTheInitialBusinessCombination_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_FairValueAmountIssued_lbl0" xml:lang="en-US">Fair value amount issued.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_FairValueAmountIssued" xlink:to="cmiii_FairValueAmountIssued_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_GeneralAndAdministrativeCostsPaidThroughIPOPromissoryNote_lbl0" xml:lang="en-US">The amount of general and administrative costs paid through IPO promissory note.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_GeneralAndAdministrativeCostsPaidThroughIPOPromissoryNote" xlink:to="cmiii_GeneralAndAdministrativeCostsPaidThroughIPOPromissoryNote_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_InitialBusinessCombination_lbl0" xml:lang="en-US">Percentage of initial business combination.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_InitialBusinessCombination" xlink:to="cmiii_InitialBusinessCombination_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_InitialBusinessCombinationExercisableCompletionTerm_lbl0" xml:lang="en-US">Initial business combination exercisable completion term.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_InitialBusinessCombinationExercisableCompletionTerm" xlink:to="cmiii_InitialBusinessCombinationExercisableCompletionTerm_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_InitialBusinessCombinationExercisableTerm_lbl0" xml:lang="en-US">Initial Business Combination exercisable term.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_InitialBusinessCombinationExercisableTerm" xlink:to="cmiii_InitialBusinessCombinationExercisableTerm_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_InitialPublicOfferingTextBlock_lbl0" xml:lang="en-US">Disclosure for initial public offering.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_InitialPublicOfferingTextBlock" xlink:to="cmiii_InitialPublicOfferingTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_InterestEquivalentAggregateShares_lbl0" xml:lang="en-US">Interest equivalent aggregate shares.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_InterestEquivalentAggregateShares" xlink:to="cmiii_InterestEquivalentAggregateShares_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_LiquidityAndCapitalResourcesPolicyPolicyTextBlock_lbl0" xml:lang="en-US">Disclosure of accounting policy for liquidity and capital resources.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_LiquidityAndCapitalResourcesPolicyPolicyTextBlock" xlink:to="cmiii_LiquidityAndCapitalResourcesPolicyPolicyTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_MarketableValuePerShare_lbl0" xml:lang="en-US">Per share of marketable value.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_MarketableValuePerShare" xlink:to="cmiii_MarketableValuePerShare_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_MaximumInterestEarnedFromTrustAccountUsedForDissolution_lbl0" xml:lang="en-US">Maximum amount of interest earned from trust account used for dissolution expense.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_MaximumInterestEarnedFromTrustAccountUsedForDissolution" xlink:to="cmiii_MaximumInterestEarnedFromTrustAccountUsedForDissolution_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_MaximumNumberOfAdditionalUnitsOfferedForPurchase_lbl0" xml:lang="en-US">Maximum number of additional units offered to purchase by the underwriters during the option period.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_MaximumNumberOfAdditionalUnitsOfferedForPurchase" xlink:to="cmiii_MaximumNumberOfAdditionalUnitsOfferedForPurchase_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_MaximumNumberOfSharesSubjectToForfeiture_lbl0" xml:lang="en-US">Maximum number of shares that may be surrendered to the extent to which the underwriters&apos; over-allotment option is exercised.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_MaximumNumberOfSharesSubjectToForfeiture" xlink:to="cmiii_MaximumNumberOfSharesSubjectToForfeiture_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_MaximumPeriodToCompleteTheInitialBusinessCombinationAfterInitialPublicOffering_lbl0" xml:lang="en-US">Maximum period to complete the initial business combination after initial public offering, in PnYnMnDTnHnMnS&apos; format, for example, &apos;P1Y5M13D&apos; represents the reported fact of one year, five months, and thirteen days.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_MaximumPeriodToCompleteTheInitialBusinessCombinationAfterInitialPublicOffering" xlink:to="cmiii_MaximumPeriodToCompleteTheInitialBusinessCombinationAfterInitialPublicOffering_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_NetProceedsFromIssuanceInitialPublicOffering_lbl1" xml:lang="en-US">The amount of proceeds from issuance initial public offering.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_NetProceedsFromIssuanceInitialPublicOffering" xlink:to="cmiii_NetProceedsFromIssuanceInitialPublicOffering_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_NumberOfOrdinaryShares_lbl0" xml:lang="en-US">Number of ordinary shares.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_NumberOfOrdinaryShares" xlink:to="cmiii_NumberOfOrdinaryShares_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_NumberOfWarrants_lbl0" xml:lang="en-US">Number of warrants.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_NumberOfWarrants" xlink:to="cmiii_NumberOfWarrants_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_OtherOfferingCosts_lbl0" xml:lang="en-US">Represents the amount of other offering costs.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_OtherOfferingCosts" xlink:to="cmiii_OtherOfferingCosts_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_OverAllotmentPeriod_lbl0" xml:lang="en-US">Period to exercise the over-allotment option, in &apos;PnYnMnDTnHnMnS&apos; format, for example, &apos;P1Y5M13D&apos; represents reported fact of one year, five months, and thirteen days.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_OverAllotmentPeriod" xlink:to="cmiii_OverAllotmentPeriod_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_PercentOfPublicSharesToBeRedeemedIfBusinessCombinationNotCompleted_lbl0" xml:lang="en-US">Percentage of public shares to be redeemed if the entity has not completed the business combination within the given time frame.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_PercentOfPublicSharesToBeRedeemedIfBusinessCombinationNotCompleted" xlink:to="cmiii_PercentOfPublicSharesToBeRedeemedIfBusinessCombinationNotCompleted_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_PrepaidServicesPaidThroughIPOPromissoryNote_lbl0" xml:lang="en-US">The amount of prepaid services paid through IPO promissory note.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_PrepaidServicesPaidThroughIPOPromissoryNote" xlink:to="cmiii_PrepaidServicesPaidThroughIPOPromissoryNote_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_PrivatePlacementTextBlock_lbl0" xml:lang="en-US">The entire disclosure on information about initial private placement.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_PrivatePlacementTextBlock" xlink:to="cmiii_PrivatePlacementTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_RedeemPublicSharesPercentage_lbl0" xml:lang="en-US">Percentage of redeem public shares.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_RedeemPublicSharesPercentage" xlink:to="cmiii_RedeemPublicSharesPercentage_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_RelatedPartyTransactionMonthlyAdministrativeExpenses_lbl0" xml:lang="en-US">Amount of monthly administrative expenses agreed with the related party under the agreement.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_RelatedPartyTransactionMonthlyAdministrativeExpenses" xlink:to="cmiii_RelatedPartyTransactionMonthlyAdministrativeExpenses_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_ThresholdFairMarketValueOfTargetBusinessAsPercentOfNetBalanceInTrustAccount_lbl0" xml:lang="en-US">Threshold fair market value of target businesses as a percent of net balance in trust account.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ThresholdFairMarketValueOfTargetBusinessAsPercentOfNetBalanceInTrustAccount" xlink:to="cmiii_ThresholdFairMarketValueOfTargetBusinessAsPercentOfNetBalanceInTrustAccount_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_ThresholdNumberOfDaysForFilingRegistrationStatementAfterBusinessCombinationClosing_lbl0" xml:lang="en-US">Threshold period for filing registration statement after closing of business combination.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ThresholdNumberOfDaysForFilingRegistrationStatementAfterBusinessCombinationClosing" xlink:to="cmiii_ThresholdNumberOfDaysForFilingRegistrationStatementAfterBusinessCombinationClosing_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_ThresholdNumberOfDaysForRestrictionToExerciseWarrantsFromCompletionOfInitialBusinessCombination_lbl0" xml:lang="en-US">Threshold number of days for restriction to exercise warrants from completion of business combination.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ThresholdNumberOfDaysForRestrictionToExerciseWarrantsFromCompletionOfInitialBusinessCombination" xlink:to="cmiii_ThresholdNumberOfDaysForRestrictionToExerciseWarrantsFromCompletionOfInitialBusinessCombination_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_ThresholdOwnershipPercentageInTargetCompany_lbl0" xml:lang="en-US">Percentage of ownership interest to be acquired.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ThresholdOwnershipPercentageInTargetCompany" xlink:to="cmiii_ThresholdOwnershipPercentageInTargetCompany_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_ThresholdPeriodForMakingRegistrationStatementEffectiveAfterBusinessCombinationClosing_lbl0" xml:lang="en-US">Threshold period for making the registration statement effective after closing of initial business combination, in &apos;PnYnMnDTnHnMnS&apos; format, for example, &apos;P1Y5M13D&apos; represents reported fact of one year, five months, and thirteen days.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ThresholdPeriodForMakingRegistrationStatementEffectiveAfterBusinessCombinationClosing" xlink:to="cmiii_ThresholdPeriodForMakingRegistrationStatementEffectiveAfterBusinessCombinationClosing_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_TradingDaysForComputationOfFairMarketValue_lbl0" xml:lang="en-US">Number of trading days used to compute the average closing price for determining fair market value under the warrant agreement.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_TradingDaysForComputationOfFairMarketValue" xlink:to="cmiii_TradingDaysForComputationOfFairMarketValue_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_TransactionCosts_lbl0" xml:lang="en-US">The amount of transaction costs.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_TransactionCosts" xlink:to="cmiii_TransactionCosts_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_TrustValueActualPerShare_lbl0" xml:lang="en-US">The per-share amount remaining in the trust account at liquidation, which may be less than $10 and limits the sponsor&apos;s indemnity.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_TrustValueActualPerShare" xlink:to="cmiii_TrustValueActualPerShare_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_UnitsIssuedDuringPeriodNewIssues_lbl0" xml:lang="en-US">The number of units issued during the period.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_UnitsIssuedDuringPeriodNewIssues" xlink:to="cmiii_UnitsIssuedDuringPeriodNewIssues_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_UnitsIssuedDuringPeriodSharesNewIssues_lbl3" xml:lang="en-US">Number of new units issued during the period.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_UnitsIssuedDuringPeriodSharesNewIssues" xlink:to="cmiii_UnitsIssuedDuringPeriodSharesNewIssues_lbl3"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_WarrantInstrumentsPolicyPolicyTextBlock_lbl0" xml:lang="en-US">Disclosure of accounting policy for warrant instruments.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_WarrantInstrumentsPolicyPolicyTextBlock" xlink:to="cmiii_WarrantInstrumentsPolicyPolicyTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_WorkingCapitalDeficit_lbl0" xml:lang="en-US">The amount of working capital deficit.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_WorkingCapitalDeficit" xlink:to="cmiii_WorkingCapitalDeficit_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_WorkingCapitalLoans_lbl0" xml:lang="en-US">The amount of working capital loans.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_WorkingCapitalLoans" xlink:to="cmiii_WorkingCapitalLoans_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="cmiii_YearOfInception_lbl0" xml:lang="en-US">Year of inception.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_YearOfInception" xlink:to="cmiii_YearOfInception_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_CityAreaCode_lbl0" xml:lang="en-US">City Area Code</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_CityAreaCode" xlink:to="dei_CityAreaCode_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsForRent_lbl0" xml:lang="en-US">Payments for Rent</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsForRent" xlink:to="us-gaap_PaymentsForRent_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_UseOfEstimates_lbl0" xml:lang="en-US">Use of Estimates, Policy [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_UseOfEstimates" xlink:to="us-gaap_UseOfEstimates_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensationForfeited_lbl0" xml:lang="en-US">Shares Issued, Shares, Share-Based Payment Arrangement, Forfeited</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensationForfeited" xlink:to="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensationForfeited_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityAddressCityOrTown_lbl0" xml:lang="en-US">Entity Address, City or Town</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressCityOrTown" xlink:to="dei_EntityAddressCityOrTown_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntitySmallBusiness_lbl0" xml:lang="en-US">Entity Small Business</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntitySmallBusiness" xlink:to="dei_EntitySmallBusiness_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_ThresholdPeriodForMakingRegistrationStatementEffectiveAfterBusinessCombinationClosing_lbl1" xml:lang="en-US">Threshold Period For Making Registration Statement Effective After Business Combination Closing</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ThresholdPeriodForMakingRegistrationStatementEffectiveAfterBusinessCombinationClosing" xlink:to="cmiii_ThresholdPeriodForMakingRegistrationStatementEffectiveAfterBusinessCombinationClosing_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsAbstract_lbl0" xml:lang="en-US">Assets [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsAbstract" xlink:to="us-gaap_AssetsAbstract_lbl0"/>
    <loc xlink:type="locator" xlink:label="cmiii_InitialPublicOfferingAbstract" xlink:href="cmiii-20260630.xsd#cmiii_InitialPublicOfferingAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_InitialPublicOfferingAbstract_lbl" xml:lang="en-US">Initial Public Offering Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_InitialPublicOfferingAbstract" xlink:to="cmiii_InitialPublicOfferingAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_AccruedOfferingCostsCurrent_lbl1" xml:lang="en-US">Accrued Offering Costs Current</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_AccruedOfferingCostsCurrent" xlink:to="cmiii_AccruedOfferingCostsCurrent_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EarningsPerShareDiluted_lbl0" xml:lang="en-US">Earnings Per Share, Diluted</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerShareDiluted" xlink:to="us-gaap_EarningsPerShareDiluted_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RetainedEarningsMember_lbl0" xml:lang="en-US">Retained Earnings [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RetainedEarningsMember" xlink:to="us-gaap_RetainedEarningsMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl0" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentConvertibleConversionPrice1_lbl0" xml:lang="en-US">Debt Instrument, Convertible, Conversion Price</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentConvertibleConversionPrice1" xlink:to="us-gaap_DebtInstrumentConvertibleConversionPrice1_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockValue_lbl0" xml:lang="en-US">Common Stock, Value, Issued</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockValue" xlink:to="us-gaap_CommonStockValue_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="ecd_NonRule10b51ArrTrmntdFlag_lbl0" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated [Flag]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ecd_NonRule10b51ArrTrmntdFlag" xlink:to="ecd_NonRule10b51ArrTrmntdFlag_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_PublicWarrantsMember_lbl0" xml:lang="en-US">Public Warrants Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_PublicWarrantsMember" xlink:to="cmiii_PublicWarrantsMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_CashUnderwritingDiscountGrossProceeds_lbl1" xml:lang="en-US">Cash Underwriting Discount Gross Proceeds</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_CashUnderwritingDiscountGrossProceeds" xlink:to="cmiii_CashUnderwritingDiscountGrossProceeds_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IPOMember_lbl0" xml:lang="en-US">IPO [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IPOMember" xlink:to="us-gaap_IPOMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtConversionOriginalDebtAmount1_lbl0" xml:lang="en-US">Debt Conversion, Original Debt, Amount</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtConversionOriginalDebtAmount1" xlink:to="us-gaap_DebtConversionOriginalDebtAmount1_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsForUnderwritingExpense_lbl0" xml:lang="en-US">Payments for Underwriting Expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsForUnderwritingExpense" xlink:to="us-gaap_PaymentsForUnderwritingExpense_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_FairValueAmountIssued_lbl1" xml:lang="en-US">Fair Value Amount Issued</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_FairValueAmountIssued" xlink:to="cmiii_FairValueAmountIssued_lbl1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract_lbl" xml:lang="en-US">Statement of Stockholders&apos; Equity [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="us-gaap_StatementOfStockholdersEquityAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl1" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_LocalPhoneNumber_lbl0" xml:lang="en-US">Local Phone Number</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_LocalPhoneNumber" xlink:to="dei_LocalPhoneNumber_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl0" xml:lang="en-US">Basis of Accounting, Policy [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:to="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl1" xml:lang="en-US">Stock Issued During Period, Value, New Issues</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:to="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_OtherOfferingCosts_lbl1" xml:lang="en-US">Other Offering Costs</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_OtherOfferingCosts" xlink:to="cmiii_OtherOfferingCosts_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_RedeemableWarrantsEachWholeWarrantExercisableForOneClassAOrdinaryShareAtAnExercisePriceOf1150PerShareMember_lbl0" xml:lang="en-US">Redeemable Warrants Each Whole Warrant Exercisable For One Class AOrdinary Share At An Exercise Price Of1150 Per Share Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_RedeemableWarrantsEachWholeWarrantExercisableForOneClassAOrdinaryShareAtAnExercisePriceOf1150PerShareMember" xlink:to="cmiii_RedeemableWarrantsEachWholeWarrantExercisableForOneClassAOrdinaryShareAtAnExercisePriceOf1150PerShareMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl0" xml:lang="en-US">Entity Common Stock, Shares Outstanding</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityCommonStockSharesOutstanding" xlink:to="dei_EntityCommonStockSharesOutstanding_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl1" xml:lang="en-US">Stock Issued During Period, Shares, New Issues</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:to="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeStatementAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeStatementAbstract_lbl" xml:lang="en-US">Income Statement [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeStatementAbstract" xlink:to="us-gaap_IncomeStatementAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl0" xml:lang="en-US">New Accounting Pronouncements, Policy [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_MaximumInterestEarnedFromTrustAccountUsedForDissolution_lbl1" xml:lang="en-US">Maximum Interest Earned From Trust Account Used For Dissolution</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_MaximumInterestEarnedFromTrustAccountUsedForDissolution" xlink:to="cmiii_MaximumInterestEarnedFromTrustAccountUsedForDissolution_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_Security12bTitle_lbl0" xml:lang="en-US">Title of 12(b) Security</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_Security12bTitle" xlink:to="dei_Security12bTitle_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl0" xml:lang="en-US">Segment Reporting [Table Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:to="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdditionalPaidInCapital_lbl0" xml:lang="en-US">Additional Paid in Capital</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdditionalPaidInCapital" xlink:to="us-gaap_AdditionalPaidInCapital_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EarningsPerShareBasic_lbl0" xml:lang="en-US">Earnings Per Share, Basic</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerShareBasic" xlink:to="us-gaap_EarningsPerShareBasic_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProfitLoss_lbl0" xml:lang="en-US">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProfitLoss" xlink:to="us-gaap_ProfitLoss_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Assets_lbl0" xml:lang="en-US">Assets</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Assets" xlink:to="us-gaap_Assets_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquityAbstract_lbl0" xml:lang="en-US">Equity, Attributable to Parent [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityAbstract" xlink:to="us-gaap_StockholdersEquityAbstract_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PrepaidExpenseCurrent_lbl0" xml:lang="en-US">Prepaid Expense, Current</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PrepaidExpenseCurrent" xlink:to="us-gaap_PrepaidExpenseCurrent_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl0" xml:lang="en-US">Subsequent Events [Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventsTextBlock" xlink:to="us-gaap_SubsequentEventsTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityAddressStateOrProvince_lbl0" xml:lang="en-US">Entity Address, State or Province</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressStateOrProvince" xlink:to="dei_EntityAddressStateOrProvince_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_DeferredOfferingCostsPaidThroughIPOPromissoryNote_lbl1" xml:lang="en-US">Deferred Offering Costs Paid Through IPOPromissory Note</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_DeferredOfferingCostsPaidThroughIPOPromissoryNote" xlink:to="cmiii_DeferredOfferingCostsPaidThroughIPOPromissoryNote_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="ecd_Rule10b51ArrTrmntdFlag_lbl0" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated [Flag]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ecd_Rule10b51ArrTrmntdFlag" xlink:to="ecd_Rule10b51ArrTrmntdFlag_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityShellCompany_lbl0" xml:lang="en-US">Entity Shell Company</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityShellCompany" xlink:to="dei_EntityShellCompany_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_SecurityExchangeName_lbl0" xml:lang="en-US">Security Exchange Name</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_SecurityExchangeName" xlink:to="dei_SecurityExchangeName_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl0" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_TrustValueActualPerShare_lbl1" xml:lang="en-US">Trust Value Actual Per Share</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_TrustValueActualPerShare" xlink:to="cmiii_TrustValueActualPerShare_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_TradingDaysForComputationOfFairMarketValue_lbl1" xml:lang="en-US">Trading Days For Computation Of Fair Market Value</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_TradingDaysForComputationOfFairMarketValue" xlink:to="cmiii_TradingDaysForComputationOfFairMarketValue_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl0" xml:lang="en-US">Common Stock, Shares, Outstanding</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesOutstanding" xlink:to="us-gaap_CommonStockSharesOutstanding_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl0" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_OverAllotmentPeriod_lbl1" xml:lang="en-US">Over Allotment Period</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_OverAllotmentPeriod" xlink:to="cmiii_OverAllotmentPeriod_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SharesIssued_lbl1" xml:lang="en-US">Shares, Issued</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharesIssued" xlink:to="us-gaap_SharesIssued_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_lbl0" xml:lang="en-US">Share-Based Payment Arrangement [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:to="us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_lbl0" xml:lang="en-US">Shares Issued, Shares, Share-Based Payment Arrangement, after Forfeiture</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:to="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl0" xml:lang="en-US">Preferred Stock, Shares Outstanding</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockSharesOutstanding" xlink:to="us-gaap_PreferredStockSharesOutstanding_lbl0"/>
    <loc xlink:type="locator" xlink:label="cmiii_ScheduleOfCompanyPerformanceAndMakingKeyDecisionsAbstract" xlink:href="cmiii-20260630.xsd#cmiii_ScheduleOfCompanyPerformanceAndMakingKeyDecisionsAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_ScheduleOfCompanyPerformanceAndMakingKeyDecisionsAbstract_lbl" xml:lang="en-US">Schedule Of Company Performance And Making Key Decisions Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ScheduleOfCompanyPerformanceAndMakingKeyDecisionsAbstract" xlink:to="cmiii_ScheduleOfCompanyPerformanceAndMakingKeyDecisionsAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_WarrantsAndRightsOutstandingTerm_lbl0" xml:lang="en-US">Warrants and Rights Outstanding, Term</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WarrantsAndRightsOutstandingTerm" xlink:to="us-gaap_WarrantsAndRightsOutstandingTerm_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilities_lbl0" xml:lang="en-US">Increase (Decrease) in Accrued Liabilities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:to="us-gaap_IncreaseDecreaseInAccruedLiabilities_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_MarketableValuePerShare_lbl1" xml:lang="en-US">Marketable Value Per Share</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_MarketableValuePerShare" xlink:to="cmiii_MarketableValuePerShare_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityIncorporationStateCountryCode_lbl0" xml:lang="en-US">Entity Incorporation, State or Country Code</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityIncorporationStateCountryCode" xlink:to="dei_EntityIncorporationStateCountryCode_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityAddressAddressLine1_lbl0" xml:lang="en-US">Entity Address, Address Line One</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressAddressLine1" xlink:to="dei_EntityAddressAddressLine1_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeTaxPolicyTextBlock_lbl0" xml:lang="en-US">Income Tax, Policy [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxPolicyTextBlock" xlink:to="us-gaap_IncomeTaxPolicyTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl1" xml:lang="en-US">Preferred Stock, Shares Authorized</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PreferredStockSharesAuthorized" xlink:to="us-gaap_PreferredStockSharesAuthorized_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl1" xml:lang="en-US">Common Stock, Shares Authorized</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockSharesAuthorized" xlink:to="us-gaap_CommonStockSharesAuthorized_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="ecd_NonRule10b51ArrAdoptedFlag_lbl0" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted [Flag]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="ecd_NonRule10b51ArrAdoptedFlag" xlink:to="ecd_NonRule10b51ArrAdoptedFlag_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_InitialBusinessCombinationExercisableCompletionTerm_lbl1" xml:lang="en-US">Initial Business Combination Exercisable Completion Term</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_InitialBusinessCombinationExercisableCompletionTerm" xlink:to="cmiii_InitialBusinessCombinationExercisableCompletionTerm_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl0" xml:lang="en-US">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Increase (Decrease) in Operating Capital [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:to="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventMember_lbl0" xml:lang="en-US">Subsequent Event [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventMember" xlink:to="us-gaap_SubsequentEventMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_WarrantMember_lbl0" xml:lang="en-US">Warrant [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WarrantMember" xlink:to="us-gaap_WarrantMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_AmendmentFlag_lbl0" xml:lang="en-US">Amendment Flag</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_AmendmentFlag" xlink:to="dei_AmendmentFlag_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_ThresholdNumberOfDaysForFilingRegistrationStatementAfterBusinessCombinationClosing_lbl1" xml:lang="en-US">Threshold Number Of Days For Filing Registration Statement After Business Combination Closing</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ThresholdNumberOfDaysForFilingRegistrationStatementAfterBusinessCombinationClosing" xlink:to="cmiii_ThresholdNumberOfDaysForFilingRegistrationStatementAfterBusinessCombinationClosing_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_EntityPricePerUnit_lbl1" xml:lang="en-US">Entity Price Per Unit</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_EntityPricePerUnit" xlink:to="cmiii_EntityPricePerUnit_lbl1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureAbstract_lbl" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:to="us-gaap_CommitmentsAndContingenciesDisclosureAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl0" xml:lang="en-US">Additional Paid-in Capital [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdditionalPaidInCapitalMember" xlink:to="us-gaap_AdditionalPaidInCapitalMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredChargesPolicyTextBlock_lbl0" xml:lang="en-US">Deferred Charges, Policy [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredChargesPolicyTextBlock" xlink:to="us-gaap_DeferredChargesPolicyTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityCentralIndexKey_lbl0" xml:lang="en-US">Entity Central Index Key</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_ThresholdNumberOfDaysForRestrictionToExerciseWarrantsFromCompletionOfInitialBusinessCombination_lbl1" xml:lang="en-US">Threshold Number Of Days For Restriction To Exercise Warrants From Completion Of Initial Business Combination</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ThresholdNumberOfDaysForRestrictionToExerciseWarrantsFromCompletionOfInitialBusinessCombination" xlink:to="cmiii_ThresholdNumberOfDaysForRestrictionToExerciseWarrantsFromCompletionOfInitialBusinessCombination_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_PrivatePlacementWarrantsMember_lbl0" xml:lang="en-US">Private Placement Warrants Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_PrivatePlacementWarrantsMember" xlink:to="cmiii_PrivatePlacementWarrantsMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_TransactionCosts_lbl1" xml:lang="en-US">Transaction Costs</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_WarrantInstrumentsPolicyPolicyTextBlock_lbl1" xml:lang="en-US">Warrant Instruments Policy Policy Text Block</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_WarrantInstrumentsPolicyPolicyTextBlock" xlink:to="cmiii_WarrantInstrumentsPolicyPolicyTextBlock_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_DeferredOfferingCostsIncludedInAccruedOfferingCosts_lbl1" xml:lang="en-US">Deferred Offering Costs Included In Accrued Offering Costs</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_DeferredOfferingCostsIncludedInAccruedOfferingCosts" xlink:to="cmiii_DeferredOfferingCostsIncludedInAccruedOfferingCosts_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl0" xml:lang="en-US">Significant Accounting Policies [Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="us-gaap_SignificantAccountingPoliciesTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_NumberOfOrdinaryShares_lbl1" xml:lang="en-US">Number Of Ordinary Shares</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect_lbl0" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Excluding Exchange Rate Effect, Including Discontinued Operation</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl0" xml:lang="en-US">Sale of Stock, Price Per Share</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityRegistrantName_lbl0" xml:lang="en-US">Entity Registrant Name</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_MaximumPeriodToCompleteTheInitialBusinessCombinationAfterInitialPublicOffering_lbl1" xml:lang="en-US">Maximum Period To Complete The Initial Business Combination After Initial Public Offering</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommitmentsAndContingencies_lbl0" xml:lang="en-US">Commitments and Contingencies</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_WorkingCapitalLoansMember_lbl0" xml:lang="en-US">Working Capital Loans Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_WorkingCapitalLoansMember" xlink:to="cmiii_WorkingCapitalLoansMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonClassAMember_lbl2" xml:lang="en-US">Common Class A [Member]</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_RedeemPublicSharesPercentage_lbl1" xml:lang="en-US">Redeem Public Shares Percentage</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockMember_lbl0" xml:lang="en-US">Common Stock [Member]</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_ClassOfWarrantOrRightRedemptionWarrantOrRightThresholdTradingDays_lbl1" xml:lang="en-US">Class Of Warrant Or Right Redemption Warrant Or Right Threshold Trading Days</label>
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    <loc xlink:type="locator" xlink:label="us-gaap_RelatedPartyTransactionsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionsAbstract_lbl" xml:lang="en-US">Related Party Transactions [Abstract]</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_ThresholdOwnershipPercentageInTargetCompany_lbl1" xml:lang="en-US">Threshold Ownership Percentage In Target Company</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ThresholdOwnershipPercentageInTargetCompany" xlink:to="cmiii_ThresholdOwnershipPercentageInTargetCompany_lbl1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementOfCashFlowsAbstract_lbl" xml:lang="en-US">Statement of Cash Flows [Abstract]</label>
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    <loc xlink:type="locator" xlink:label="ecd_InsiderTradingArrLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTradingArrLineItems"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="ecd_InsiderTradingArrLineItems_lbl" xml:lang="en-US">Insider Trading Arrangements [Line Items]</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_DeferredOfferingCostsPaidThroughPrepaidExpenses_lbl1" xml:lang="en-US">Deferred Offering Costs Paid Through Prepaid Expenses</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_UnitsEachConsistingOfOneClassAOrdinaryShareAndOnethirdOfOneRedeemableWarrantMember_lbl0" xml:lang="en-US">Units Each Consisting Of One Class AOrdinary Share And Onethird Of One Redeemable Warrant Member</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_CashUnderwritingDiscountPercent_lbl2" xml:lang="en-US">Cash Underwriting Discount Percent</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_CashUnderwritingDiscountPercent" xlink:to="cmiii_CashUnderwritingDiscountPercent_lbl2"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_lbl0" xml:lang="en-US">Related Party Transactions Disclosure [Text Block]</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl0" xml:lang="en-US">Liabilities, Current [Abstract]</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebtAverageAmountOutstanding_lbl0" xml:lang="en-US">Long-Term Debt, Average Amount Outstanding</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_lbl0" xml:lang="en-US">Cash Flow, Noncash Investing and Financing Activities Disclosure [Abstract]</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_WorkingCapitalDeficit_lbl1" xml:lang="en-US">Working Capital Deficit</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl0" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_PrivatePlacementUnitsMember_lbl0" xml:lang="en-US">Private Placement Units Member</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod_lbl0" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Net of Forfeitures</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_YearOfInception_lbl1" xml:lang="en-US">Year Of Inception</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_ClassOfWarrantRightThresholdPriorWrittenNoticePeriodForRedemptionOfWarrants_lbl1" xml:lang="en-US">Class Of Warrant Right Threshold Prior Written Notice Period For Redemption Of Warrants</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueOfFinancialInstrumentsPolicy_lbl0" xml:lang="en-US">Fair Value of Financial Instruments, Policy [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:to="us-gaap_FairValueOfFinancialInstrumentsPolicy_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockRepurchasedDuringPeriodShares_lbl0" xml:lang="en-US">Stock Repurchased During Period, Shares</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_ThresholdFairMarketValueOfTargetBusinessAsPercentOfNetBalanceInTrustAccount_lbl1" xml:lang="en-US">Threshold Fair Market Value Of Target Business As Percent Of Net Balance In Trust Account</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ThresholdFairMarketValueOfTargetBusinessAsPercentOfNetBalanceInTrustAccount" xlink:to="cmiii_ThresholdFairMarketValueOfTargetBusinessAsPercentOfNetBalanceInTrustAccount_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightStockPriceTrigger_lbl1" xml:lang="en-US">Class Of Warrant Or Right Redemption Of Warrant Or Right Stock Price Trigger</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityExTransitionPeriod_lbl0" xml:lang="en-US">Entity Ex Transition Period</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_InitialPublicOfferingTextBlock_lbl1" xml:lang="en-US">Initial Public Offering Text Block</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SharePrice_lbl0" xml:lang="en-US">Share Price</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NatureOfOperations_lbl0" xml:lang="en-US">Nature of Operations [Text Block]</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_InitialBusinessCombinationExercisableTerm_lbl1" xml:lang="en-US">Initial Business Combination Exercisable Term</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SecuredDebt_lbl0" xml:lang="en-US">Secured Debt</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_InterestEquivalentAggregateShares_lbl1" xml:lang="en-US">Interest Equivalent Aggregate Shares</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_UnitsIssuedDuringPeriodNewIssues_lbl1" xml:lang="en-US">Units Issued During Period New Issues</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquity_lbl2" xml:lang="en-US">Equity, Attributable to Parent</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl0" xml:lang="en-US">General and Administrative Expense</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_PrivatePlacementTextBlock_lbl1" xml:lang="en-US">Private Placement Text Block</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NotesPayableCurrent_lbl1" xml:lang="en-US">Notes Payable, Current</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_CurrentFiscalYearEndDate_lbl0" xml:lang="en-US">Current Fiscal Year End Date</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_RelatedPartyTransactionMonthlyAdministrativeExpenses_lbl1" xml:lang="en-US">Related Party Transaction Monthly Administrative Expenses</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_DocumentFiscalYearFocus_lbl0" xml:lang="en-US">Document Fiscal Year Focus</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_PercentOfPublicSharesToBeRedeemedIfBusinessCombinationNotCompleted_lbl1" xml:lang="en-US">Percent Of Public Shares To Be Redeemed If Business Combination Not Completed</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_LiquidityAndCapitalResourcesPolicyPolicyTextBlock_lbl1" xml:lang="en-US">Liquidity And Capital Resources Policy Policy Text Block</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_GeneralAndAdministrativeCostsPaidThroughIPOPromissoryNote_lbl1" xml:lang="en-US">General And Administrative Costs Paid Through IPOPromissory Note</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_ClassAOrdinarySharesParValue00001PerShareMember_lbl0" xml:lang="en-US">Class AOrdinary Shares Par Value00001 Per Share Member</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl0" xml:lang="en-US">Segment Reporting [Text Block]</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromIssuanceOfPrivatePlacement_lbl0" xml:lang="en-US">Proceeds from Issuance of Private Placement</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityCurrentReportingStatus_lbl0" xml:lang="en-US">Entity Current Reporting Status</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityEmergingGrowthCompany_lbl0" xml:lang="en-US">Entity Emerging Growth Company</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_PrepaidServicesPaidThroughIPOPromissoryNote_lbl1" xml:lang="en-US">Prepaid Services Paid Through IPOPromissory Note</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityAddressPostalZipCode_lbl0" xml:lang="en-US">Entity Address, Postal Zip Code</label>
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    <loc xlink:type="locator" xlink:label="cmiii_PrivatePlacementAbstract" xlink:href="cmiii-20260630.xsd#cmiii_PrivatePlacementAbstract"/>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="ecd_Rule10b51ArrAdoptedFlag_lbl0" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted [Flag]</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockSharesIssued_lbl0" xml:lang="en-US">Preferred Stock, Shares Issued</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_FounderShareMember_lbl0" xml:lang="en-US">Founder Share Member</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_DirectorMember_lbl0" xml:lang="en-US">Director [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_DirectorMember" xlink:to="srt_DirectorMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PrivatePlacementMember_lbl0" xml:lang="en-US">Private Placement [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PrivatePlacementMember" xlink:to="us-gaap_PrivatePlacementMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_DocumentTransitionReport_lbl0" xml:lang="en-US">Document Transition Report</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentTransitionReport" xlink:to="dei_DocumentTransitionReport_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightThresholdCommencementPeriodAfterInitialBusinessCombinationClosing_lbl1" xml:lang="en-US">Class Of Warrant Or Right Redemption Of Warrant Or Right Threshold Commencement Period After Initial Business Combination Closing</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightThresholdCommencementPeriodAfterInitialBusinessCombinationClosing" xlink:to="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightThresholdCommencementPeriodAfterInitialBusinessCombinationClosing_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_NumberOfWarrants_lbl1" xml:lang="en-US">Number Of Warrants</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetIncomeLoss_lbl0" xml:lang="en-US">Net Income (Loss) Attributable to Parent</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyMember_lbl0" xml:lang="en-US">Related Party [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyMember" xlink:to="us-gaap_RelatedPartyMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl0" xml:lang="en-US">Debt Instrument, Face Amount</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentFaceAmount" xlink:to="us-gaap_DebtInstrumentFaceAmount_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl0" xml:lang="en-US">Equity [Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsCurrentAbstract_lbl0" xml:lang="en-US">Assets, Current [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsCurrentAbstract" xlink:to="us-gaap_AssetsCurrentAbstract_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_DocumentQuarterlyReport_lbl0" xml:lang="en-US">Document Quarterly Report</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentQuarterlyReport" xlink:to="dei_DocumentQuarterlyReport_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_LiabilitiesAndShareholderSDeficitEquityAbstract_lbl0" xml:lang="en-US">Liabilities And Shareholder SDeficit Equity Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_LiabilitiesAndShareholderSDeficitEquityAbstract" xlink:to="cmiii_LiabilitiesAndShareholderSDeficitEquityAbstract_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl1" xml:lang="en-US">Sale of Stock, Number of Shares Issued in Transaction</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:to="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SubsequentEventsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventsAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventsAbstract_lbl" xml:lang="en-US">Subsequent Events [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventsAbstract" xlink:to="us-gaap_SubsequentEventsAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Cash_lbl0" xml:lang="en-US">Cash</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Cash" xlink:to="us-gaap_Cash_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_PromissoryNoteMember_lbl0" xml:lang="en-US">Promissory Note Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_PromissoryNoteMember" xlink:to="cmiii_PromissoryNoteMember_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementOfFinancialPositionAbstract_lbl" xml:lang="en-US">Statement of Financial Position [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementOfFinancialPositionAbstract" xlink:to="us-gaap_StatementOfFinancialPositionAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityTaxIdentificationNumber_lbl0" xml:lang="en-US">Entity Tax Identification Number</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityTaxIdentificationNumber" xlink:to="dei_EntityTaxIdentificationNumber_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_InitialBusinessCombination_lbl1" xml:lang="en-US">Initial Business Combination</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesCurrent_lbl0" xml:lang="en-US">Liabilities, Current</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesCurrent" xlink:to="us-gaap_LiabilitiesCurrent_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl0" xml:lang="en-US">Accrued Liabilities, Current</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccruedLiabilitiesCurrent" xlink:to="us-gaap_AccruedLiabilitiesCurrent_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_lbl0" xml:lang="en-US">Class of Warrant or Right, Exercise Price of Warrants or Rights</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_DocumentType_lbl0" xml:lang="en-US">Document Type</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentType" xlink:to="dei_DocumentType_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityFileNumber_lbl0" xml:lang="en-US">Entity File Number</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityFileNumber" xlink:to="dei_EntityFileNumber_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SegmentReportingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentReportingAbstract_lbl" xml:lang="en-US">Segment Reporting [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingAbstract" xlink:to="us-gaap_SegmentReportingAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl0" xml:lang="en-US">Commitments and Contingencies Disclosure [Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:to="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_MaximumNumberOfSharesSubjectToForfeiture_lbl1" xml:lang="en-US">Maximum Number Of Shares Subject To Forfeiture</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_MaximumNumberOfSharesSubjectToForfeiture" xlink:to="cmiii_MaximumNumberOfSharesSubjectToForfeiture_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_NetProceedsFromIssuanceInitialPublicOffering_lbl2" xml:lang="en-US">Net Proceeds From Issuance Initial Public Offering</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_NetProceedsFromIssuanceInitialPublicOffering" xlink:to="cmiii_NetProceedsFromIssuanceInitialPublicOffering_lbl2"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_DocumentPeriodEndDate_lbl0" xml:lang="en-US">Document Period End Date</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentPeriodEndDate" xlink:to="dei_DocumentPeriodEndDate_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_RelatedPartyPromissoryNoteLoanMember_lbl0" xml:lang="en-US">Related Party Promissory Note Loan Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_RelatedPartyPromissoryNoteLoanMember" xlink:to="cmiii_RelatedPartyPromissoryNoteLoanMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl0" xml:lang="en-US">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity [Abstract]</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityInteractiveDataCurrent_lbl0" xml:lang="en-US">Entity Interactive Data Current</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityInteractiveDataCurrent" xlink:to="dei_EntityInteractiveDataCurrent_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityFilerCategory_lbl0" xml:lang="en-US">Entity Filer Category</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityFilerCategory" xlink:to="dei_EntityFilerCategory_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OverAllotmentOptionMember_lbl0" xml:lang="en-US">Over-Allotment Option [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OverAllotmentOptionMember" xlink:to="us-gaap_OverAllotmentOptionMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NumberOfReportableSegments_lbl0" xml:lang="en-US">Number of Reportable Segments</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NumberOfReportableSegments" xlink:to="us-gaap_NumberOfReportableSegments_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_EmergingGrowthCompanyPolicyTextBlock_lbl1" xml:lang="en-US">Emerging Growth Company Policy Text Block</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl0" xml:lang="en-US">Liabilities and Equity</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredCosts_lbl0" xml:lang="en-US">Deferred Costs, Noncurrent</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_AdministrativeServicesAgreementMember_lbl0" xml:lang="en-US">Administrative Services Agreement Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_AdministrativeServicesAgreementMember" xlink:to="cmiii_AdministrativeServicesAgreementMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_MaximumNumberOfAdditionalUnitsOfferedForPurchase_lbl1" xml:lang="en-US">Maximum Number Of Additional Units Offered For Purchase</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="cmiii_MaximumNumberOfAdditionalUnitsOfferedForPurchase" xlink:to="cmiii_MaximumNumberOfAdditionalUnitsOfferedForPurchase_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_RepresentativesMember_lbl0" xml:lang="en-US">Representatives Member</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_ClassOfWarrantOrRightRedemptionOfWarrantOrRightThresholdConsecutiveTradingDays_lbl1" xml:lang="en-US">Class Of Warrant Or Right Redemption Of Warrant Or Right Threshold Consecutive Trading Days</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredOfferingCosts_lbl0" xml:lang="en-US">Deferred Offering Costs</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_TradingSymbol_lbl0" xml:lang="en-US">Trading Symbol</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="cmiii_WorkingCapitalLoans_lbl1" xml:lang="en-US">Working Capital Loans</label>
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