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<!-- Generated by CompSci Transform (tm) - http://www.compsciresources.com -->    
<!-- Created: Tue Feb 10 02:04:22 UTC 2026 -->  
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  <roleRef xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/negated-2009-12-16.xsd#negatedLabel" roleURI="http://www.xbrl.org/2009/role/negatedLabel"/>    
  <roleRef xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/role/net-2009-12-16.xsd#netLabel" roleURI="http://www.xbrl.org/2009/role/netLabel"/>  
  <labelLink xlink:role="http://www.xbrl.org/2003/role/link" xlink:type="extended">    
    <loc xlink:type="locator" xlink:label="us-gaap_AssetsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsCurrent"/>     
    <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>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsCurrent" xlink:to="us-gaap_AssetsCurrent_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Assets"/> 
    <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>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Assets" xlink:to="us-gaap_Assets_lbl"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_LiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesCurrent"/>     
    <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>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesCurrent" xlink:to="us-gaap_LiabilitiesCurrent_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Liabilities"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_Liabilities_lbl" xml:lang="en-US">TOTAL LIABILITIES</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_Liabilities_lbl"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_StatementClassOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementClassOfStockAxis"/>    
    <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> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementClassOfStockAxis" xlink:to="us-gaap_StatementClassOfStockAxis_lbl"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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 SHAREHOLDERS&#8217; DEFICIT</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_StockholdersEquity_lbl"/>   
    <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>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_StockholdersEquity_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_StockholdersEquity_lbl1" xml:lang="en-US">Balance</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_StockholdersEquity_lbl1"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>   
    <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, CLASS A ORDINARY SHARES SUBJECT TO POSSIBLE REDEMPTION AND SHAREHOLDERS&#8217; DEFICIT</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_LiabilitiesAndStockholdersEquity_lbl"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_OperatingIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingIncomeLoss"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xml:lang="en-US">Loss from operations</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingIncomeLoss" xlink:to="us-gaap_OperatingIncomeLoss_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_NonoperatingIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NonoperatingIncomeExpense"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NonoperatingIncomeExpense_lbl" xml:lang="en-US">Total other income</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NonoperatingIncomeExpense" xlink:to="us-gaap_NonoperatingIncomeExpense_lbl"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLoss"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetIncomeLoss_lbl" xml:lang="en-US">NET INCOME (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"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetIncomeLoss_lbl0" xml:lang="en-US">Net income (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_lbl0"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_SharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharesOutstanding"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_SharesOutstanding_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_SharesOutstanding" xlink:to="us-gaap_SharesOutstanding_lbl"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_SharesOutstanding_lbl0" 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_SharesOutstanding" xlink:to="us-gaap_SharesOutstanding_lbl0"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementEquityComponentsAxis" xlink:to="us-gaap_StatementEquityComponentsAxis_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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/2025/elts/us-gaap-2025.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 &#8211; beginning of 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 &#8211; end of 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"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl1" xml:lang="en-US">Cash</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"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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">Description of 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="us-gaap_AccountingPoliciesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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">Significant 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="bacq_ScheduleOfValuationOfThePublicRightsAbstract" xlink:href="bacq-20250930.xsd#bacq_ScheduleOfValuationOfThePublicRightsAbstract"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_ScheduleOfValuationOfThePublicRightsAbstract_lbl" xml:lang="en-US">Schedule of Valuation of the Public Rights [Abstract]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ScheduleOfValuationOfThePublicRightsAbstract" xlink:to="bacq_ScheduleOfValuationOfThePublicRightsAbstract_lbl"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_TemporaryEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityAbstract"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TemporaryEquityAbstract_lbl" xml:lang="en-US">Schedule of Class A Ordinary Share subject to Possible Redemption [Abstract]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityAbstract" xlink:to="us-gaap_TemporaryEquityAbstract_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_ClassOfStockDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfStockDisclosuresAbstract"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ClassOfStockDisclosuresAbstract_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="us-gaap_ClassOfStockDisclosuresAbstract" xlink:to="us-gaap_ClassOfStockDisclosuresAbstract_lbl"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_WarrantsAndRightsNoteDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WarrantsAndRightsNoteDisclosureAbstract"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_WarrantsAndRightsNoteDisclosureAbstract_lbl" xml:lang="en-US">Private Placement [Abstract]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WarrantsAndRightsNoteDisclosureAbstract" xlink:to="us-gaap_WarrantsAndRightsNoteDisclosureAbstract_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_RelatedPartyTransactionsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionsAbstract" xlink:to="us-gaap_RelatedPartyTransactionsAbstract_lbl"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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 [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"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_StockholdersEquityNoteAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityNoteAbstract"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquityNoteAbstract_lbl" xml:lang="en-US">Shareholders&#8217; Deficit [Abstract]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityNoteAbstract" xlink:to="us-gaap_StockholdersEquityNoteAbstract_lbl"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresAbstract"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueDisclosuresAbstract_lbl" xml:lang="en-US">Fair Value Measurements [Abstract]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueDisclosuresAbstract" xlink:to="us-gaap_FairValueDisclosuresAbstract_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_SegmentReportingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_SubsequentEventsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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"/>     
    <loc xlink:type="locator" xlink:label="bacq_ScheduleOfOrdinaryShareSubjectToPossibleRedemptionAbstract" xlink:href="bacq-20250930.xsd#bacq_ScheduleOfOrdinaryShareSubjectToPossibleRedemptionAbstract"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_ScheduleOfOrdinaryShareSubjectToPossibleRedemptionAbstract_lbl" xml:lang="en-US">Schedule of Ordinary Share subject to Possible Redemption [Abstract]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ScheduleOfOrdinaryShareSubjectToPossibleRedemptionAbstract" xlink:to="bacq_ScheduleOfOrdinaryShareSubjectToPossibleRedemptionAbstract_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_ScheduleOfNetIncomeOrLossAndTotalAssetsAbstract" xlink:href="bacq-20250930.xsd#bacq_ScheduleOfNetIncomeOrLossAndTotalAssetsAbstract"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_ScheduleOfNetIncomeOrLossAndTotalAssetsAbstract_lbl" xml:lang="en-US">Schedule of Net Income or Loss and Total Assets [Abstract]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ScheduleOfNetIncomeOrLossAndTotalAssetsAbstract" xlink:to="bacq_ScheduleOfNetIncomeOrLossAndTotalAssetsAbstract_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_StatementBusinessSegmentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementBusinessSegmentsAxis"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementBusinessSegmentsAxis_lbl" xml:lang="en-US">Segments [Axis]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementBusinessSegmentsAxis" xlink:to="us-gaap_StatementBusinessSegmentsAxis_lbl"/>     
    <loc xlink:type="locator" xlink:label="bacq_NewMerlinMember" xlink:href="bacq-20250930.xsd#bacq_NewMerlinMember"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_NewMerlinMember_lbl" xml:lang="en-US">New Merlin [Member]</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_NewMerlinMember" xlink:to="bacq_NewMerlinMember_lbl"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_PrivatePlacementMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PrivatePlacementMember_lbl0" xml:lang="en-US">Initial Public Offering [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"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_IPOMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_IPOMember_lbl0" xml:lang="en-US">Initial Public Offering [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"/> 
    <loc xlink:type="locator" xlink:label="bacq_NetTangibleBookValueMember" xlink:href="bacq-20250930.xsd#bacq_NetTangibleBookValueMember"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_NetTangibleBookValueMember_lbl" xml:lang="en-US">Net Tangible Book Value [Member]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_NetTangibleBookValueMember" xlink:to="bacq_NetTangibleBookValueMember_lbl"/>   
    <loc xlink:type="locator" xlink:label="bacq_AnticipatedTransactionExpensesMember" xlink:href="bacq-20250930.xsd#bacq_AnticipatedTransactionExpensesMember"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_AnticipatedTransactionExpensesMember_lbl" xml:lang="en-US">Anticipated Transaction Expenses [Member]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_AnticipatedTransactionExpensesMember" xlink:to="bacq_AnticipatedTransactionExpensesMember_lbl"/>   
    <loc xlink:type="locator" xlink:label="bacq_PIPEInvestmentProceedsMember" xlink:href="bacq-20250930.xsd#bacq_PIPEInvestmentProceedsMember"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_PIPEInvestmentProceedsMember_lbl" xml:lang="en-US">PIPE Investment Proceeds [Member]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PIPEInvestmentProceedsMember" xlink:to="bacq_PIPEInvestmentProceedsMember_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_RedemptionsFromTrustAccountMember" xlink:href="bacq-20250930.xsd#bacq_RedemptionsFromTrustAccountMember"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_RedemptionsFromTrustAccountMember_lbl" xml:lang="en-US">Redemptions From Trust Account [Member]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_RedemptionsFromTrustAccountMember" xlink:to="bacq_RedemptionsFromTrustAccountMember_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_SponsorMember" xlink:href="bacq-20250930.xsd#bacq_SponsorMember"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_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="bacq_SponsorMember" xlink:to="bacq_SponsorMember_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_PIPEInvestorsMember" xlink:href="bacq-20250930.xsd#bacq_PIPEInvestorsMember"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_PIPEInvestorsMember_lbl" xml:lang="en-US">PIPE Investors [Member]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PIPEInvestorsMember" xlink:to="bacq_PIPEInvestorsMember_lbl"/>    
    <loc xlink:type="locator" xlink:label="bacq_InflectionPointMember" xlink:href="bacq-20250930.xsd#bacq_InflectionPointMember"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_InflectionPointMember_lbl" xml:lang="en-US">Inflection Point [Member]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_InflectionPointMember" xlink:to="bacq_InflectionPointMember_lbl"/>   
    <loc xlink:type="locator" xlink:label="bacq_UnaffiliatedInflectionPointPublicShareholdersMember" xlink:href="bacq-20250930.xsd#bacq_UnaffiliatedInflectionPointPublicShareholdersMember"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_UnaffiliatedInflectionPointPublicShareholdersMember_lbl" xml:lang="en-US">Unaffiliated Inflection Point Public Shareholders [Member]</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnaffiliatedInflectionPointPublicShareholdersMember" xlink:to="bacq_UnaffiliatedInflectionPointPublicShareholdersMember_lbl"/>   
    <loc xlink:type="locator" xlink:label="dei_AmendmentDescription" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AmendmentDescription"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_AmendmentDescription_lbl" xml:lang="en-US">Amendment Description</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_AmendmentDescription" xlink:to="dei_AmendmentDescription_lbl"/>    
    <loc xlink:type="locator" xlink:label="dei_DocumentType" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.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_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.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/2025/dei-2025.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>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityIncorporationStateCountryCode" xlink:to="dei_EntityIncorporationStateCountryCode_lbl"/>    
    <loc xlink:type="locator" xlink:label="dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.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/2025/dei-2025.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/2025/dei-2025.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/2025/dei-2025.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_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.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/2025/dei-2025.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="us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AssetsAbstract_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_AssetsAbstract" xlink:to="us-gaap_AssetsAbstract_lbl0"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_AssetsCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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/2025/elts/us-gaap-2025.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="bacq_ShortTermPrepaidInsurance" xlink:href="bacq-20250930.xsd#bacq_ShortTermPrepaidInsurance"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_ShortTermPrepaidInsurance_lbl" xml:lang="en-US">Short-term prepaid insurance</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ShortTermPrepaidInsurance" xlink:to="bacq_ShortTermPrepaidInsurance_lbl"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_PrepaidExpenseNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PrepaidExpenseNoncurrent"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PrepaidExpenseNoncurrent_lbl" xml:lang="en-US">Long-term prepaid insurance</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PrepaidExpenseNoncurrent" xlink:to="us-gaap_PrepaidExpenseNoncurrent_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_AssetsHeldInTrustNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsHeldInTrustNoncurrent"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetsHeldInTrustNoncurrent_lbl" xml:lang="en-US">Investments held in Trust Account</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsHeldInTrustNoncurrent" xlink:to="us-gaap_AssetsHeldInTrustNoncurrent_lbl"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AssetsHeldInTrustNoncurrent_lbl0" xml:lang="en-US">Investments held in Trust Account &#8211; U.S. Treasury Securities</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsHeldInTrustNoncurrent" xlink:to="us-gaap_AssetsHeldInTrustNoncurrent_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:label="us-gaap_AssetsHeldInTrustNoncurrent_lbl1" xml:lang="en-US">Trust Account</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsHeldInTrustNoncurrent" xlink:to="us-gaap_AssetsHeldInTrustNoncurrent_lbl1"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsHeldInTrustNoncurrent_lbl2" xml:lang="en-US">Assets held in the trust account</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsHeldInTrustNoncurrent" xlink:to="us-gaap_AssetsHeldInTrustNoncurrent_lbl2"/>  
    <loc xlink:type="locator" xlink:label="bacq_LiabilitiesClassAOrdinarySharesSubjectToPossibleRedemptionAndShareholdersDeficitAbstract" xlink:href="bacq-20250930.xsd#bacq_LiabilitiesClassAOrdinarySharesSubjectToPossibleRedemptionAndShareholdersDeficitAbstract"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_LiabilitiesClassAOrdinarySharesSubjectToPossibleRedemptionAndShareholdersDeficitAbstract_lbl" xml:lang="en-US">LIABILITIES, CLASS A ORDINARY SHARES SUBJECT TO POSSIBLE REDEMPTION AND SHAREHOLDERS&#8217; DEFICIT</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_LiabilitiesClassAOrdinarySharesSubjectToPossibleRedemptionAndShareholdersDeficitAbstract" xlink:to="bacq_LiabilitiesClassAOrdinarySharesSubjectToPossibleRedemptionAndShareholdersDeficitAbstract_lbl"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_LiabilitiesCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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/2025/elts/us-gaap-2025.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="bacq_AccruedOfferingCostsCurrent" xlink:href="bacq-20250930.xsd#bacq_AccruedOfferingCostsCurrent"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_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="bacq_AccruedOfferingCostsCurrent" xlink:to="bacq_AccruedOfferingCostsCurrent_lbl"/>     
    <loc xlink:type="locator" xlink:label="bacq_CashUnderwritingFeePayable" xlink:href="bacq-20250930.xsd#bacq_CashUnderwritingFeePayable"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_CashUnderwritingFeePayable_lbl" xml:lang="en-US">Cash underwriting fee payable</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_CashUnderwritingFeePayable" xlink:to="bacq_CashUnderwritingFeePayable_lbl"/>   
    <loc xlink:type="locator" xlink:label="bacq_DeferredUnderwritingFeePayableNoncurrent" xlink:href="bacq-20250930.xsd#bacq_DeferredUnderwritingFeePayableNoncurrent"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_DeferredUnderwritingFeePayableNoncurrent_lbl" xml:lang="en-US">Deferred underwriting fee payable</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_DeferredUnderwritingFeePayableNoncurrent" xlink:to="bacq_DeferredUnderwritingFeePayableNoncurrent_lbl"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_CommitmentsAndContingencies" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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_TemporaryEquityCarryingAmountAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityCarryingAmountAttributableToParent"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TemporaryEquityCarryingAmountAttributableToParent_lbl" xml:lang="en-US">Class A ordinary shares subject to possible redemption, $0.0001 par value; 500,000,000 shares authorized; 25,000,000 shares issued and outstanding, at redemption value of approximately $10.39 and $10.07 per share at September 30, 2025 and December 31, 2024, respectively</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:to="us-gaap_TemporaryEquityCarryingAmountAttributableToParent_lbl"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_TemporaryEquityCarryingAmountAttributableToParent_lbl0" xml:lang="en-US">Class A ordinary shares subject to possible redemption</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:to="us-gaap_TemporaryEquityCarryingAmountAttributableToParent_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:label="us-gaap_TemporaryEquityCarryingAmountAttributableToParent_lbl1" xml:lang="en-US">Class A ordinary shares subject to possible redemption, December 31, 2024</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:to="us-gaap_TemporaryEquityCarryingAmountAttributableToParent_lbl1"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_TemporaryEquityParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityParOrStatedValuePerShare"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TemporaryEquityParOrStatedValuePerShare_lbl" xml:lang="en-US">Ordinary shares subject to possible redemption, 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_TemporaryEquityParOrStatedValuePerShare" xlink:to="us-gaap_TemporaryEquityParOrStatedValuePerShare_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_TemporaryEquitySharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquitySharesAuthorized"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TemporaryEquitySharesAuthorized_lbl" xml:lang="en-US">Ordinary shares subject to possible redemption, shares authorized (in Shares)</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquitySharesAuthorized" xlink:to="us-gaap_TemporaryEquitySharesAuthorized_lbl"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_TemporaryEquitySharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquitySharesIssued"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TemporaryEquitySharesIssued_lbl" xml:lang="en-US">Ordinary shares subject to possible redemption, shares issued (in Shares)</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquitySharesIssued" xlink:to="us-gaap_TemporaryEquitySharesIssued_lbl"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_TemporaryEquitySharesIssued_lbl0" xml:lang="en-US">Shares subject to possible redemption, shares issued</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquitySharesIssued" xlink:to="us-gaap_TemporaryEquitySharesIssued_lbl0"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_TemporaryEquitySharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquitySharesOutstanding"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TemporaryEquitySharesOutstanding_lbl" xml:lang="en-US">Ordinary shares subject to possible redemption, shares outstanding (in Shares)</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquitySharesOutstanding" xlink:to="us-gaap_TemporaryEquitySharesOutstanding_lbl"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_TemporaryEquitySharesOutstanding_lbl0" xml:lang="en-US">Shares subject to possible redemption, shares outstanding</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquitySharesOutstanding" xlink:to="us-gaap_TemporaryEquitySharesOutstanding_lbl0"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_TemporaryEquityRedemptionPricePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityRedemptionPricePerShare"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TemporaryEquityRedemptionPricePerShare_lbl" xml:lang="en-US">Ordinary shares subject to possible redemption, 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_TemporaryEquityRedemptionPricePerShare" xlink:to="us-gaap_TemporaryEquityRedemptionPricePerShare_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_StockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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">SHAREHOLDERS&#8217; DEFICIT</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"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_StockholdersEquityAbstract_lbl0" xml:lang="en-US">Shareholders&#8217; Deficit</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"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_PreferredStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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 and outstanding at September 30, 2025 and December 31, 2024</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/2025/elts/us-gaap-2025.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">Preference 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"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl0" xml:lang="en-US">Preferred Stock, par value 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_PreferredStockParOrStatedValuePerShare" xlink:to="us-gaap_PreferredStockParOrStatedValuePerShare_lbl0"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_PreferredStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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">Preference 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">Preference 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/2025/elts/us-gaap-2025.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">Preference 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"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PreferredStockSharesIssued_lbl0" xml:lang="en-US">Preference shares issued</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_lbl0"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_PreferredStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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">Preference 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"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl0" xml:lang="en-US">Shares of preferred stock (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_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl1" xml:lang="en-US">Preference 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_lbl1"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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">Ordinary shares, 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/2025/elts/us-gaap-2025.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"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl0" xml:lang="en-US">Common stock, par value 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_CommonStockParOrStatedValuePerShare" xlink:to="us-gaap_CommonStockParOrStatedValuePerShare_lbl0"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_CommonStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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 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/2025/elts/us-gaap-2025.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, 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"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CommonStockSharesIssued_lbl0" xml:lang="en-US">Ordinary shares, issued</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_lbl0"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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, 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"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl0" xml:lang="en-US">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"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_AdditionalPaidInCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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/2025/elts/us-gaap-2025.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="bacq_LiabilitiesClassAOrdinarySharesSubjectToPossibleRedemptionAndShareholdersDeficitAbstract0" xlink:href="bacq-20250930.xsd#bacq_LiabilitiesClassAOrdinarySharesSubjectToPossibleRedemptionAndShareholdersDeficitAbstract0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_LiabilitiesClassAOrdinarySharesSubjectToPossibleRedemptionAndShareholdersDeficitAbstract0_lbl" xml:lang="en-US">Liabilities, Class A Ordinary Shares Subject to Possible Redemption, and Shareholders&#8217; Deficit</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_LiabilitiesClassAOrdinarySharesSubjectToPossibleRedemptionAndShareholdersDeficitAbstract0" xlink:to="bacq_LiabilitiesClassAOrdinarySharesSubjectToPossibleRedemptionAndShareholdersDeficitAbstract0_lbl"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_GeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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 expenses</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_OtherIncomeAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherIncomeAbstract"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherIncomeAbstract_lbl" xml:lang="en-US">OTHER INCOME</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherIncomeAbstract" xlink:to="us-gaap_OtherIncomeAbstract_lbl"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_OtherIncomeAbstract_lbl0" xml:lang="en-US">Other income:</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherIncomeAbstract" xlink:to="us-gaap_OtherIncomeAbstract_lbl0"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_InvestmentIncomeInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeInterest"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InvestmentIncomeInterest_lbl" xml:lang="en-US">Interest earned on bank account</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentIncomeInterest" xlink:to="us-gaap_InvestmentIncomeInterest_lbl"/>     
    <loc xlink:type="locator" xlink:label="bacq_InterestIncomeOnInvestmentsHeldInTrustAccount" xlink:href="bacq-20250930.xsd#bacq_InterestIncomeOnInvestmentsHeldInTrustAccount"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_InterestIncomeOnInvestmentsHeldInTrustAccount_lbl" xml:lang="en-US">Interest earned on investments held in Trust Account</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_InterestIncomeOnInvestmentsHeldInTrustAccount" xlink:to="bacq_InterestIncomeOnInvestmentsHeldInTrustAccount_lbl"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="bacq_InterestIncomeOnInvestmentsHeldInTrustAccount_lbl0" xml:lang="en-US">Interest earned on marketable securities held in Trust Account</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_InterestIncomeOnInvestmentsHeldInTrustAccount" xlink:to="bacq_InterestIncomeOnInvestmentsHeldInTrustAccount_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bacq_InterestIncomeOnInvestmentsHeldInTrustAccount_lbl1" xml:lang="en-US">Interest earned on the Trust Account</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_InterestIncomeOnInvestmentsHeldInTrustAccount" xlink:to="bacq_InterestIncomeOnInvestmentsHeldInTrustAccount_lbl1"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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">Weighted average 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"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl0" xml:lang="en-US">Basic weighted average shares outstanding</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/2009/role/netLabel" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl1" xml:lang="en-US">Weighted-average shares outstanding</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_lbl1"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_EarningsPerShareBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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 net income (loss) per 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"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_EarningsPerShareBasic_lbl0" xml:lang="en-US">Basic net income (loss) per ordinary 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_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:label="us-gaap_EarningsPerShareBasic_lbl1" xml:lang="en-US">Basic net income per common stock</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_lbl1"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_EarningsPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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">Diluted net income (loss) per 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"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_EarningsPerShareDiluted_lbl0" xml:lang="en-US">Diluted net income (loss) per ordinary 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_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:label="us-gaap_EarningsPerShareDiluted_lbl1" xml:lang="en-US">Diluted net income per common stock</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_lbl1"/>    
    <loc xlink:type="locator" xlink:label="bacq_UnlabeledAbstract" xlink:href="bacq-20250930.xsd#bacq_UnlabeledAbstract"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_UnlabeledAbstract_lbl" xml:lang="en-US"></label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnlabeledAbstract" xlink:to="bacq_UnlabeledAbstract_lbl"/>     
    <loc xlink:type="locator" xlink:label="bacq_UnlabeledAbstract0" xlink:href="bacq-20250930.xsd#bacq_UnlabeledAbstract0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_UnlabeledAbstract0_lbl" xml:lang="en-US"></label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnlabeledAbstract0" xlink:to="bacq_UnlabeledAbstract0_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_UnlabeledAbstract1" xlink:href="bacq-20250930.xsd#bacq_UnlabeledAbstract1"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_UnlabeledAbstract1_lbl" xml:lang="en-US"></label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnlabeledAbstract1" xlink:to="bacq_UnlabeledAbstract1_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_UnlabeledAbstract2" xlink:href="bacq-20250930.xsd#bacq_UnlabeledAbstract2"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_UnlabeledAbstract2_lbl" xml:lang="en-US"></label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnlabeledAbstract2" xlink:to="bacq_UnlabeledAbstract2_lbl"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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">Issuance of Class B ordinary shares to Sponsor</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">Capital contribution (in Dollars)</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_StockIssuedDuringPeriodSharesNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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">Issuance of Class B ordinary shares to Sponsor (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">Sponsor additional shares (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"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl1" xml:lang="en-US">Issuance of ordinary 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_lbl1"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl2" xml:lang="en-US">Aggregate founder 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_lbl2"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl3" xml:lang="en-US">Issued founder 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_lbl3"/>    
    <loc xlink:type="locator" xlink:label="bacq_UnlabeledAbstract3" xlink:href="bacq-20250930.xsd#bacq_UnlabeledAbstract3"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_UnlabeledAbstract3_lbl" xml:lang="en-US"></label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnlabeledAbstract3" xlink:to="bacq_UnlabeledAbstract3_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_StockIssuedDuringPeriodValueSaleOfPrivatePlacementUnits" xlink:href="bacq-20250930.xsd#bacq_StockIssuedDuringPeriodValueSaleOfPrivatePlacementUnits"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_StockIssuedDuringPeriodValueSaleOfPrivatePlacementUnits_lbl" xml:lang="en-US">Sale of Private Placement units</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_StockIssuedDuringPeriodValueSaleOfPrivatePlacementUnits" xlink:to="bacq_StockIssuedDuringPeriodValueSaleOfPrivatePlacementUnits_lbl"/> 
    <loc xlink:type="locator" xlink:label="bacq_StockIssuedDuringPeriodSharesSaleOfPrivatePlacementUnits" xlink:href="bacq-20250930.xsd#bacq_StockIssuedDuringPeriodSharesSaleOfPrivatePlacementUnits"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_StockIssuedDuringPeriodSharesSaleOfPrivatePlacementUnits_lbl" xml:lang="en-US">Sale of Private Placement units (in Shares)</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_StockIssuedDuringPeriodSharesSaleOfPrivatePlacementUnits" xlink:to="bacq_StockIssuedDuringPeriodSharesSaleOfPrivatePlacementUnits_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalWarrantIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalWarrantIssued"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalWarrantIssued_lbl" xml:lang="en-US">Fair value of public warrants at issuance</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdjustmentsToAdditionalPaidInCapitalWarrantIssued" xlink:to="us-gaap_AdjustmentsToAdditionalPaidInCapitalWarrantIssued_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_StockIssuedDuringPeriodValueOther" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueOther"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodValueOther_lbl" xml:lang="en-US">Allocated value of transaction costs to Class A shares</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodValueOther" xlink:to="us-gaap_StockIssuedDuringPeriodValueOther_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_StockIssuedDuringPeriodValueShareBasedCompensationForfeited" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueShareBasedCompensationForfeited"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodValueShareBasedCompensationForfeited_lbl" xml:lang="en-US">Forfeiture of founder shares</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodValueShareBasedCompensationForfeited" xlink:to="us-gaap_StockIssuedDuringPeriodValueShareBasedCompensationForfeited_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensationForfeited" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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">Forfeiture of founder shares (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_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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 income (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"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl0" xml:lang="en-US">Adjustments to reconcile net income 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_lbl0"/> 
    <loc xlink:type="locator" xlink:label="bacq_PaymentOfOperationCostsThroughPromissoryNote" xlink:href="bacq-20250930.xsd#bacq_PaymentOfOperationCostsThroughPromissoryNote"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_PaymentOfOperationCostsThroughPromissoryNote_lbl" xml:lang="en-US">Payment of expenses through promissory note &#8211; related party</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PaymentOfOperationCostsThroughPromissoryNote" xlink:to="bacq_PaymentOfOperationCostsThroughPromissoryNote_lbl"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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/2025/elts/us-gaap-2025.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/2025/elts/us-gaap-2025.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">Non-Cash 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"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_lbl0" xml:lang="en-US">Non &#8211; Cash 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_lbl0"/> 
    <loc xlink:type="locator" xlink:label="bacq_DeferredOfferingCostsIncludedInAccruedOfferingCosts" xlink:href="bacq-20250930.xsd#bacq_DeferredOfferingCostsIncludedInAccruedOfferingCosts"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_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="bacq_DeferredOfferingCostsIncludedInAccruedOfferingCosts" xlink:to="bacq_DeferredOfferingCostsIncludedInAccruedOfferingCosts_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_StockIssued1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssued1"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssued1_lbl" xml:lang="en-US">Deferred offering costs paid through promissory note &#8211; related party</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssued1" xlink:to="us-gaap_StockIssued1_lbl"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_NotesIssued1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NotesIssued1"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NotesIssued1_lbl" xml:lang="en-US">Deferred offering costs paid by Sponsor in exchange for issuance of Class B ordinary shares</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NotesIssued1" xlink:to="us-gaap_NotesIssued1_lbl"/> 
    <loc xlink:type="locator" xlink:label="bacq_PrepaidServicesPaidBySponsorThroughThePromissoryNoteRelatedParty" xlink:href="bacq-20250930.xsd#bacq_PrepaidServicesPaidBySponsorThroughThePromissoryNoteRelatedParty"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_PrepaidServicesPaidBySponsorThroughThePromissoryNoteRelatedParty_lbl" xml:lang="en-US">Prepaid services paid by Sponsor through the promissory note &#8211; related party</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PrepaidServicesPaidBySponsorThroughThePromissoryNoteRelatedParty" xlink:to="bacq_PrepaidServicesPaidBySponsorThroughThePromissoryNoteRelatedParty_lbl"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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="bacq_FormationCosts" xlink:href="bacq-20250930.xsd#bacq_FormationCosts"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_FormationCosts_lbl" xml:lang="en-US">Formation cost paid by Sponsor in exchange for issuance of Class B ordinary shares</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_FormationCosts" xlink:to="bacq_FormationCosts_lbl"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_CostsAndExpensesRelatedParty" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CostsAndExpensesRelatedParty"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CostsAndExpensesRelatedParty_lbl" xml:lang="en-US">Payment of operation costs through promissory note &#8211; related party</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CostsAndExpensesRelatedParty" xlink:to="us-gaap_CostsAndExpensesRelatedParty_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xml:lang="en-US">Cash Flows from Investing Activities:</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xml:lang="en-US">Net cash used in investing activities</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xml:lang="en-US">Cash Flows from Financing Activities:</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_ProceedsFromOtherEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromOtherEquity"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromOtherEquity_lbl" xml:lang="en-US">Proceeds from sale of Units, net of underwriting discounts paid</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromOtherEquity" xlink:to="us-gaap_ProceedsFromOtherEquity_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_ProceedsFromIssuanceOfPrivatePlacement" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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">Proceeds from sale of Private Placements Units</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"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ProceedsFromIssuanceOfPrivatePlacement_lbl0" xml:lang="en-US">Sale of private placement units</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_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:label="us-gaap_ProceedsFromIssuanceOfPrivatePlacement_lbl1" xml:lang="en-US">Private placement amount (in Dollars)</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_lbl1"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xml:lang="en-US">Net cash provided by financing activities</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl"/> 
    <loc xlink:type="locator" xlink:label="bacq_DeferredUnderwritingFeePayable" xlink:href="bacq-20250930.xsd#bacq_DeferredUnderwritingFeePayable"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_DeferredUnderwritingFeePayable_lbl" xml:lang="en-US">Deferred underwriting fee payable</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_DeferredUnderwritingFeePayable" xlink:to="bacq_DeferredUnderwritingFeePayable_lbl"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_TemporaryEquityAccretionToRedemptionValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityAccretionToRedemptionValue"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_TemporaryEquityAccretionToRedemptionValue_lbl" xml:lang="en-US">Accretion for Class A ordinary shares to redemption amount</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityAccretionToRedemptionValue" xlink:to="us-gaap_TemporaryEquityAccretionToRedemptionValue_lbl"/>    
    <loc xlink:type="locator" xlink:label="bacq_FormationCostsPaidBySponsorInExchangeForIssuanceOfClassBOrdinaryShares" xlink:href="bacq-20250930.xsd#bacq_FormationCostsPaidBySponsorInExchangeForIssuanceOfClassBOrdinaryShares"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="bacq_FormationCostsPaidBySponsorInExchangeForIssuanceOfClassBOrdinaryShares_lbl" xml:lang="en-US">Formation costs paid by Sponsor in exchange for issuance of Class B ordinary shares</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_FormationCostsPaidBySponsorInExchangeForIssuanceOfClassBOrdinaryShares" xlink:to="bacq_FormationCostsPaidBySponsorInExchangeForIssuanceOfClassBOrdinaryShares_lbl"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_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_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:to="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInPrepaidInsurance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInPrepaidInsurance"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_IncreaseDecreaseInPrepaidInsurance_lbl" xml:lang="en-US">Prepaid Insurance</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInPrepaidInsurance" xlink:to="us-gaap_IncreaseDecreaseInPrepaidInsurance_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_PaymentsToAcquireInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireInvestments"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsToAcquireInvestments_lbl" xml:lang="en-US">Investment of cash into Trust Account</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquireInvestments" xlink:to="us-gaap_PaymentsToAcquireInvestments_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_RepaymentsOfRelatedPartyDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RepaymentsOfRelatedPartyDebt"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_RepaymentsOfRelatedPartyDebt_lbl" xml:lang="en-US">Repayment of promissory note &#8211; related party</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RepaymentsOfRelatedPartyDebt" xlink:to="us-gaap_RepaymentsOfRelatedPartyDebt_lbl"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RepaymentsOfRelatedPartyDebt_lbl0" xml:lang="en-US">Repaid of outstanding balance of promissory note (in Dollars)</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RepaymentsOfRelatedPartyDebt" xlink:to="us-gaap_RepaymentsOfRelatedPartyDebt_lbl0"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_PaymentsOfStockIssuanceCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfStockIssuanceCosts"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsOfStockIssuanceCosts_lbl" xml:lang="en-US">Payment of offering costs</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsOfStockIssuanceCosts" xlink:to="us-gaap_PaymentsOfStockIssuanceCosts_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_CommonClassAMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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</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"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonClassAMember_lbl2" 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_lbl2"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_CommonClassBMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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">Class A 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_lbl2"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_CommonStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CommonStockMember_lbl0" 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_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:label="us-gaap_CommonStockMember_lbl1" xml:lang="en-US">Common Stock [Member]</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_lbl1"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockMember_lbl2" xml:lang="en-US">Ordinary Shares [Member]</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_lbl2"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_AdditionalPaidInCapitalMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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/2025/elts/us-gaap-2025.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_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_lbl" xml:lang="en-US">DESCRIPTION OF ORGANIZATION AND BUSINESS OPERATIONS</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:to="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_lbl"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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="bacq_ScheduleOfMarketAssumptionsInValuationOfPublicRightsTableTextBlock" xlink:href="bacq-20250930.xsd#bacq_ScheduleOfMarketAssumptionsInValuationOfPublicRightsTableTextBlock"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_ScheduleOfMarketAssumptionsInValuationOfPublicRightsTableTextBlock_lbl" xml:lang="en-US">Schedule of Valuation of The Public Rights</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ScheduleOfMarketAssumptionsInValuationOfPublicRightsTableTextBlock" xlink:to="bacq_ScheduleOfMarketAssumptionsInValuationOfPublicRightsTableTextBlock_lbl"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bacq_ScheduleOfMarketAssumptionsInValuationOfPublicRightsTableTextBlock_lbl0" xml:lang="en-US">Schedule of Valuation of the Public Rights</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ScheduleOfMarketAssumptionsInValuationOfPublicRightsTableTextBlock" xlink:to="bacq_ScheduleOfMarketAssumptionsInValuationOfPublicRightsTableTextBlock_lbl0"/>    
    <loc xlink:type="locator" xlink:label="bacq_UnderlyingSharePrice" xlink:href="bacq-20250930.xsd#bacq_UnderlyingSharePrice"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_UnderlyingSharePrice_lbl" xml:lang="en-US">Underlying share price</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnderlyingSharePrice" xlink:to="bacq_UnderlyingSharePrice_lbl"/> 
    <loc xlink:type="locator" xlink:label="bacq_PreadjustedValuePerShareRight" xlink:href="bacq-20250930.xsd#bacq_PreadjustedValuePerShareRight"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_PreadjustedValuePerShareRight_lbl" xml:lang="en-US">Pre-adjusted value per share right</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PreadjustedValuePerShareRight" xlink:to="bacq_PreadjustedValuePerShareRight_lbl"/>    
    <loc xlink:type="locator" xlink:label="bacq_MarketAdjustment" xlink:href="bacq-20250930.xsd#bacq_MarketAdjustment"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_MarketAdjustment_lbl" xml:lang="en-US">Market adjustment</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_MarketAdjustment" xlink:to="bacq_MarketAdjustment_lbl"/>   
    <loc xlink:type="locator" xlink:label="bacq_FairValuePerShareRight" xlink:href="bacq-20250930.xsd#bacq_FairValuePerShareRight"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_FairValuePerShareRight_lbl" xml:lang="en-US">Fair value per share right</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_FairValuePerShareRight" xlink:to="bacq_FairValuePerShareRight_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_TemporaryEquityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityTableTextBlock"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TemporaryEquityTableTextBlock_lbl" xml:lang="en-US">Schedule of Class A Ordinary Share Subject To Possible Redemption</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityTableTextBlock" xlink:to="us-gaap_TemporaryEquityTableTextBlock_lbl"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_TemporaryEquityTableTextBlock_lbl0" xml:lang="en-US">Schedule of Ordinary Share subject to Possible Redemption</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityTableTextBlock" xlink:to="us-gaap_TemporaryEquityTableTextBlock_lbl0"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_ProceedsFromIssuanceInitialPublicOffering" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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</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"/>    
    <loc xlink:type="locator" xlink:label="bacq_LessAbstract" xlink:href="bacq-20250930.xsd#bacq_LessAbstract"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_LessAbstract_lbl" xml:lang="en-US">Less:</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_LessAbstract" xlink:to="bacq_LessAbstract_lbl"/>     
    <loc xlink:type="locator" xlink:label="bacq_ProceedsAllocatedToPublicRights" xlink:href="bacq-20250930.xsd#bacq_ProceedsAllocatedToPublicRights"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_ProceedsAllocatedToPublicRights_lbl" xml:lang="en-US">Proceeds allocated to Public Rights</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ProceedsAllocatedToPublicRights" xlink:to="bacq_ProceedsAllocatedToPublicRights_lbl"/>   
    <loc xlink:type="locator" xlink:label="bacq_PlusAbstract" xlink:href="bacq-20250930.xsd#bacq_PlusAbstract"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_PlusAbstract_lbl" xml:lang="en-US">Plus:</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PlusAbstract" xlink:to="bacq_PlusAbstract_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment_lbl" xml:lang="en-US">Remeasurement of carrying value to redemption value</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment" xlink:to="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment_lbl"/>    
    <loc xlink:type="locator" xlink:label="bacq_PlusAbstract0" xlink:href="bacq-20250930.xsd#bacq_PlusAbstract0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_PlusAbstract0_lbl" xml:lang="en-US">Plus:</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PlusAbstract0" xlink:to="bacq_PlusAbstract0_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_PlusAbstract1" xlink:href="bacq-20250930.xsd#bacq_PlusAbstract1"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_PlusAbstract1_lbl" xml:lang="en-US">Plus:</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PlusAbstract1" xlink:to="bacq_PlusAbstract1_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_PlusAbstract2" xlink:href="bacq-20250930.xsd#bacq_PlusAbstract2"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_PlusAbstract2_lbl" xml:lang="en-US">Plus:</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PlusAbstract2" xlink:to="bacq_PlusAbstract2_lbl"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xml:lang="en-US">Schedule of Basic and Diluted Net Income Per Ordinary Share</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:to="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl0" xml:lang="en-US">Schedule of Basic and Diluted Net Income</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:to="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl0"/>   
    <loc xlink:type="locator" xlink:label="bacq_BasicAndDilutedNetIncomeLossPerOrdinaryShareAbstract" xlink:href="bacq-20250930.xsd#bacq_BasicAndDilutedNetIncomeLossPerOrdinaryShareAbstract"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_BasicAndDilutedNetIncomeLossPerOrdinaryShareAbstract_lbl" xml:lang="en-US">Basic and diluted net income (loss) per ordinary share</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_BasicAndDilutedNetIncomeLossPerOrdinaryShareAbstract" xlink:to="bacq_BasicAndDilutedNetIncomeLossPerOrdinaryShareAbstract_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract_lbl" xml:lang="en-US">Numerator:</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:to="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract_lbl"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl" xml:lang="en-US">Allocation of net income (loss)</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl0" xml:lang="en-US">Allocation of net income</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl0"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract_lbl" xml:lang="en-US">Denominator:</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:to="us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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">Diluted weighted average shares outstanding</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="bacq_InitialPublicOfferingTextBlock" xlink:href="bacq-20250930.xsd#bacq_InitialPublicOfferingTextBlock"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_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="bacq_InitialPublicOfferingTextBlock" xlink:to="bacq_InitialPublicOfferingTextBlock_lbl"/> 
    <loc xlink:type="locator" xlink:label="bacq_PrivatePlacementTextBlock" xlink:href="bacq-20250930.xsd#bacq_PrivatePlacementTextBlock"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_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="bacq_PrivatePlacementTextBlock" xlink:to="bacq_PrivatePlacementTextBlock_lbl"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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/2025/elts/us-gaap-2025.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/2025/elts/us-gaap-2025.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">SHAREHOLDERS&#8217; DEFICIT</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_FairValueDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresTextBlock"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xml:lang="en-US">FAIR VALUE MEASUREMENTS</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueDisclosuresTextBlock" xlink:to="us-gaap_FairValueDisclosuresTextBlock_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock_lbl" xml:lang="en-US">Schedule of Company&#8217;s Assets and Liabilities</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock" xlink:to="us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_OtherAssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssetsAbstract"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherAssetsAbstract_lbl" xml:lang="en-US">Asset:</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherAssetsAbstract" xlink:to="us-gaap_OtherAssetsAbstract_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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 REPORTING</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/2025/elts/us-gaap-2025.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 Net Income or Loss and Total Assets</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_Cash" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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="us-gaap_SubsequentEventsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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="bacq_LessAbstract0" xlink:href="bacq-20250930.xsd#bacq_LessAbstract0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_LessAbstract0_lbl" xml:lang="en-US">Less:</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_LessAbstract0" xlink:to="bacq_LessAbstract0_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_PlusAbstract3" xlink:href="bacq-20250930.xsd#bacq_PlusAbstract3"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_PlusAbstract3_lbl" xml:lang="en-US">Plus:</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PlusAbstract3" xlink:to="bacq_PlusAbstract3_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_BasicAndDilutedNetIncomePerShareOfCommonStockAbstract" xlink:href="bacq-20250930.xsd#bacq_BasicAndDilutedNetIncomePerShareOfCommonStockAbstract"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_BasicAndDilutedNetIncomePerShareOfCommonStockAbstract_lbl" xml:lang="en-US">Basic and diluted net income per share of common stock:</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_BasicAndDilutedNetIncomePerShareOfCommonStockAbstract" xlink:to="bacq_BasicAndDilutedNetIncomePerShareOfCommonStockAbstract_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_NumeratorAbstract" xlink:href="bacq-20250930.xsd#bacq_NumeratorAbstract"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_NumeratorAbstract_lbl" xml:lang="en-US">Numerator:</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_NumeratorAbstract" xlink:to="bacq_NumeratorAbstract_lbl"/>     
    <loc xlink:type="locator" xlink:label="bacq_DenominatorAbstract" xlink:href="bacq-20250930.xsd#bacq_DenominatorAbstract"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_DenominatorAbstract_lbl" xml:lang="en-US">Denominator:</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_DenominatorAbstract" xlink:to="bacq_DenominatorAbstract_lbl"/>    
    <loc xlink:type="locator" xlink:label="bacq_AssetAbstract" xlink:href="bacq-20250930.xsd#bacq_AssetAbstract"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_AssetAbstract_lbl" xml:lang="en-US">Asset:</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_AssetAbstract" xlink:to="bacq_AssetAbstract_lbl"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_PaymentOfFinancingAndStockIssuanceCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentOfFinancingAndStockIssuanceCosts"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentOfFinancingAndStockIssuanceCosts_lbl" xml:lang="en-US">Class A ordinary shares issuance costs</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentOfFinancingAndStockIssuanceCosts" xlink:to="us-gaap_PaymentOfFinancingAndStockIssuanceCosts_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_FairValueInputsLevel1Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel1Member"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl" xml:lang="en-US">Level 1 [Member]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueInputsLevel1Member" xlink:to="us-gaap_FairValueInputsLevel1Member_lbl"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl0" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueInputsLevel1Member" xlink:to="us-gaap_FairValueInputsLevel1Member_lbl0"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_CorporateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CorporateMember"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CorporateMember_lbl" xml:lang="en-US">Corporate Segment [Member]</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CorporateMember" xlink:to="us-gaap_CorporateMember_lbl"/>  
    <loc xlink:type="locator" xlink:label="spac_SecurityClassAxis" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_SecurityClassAxis"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_SecurityClassAxis_lbl" xml:lang="en-US">Security Class [Axis]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_SecurityClassAxis" xlink:to="spac_SecurityClassAxis_lbl"/>     
    <loc xlink:type="locator" xlink:label="spac_SpacSponsorAffiliateOrPromoterAxis" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_SpacSponsorAffiliateOrPromoterAxis"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_SpacSponsorAffiliateOrPromoterAxis_lbl" xml:lang="en-US">SPAC Sponsor, Affiliate, or Promoter [Axis]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_SpacSponsorAffiliateOrPromoterAxis" xlink:to="spac_SpacSponsorAffiliateOrPromoterAxis_lbl"/>    
    <loc xlink:type="locator" xlink:label="spac_RedemptionLevelAxis" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_RedemptionLevelAxis"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_RedemptionLevelAxis_lbl" xml:lang="en-US">Redemption Level [Axis]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_RedemptionLevelAxis" xlink:to="spac_RedemptionLevelAxis_lbl"/>    
    <loc xlink:type="locator" xlink:label="spac_DilutionSourceAxis" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DilutionSourceAxis"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DilutionSourceAxis_lbl" xml:lang="en-US">Dilution Source [Axis]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DilutionSourceAxis" xlink:to="spac_DilutionSourceAxis_lbl"/>  
    <loc xlink:type="locator" xlink:label="spac_DeSpacAndRelatedFinancingTransactionsAffectedPartyAxis" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacAndRelatedFinancingTransactionsAffectedPartyAxis"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacAndRelatedFinancingTransactionsAffectedPartyAxis_lbl" xml:lang="en-US">De-SPAC and Related Financing Transactions Affected Party [Axis]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacAndRelatedFinancingTransactionsAffectedPartyAxis" xlink:to="spac_DeSpacAndRelatedFinancingTransactionsAffectedPartyAxis_lbl"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_SubsidiarySaleOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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/2025/elts/us-gaap-2025.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_BusinessAcquisitionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAxis"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionAxis_lbl" xml:lang="en-US">Business Combination [Axis]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionAxis" xlink:to="us-gaap_BusinessAcquisitionAxis_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_TypeOfArrangementAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TypeOfArrangementAxis"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TypeOfArrangementAxis_lbl" xml:lang="en-US">Collaborative Arrangement and Arrangement Other than Collaborative [Axis]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TypeOfArrangementAxis" xlink:to="us-gaap_TypeOfArrangementAxis_lbl"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_RelatedPartyTransactionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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="srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RangeAxis_lbl" xml:lang="en-US">Statistical Measurement [Axis]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RangeAxis" xlink:to="srt_RangeAxis_lbl"/>  
    <loc xlink:type="locator" xlink:label="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_lbl" xml:lang="en-US">Investment, Name [Axis]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:to="srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_lbl"/>    
    <loc xlink:type="locator" xlink:label="spac_DeSpacForepartBoardDeterminationTextBlock" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacForepartBoardDeterminationTextBlock"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_DeSpacForepartBoardDeterminationTextBlock_lbl" xml:lang="en-US">De-SPAC Forepart, Board Determination [Text Block]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacForepartBoardDeterminationTextBlock" xlink:to="spac_DeSpacForepartBoardDeterminationTextBlock_lbl"/>   
    <loc xlink:type="locator" xlink:label="spac_DeSpacBackgroundProspectusSummaryTextBlock" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacBackgroundProspectusSummaryTextBlock"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_DeSpacBackgroundProspectusSummaryTextBlock_lbl" xml:lang="en-US">De-SPAC, Background, Prospectus Summary [Text Block]</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacBackgroundProspectusSummaryTextBlock" xlink:to="spac_DeSpacBackgroundProspectusSummaryTextBlock_lbl"/>     
    <loc xlink:type="locator" xlink:label="spac_DeSpacForepartMaterialFinancingTransactionsOccurredDescriptionTextBlock" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacForepartMaterialFinancingTransactionsOccurredDescriptionTextBlock"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_DeSpacForepartMaterialFinancingTransactionsOccurredDescriptionTextBlock_lbl" xml:lang="en-US">De-SPAC Forepart, Material Financing Transactions Occurred, Description [Text Block]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacForepartMaterialFinancingTransactionsOccurredDescriptionTextBlock" xlink:to="spac_DeSpacForepartMaterialFinancingTransactionsOccurredDescriptionTextBlock_lbl"/>   
    <loc xlink:type="locator" xlink:label="spac_DeSpacForepartSponsorCompensationMaterialDilutionFlag" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacForepartSponsorCompensationMaterialDilutionFlag"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_DeSpacForepartSponsorCompensationMaterialDilutionFlag_lbl" xml:lang="en-US">De-SPAC Forepart, Sponsor Compensation, Material Dilution [Flag]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacForepartSponsorCompensationMaterialDilutionFlag" xlink:to="spac_DeSpacForepartSponsorCompensationMaterialDilutionFlag_lbl"/>  
    <loc xlink:type="locator" xlink:label="spac_DeSpacBoardDeterminationProspectusSummaryTextBlock" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacBoardDeterminationProspectusSummaryTextBlock"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_DeSpacBoardDeterminationProspectusSummaryTextBlock_lbl" xml:lang="en-US">De-SPAC, Board Determination, Prospectus Summary [Text Block]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacBoardDeterminationProspectusSummaryTextBlock" xlink:to="spac_DeSpacBoardDeterminationProspectusSummaryTextBlock_lbl"/> 
    <loc xlink:type="locator" xlink:label="spac_DeSpacForepartSecuritiesIssuedOrToBeIssuedShares" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacForepartSecuritiesIssuedOrToBeIssuedShares"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_DeSpacForepartSecuritiesIssuedOrToBeIssuedShares_lbl" xml:lang="en-US">De-SPAC Forepart, Securities Issued or To Be Issued, Shares</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacForepartSecuritiesIssuedOrToBeIssuedShares" xlink:to="spac_DeSpacForepartSecuritiesIssuedOrToBeIssuedShares_lbl"/>  
    <loc xlink:type="locator" xlink:label="spac_DeSpacForepartPricePaidOrToBePaidForSecuritiesPerShare" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacForepartPricePaidOrToBePaidForSecuritiesPerShare"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_DeSpacForepartPricePaidOrToBePaidForSecuritiesPerShare_lbl" xml:lang="en-US">De-SPAC Forepart, Price Paid or to be Paid for Securities, Per Share (in Dollars per share)</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacForepartPricePaidOrToBePaidForSecuritiesPerShare" xlink:to="spac_DeSpacForepartPricePaidOrToBePaidForSecuritiesPerShare_lbl"/>    
    <loc xlink:type="locator" xlink:label="spac_DeSpacSecurityHoldersRedemptionRightsSummaryTextBlock" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacSecurityHoldersRedemptionRightsSummaryTextBlock"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_DeSpacSecurityHoldersRedemptionRightsSummaryTextBlock_lbl" xml:lang="en-US">De-SPAC, Security Holders Redemption Rights Summary [Text Block]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacSecurityHoldersRedemptionRightsSummaryTextBlock" xlink:to="spac_DeSpacSecurityHoldersRedemptionRightsSummaryTextBlock_lbl"/>  
    <loc xlink:type="locator" xlink:label="spac_DeSpacSecurityHoldersAreEntitledToRedemptionRightsFlag" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacSecurityHoldersAreEntitledToRedemptionRightsFlag"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_DeSpacSecurityHoldersAreEntitledToRedemptionRightsFlag_lbl" xml:lang="en-US">De-SPAC, Security Holders are Entitled to Redemption Rights [Flag]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacSecurityHoldersAreEntitledToRedemptionRightsFlag" xlink:to="spac_DeSpacSecurityHoldersAreEntitledToRedemptionRightsFlag_lbl"/>    
    <loc xlink:type="locator" xlink:label="spac_DeSpacTransactionAccountingTreatmentTextBlock" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacTransactionAccountingTreatmentTextBlock"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_DeSpacTransactionAccountingTreatmentTextBlock_lbl" xml:lang="en-US">De-SPAC Transaction, Accounting Treatment [Text Block]</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacTransactionAccountingTreatmentTextBlock" xlink:to="spac_DeSpacTransactionAccountingTreatmentTextBlock_lbl"/> 
    <loc xlink:type="locator" xlink:label="spac_DeSpacSecurityHoldersAreEntitledToAppraisalRightsFlag" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacSecurityHoldersAreEntitledToAppraisalRightsFlag"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_DeSpacSecurityHoldersAreEntitledToAppraisalRightsFlag_lbl" xml:lang="en-US">De-SPAC, Security Holders are Entitled to Appraisal Rights [Flag]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacSecurityHoldersAreEntitledToAppraisalRightsFlag" xlink:to="spac_DeSpacSecurityHoldersAreEntitledToAppraisalRightsFlag_lbl"/>  
    <loc xlink:type="locator" xlink:label="spac_DeSpacSecurityHoldersAppraisalRightsSummaryTextBlock" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacSecurityHoldersAppraisalRightsSummaryTextBlock"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_DeSpacSecurityHoldersAppraisalRightsSummaryTextBlock_lbl" xml:lang="en-US">De-SPAC, Security Holders Appraisal Rights Summary [Text Block]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacSecurityHoldersAppraisalRightsSummaryTextBlock" xlink:to="spac_DeSpacSecurityHoldersAppraisalRightsSummaryTextBlock_lbl"/>     
    <loc xlink:type="locator" xlink:label="spac_DeSpacCompensationProspectusSummaryTableTextBlock" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacCompensationProspectusSummaryTableTextBlock"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_DeSpacCompensationProspectusSummaryTableTextBlock_lbl" xml:lang="en-US">De-SPAC, Compensation, Prospectus Summary [Table Text Block]</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacCompensationProspectusSummaryTableTextBlock" xlink:to="spac_DeSpacCompensationProspectusSummaryTableTextBlock_lbl"/>    
    <loc xlink:type="locator" xlink:label="spac_DeSpacNetTangibleBookValuePerShare" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacNetTangibleBookValuePerShare"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_DeSpacNetTangibleBookValuePerShare_lbl" xml:lang="en-US">De-SPAC, Net Tangible Book Value, Per Share (in Dollars per share)</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacNetTangibleBookValuePerShare" xlink:to="spac_DeSpacNetTangibleBookValuePerShare_lbl"/>    
    <loc xlink:type="locator" xlink:label="spac_DeSpacNetTangibleBookValueAdjusted" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacNetTangibleBookValueAdjusted"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_DeSpacNetTangibleBookValueAdjusted_lbl" xml:lang="en-US">De-SPAC, Net Tangible Book Value, Adjusted</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacNetTangibleBookValueAdjusted" xlink:to="spac_DeSpacNetTangibleBookValueAdjusted_lbl"/>    
    <loc xlink:type="locator" xlink:label="spac_DeSpacNumberOfSharesUsedAdjustment" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacNumberOfSharesUsedAdjustment"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_DeSpacNumberOfSharesUsedAdjustment_lbl" xml:lang="en-US">De-SPAC, Number of Shares Used, Adjustment (in Shares)</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacNumberOfSharesUsedAdjustment" xlink:to="spac_DeSpacNumberOfSharesUsedAdjustment_lbl"/>    
    <loc xlink:type="locator" xlink:label="spac_DeSpacNetTangibleBookValueAdjustedPerShare" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacNetTangibleBookValueAdjustedPerShare"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_DeSpacNetTangibleBookValueAdjustedPerShare_lbl" xml:lang="en-US">De-SPAC, Net Tangible Book Value, Adjusted, Per Share (in Dollars per share)</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacNetTangibleBookValueAdjustedPerShare" xlink:to="spac_DeSpacNetTangibleBookValueAdjustedPerShare_lbl"/>     
    <loc xlink:type="locator" xlink:label="spac_DeSpacNetTangibleBookValueAmountOfDilutionPerShare" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacNetTangibleBookValueAmountOfDilutionPerShare"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_DeSpacNetTangibleBookValueAmountOfDilutionPerShare_lbl" xml:lang="en-US">De-SPAC, Net Tangible Book Value, Amount of Dilution Per Share (in Dollars per share)</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacNetTangibleBookValueAmountOfDilutionPerShare" xlink:to="spac_DeSpacNetTangibleBookValueAmountOfDilutionPerShare_lbl"/> 
    <loc xlink:type="locator" xlink:label="spac_DeSpacNumberOfSharesUsedToDetermineNetTangibleBookValueAdjusted" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacNumberOfSharesUsedToDetermineNetTangibleBookValueAdjusted"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_DeSpacNumberOfSharesUsedToDetermineNetTangibleBookValueAdjusted_lbl" xml:lang="en-US">De-SPAC, Number of Shares Used to Determine Net Tangible Book Value, Adjusted (in Shares)</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacNumberOfSharesUsedToDetermineNetTangibleBookValueAdjusted" xlink:to="spac_DeSpacNumberOfSharesUsedToDetermineNetTangibleBookValueAdjusted_lbl"/>  
    <loc xlink:type="locator" xlink:label="spac_DeSpacBoardDeterminationDisclosureTextBlock" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacBoardDeterminationDisclosureTextBlock"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_DeSpacBoardDeterminationDisclosureTextBlock_lbl" xml:lang="en-US">De-SPAC, Board Determination Disclosure [Text Block]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacBoardDeterminationDisclosureTextBlock" xlink:to="spac_DeSpacBoardDeterminationDisclosureTextBlock_lbl"/>  
    <loc xlink:type="locator" xlink:label="spac_EffectsOfTheDeSpacAndRelatedFinancingTransactionsDetrimentsTextBlock" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_EffectsOfTheDeSpacAndRelatedFinancingTransactionsDetrimentsTextBlock"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_EffectsOfTheDeSpacAndRelatedFinancingTransactionsDetrimentsTextBlock_lbl" xml:lang="en-US">Effects of the de-SPAC and Related Financing Transactions, Detriments [Text Block]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_EffectsOfTheDeSpacAndRelatedFinancingTransactionsDetrimentsTextBlock" xlink:to="spac_EffectsOfTheDeSpacAndRelatedFinancingTransactionsDetrimentsTextBlock_lbl"/>  
    <loc xlink:type="locator" xlink:label="spac_EffectsOfTheDeSpacAndRelatedFinancingTransactionsBenefitsTextBlock" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_EffectsOfTheDeSpacAndRelatedFinancingTransactionsBenefitsTextBlock"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_EffectsOfTheDeSpacAndRelatedFinancingTransactionsBenefitsTextBlock_lbl" xml:lang="en-US">Effects of the de-SPAC and Related Financing Transactions, Benefits [Text Block]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_EffectsOfTheDeSpacAndRelatedFinancingTransactionsBenefitsTextBlock" xlink:to="spac_EffectsOfTheDeSpacAndRelatedFinancingTransactionsBenefitsTextBlock_lbl"/>   
    <loc xlink:type="locator" xlink:label="dei_EntityIncorporationDateOfIncorporation" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityIncorporationDateOfIncorporation"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityIncorporationDateOfIncorporation_lbl" xml:lang="en-US">Incorporation date</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityIncorporationDateOfIncorporation" xlink:to="dei_EntityIncorporationDateOfIncorporation_lbl"/>     
    <loc xlink:type="locator" xlink:label="bacq_UnitsIssuedDuringPeriodSharesNewIssues" xlink:href="bacq-20250930.xsd#bacq_UnitsIssuedDuringPeriodSharesNewIssues"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_UnitsIssuedDuringPeriodSharesNewIssues_lbl" xml:lang="en-US">Consummated units (in Shares)</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnitsIssuedDuringPeriodSharesNewIssues" xlink:to="bacq_UnitsIssuedDuringPeriodSharesNewIssues_lbl"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bacq_UnitsIssuedDuringPeriodSharesNewIssues_lbl0" xml:lang="en-US">Aggregate units</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnitsIssuedDuringPeriodSharesNewIssues" xlink:to="bacq_UnitsIssuedDuringPeriodSharesNewIssues_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:label="bacq_UnitsIssuedDuringPeriodSharesNewIssues_lbl1" 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="bacq_UnitsIssuedDuringPeriodSharesNewIssues" xlink:to="bacq_UnitsIssuedDuringPeriodSharesNewIssues_lbl1"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_SharesIssuedPricePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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">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_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, 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_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 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_lbl1"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SharesIssuedPricePerShare_lbl2" xml:lang="en-US">Share issued price (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="bacq_NumberOfSharesIssuedPerUnit" xlink:href="bacq-20250930.xsd#bacq_NumberOfSharesIssuedPerUnit"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_NumberOfSharesIssuedPerUnit_lbl" xml:lang="en-US">Number of shares per unit (in Shares)</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_NumberOfSharesIssuedPerUnit" xlink:to="bacq_NumberOfSharesIssuedPerUnit_lbl"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="bacq_NumberOfSharesIssuedPerUnit_lbl0" xml:lang="en-US">Number of ordinary shares in a unit</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_NumberOfSharesIssuedPerUnit" xlink:to="bacq_NumberOfSharesIssuedPerUnit_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:label="bacq_NumberOfSharesIssuedPerUnit_lbl1" xml:lang="en-US">Number of issued per unit</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_NumberOfSharesIssuedPerUnit" xlink:to="bacq_NumberOfSharesIssuedPerUnit_lbl1"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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">Sale of stock units (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">Aggregate units</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"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl1" xml:lang="en-US">Sponsor transferred 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_lbl1"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_SaleOfStockPricePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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 of 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_SaleOfStockPricePerShare" xlink:to="us-gaap_SaleOfStockPricePerShare_lbl"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl0" 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_SaleOfStockPricePerShare" xlink:to="us-gaap_SaleOfStockPricePerShare_lbl0"/> 
    <loc xlink:type="locator" xlink:label="bacq_TransactionCosts" xlink:href="bacq-20250930.xsd#bacq_TransactionCosts"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_TransactionCosts_lbl" xml:lang="en-US">Consisting</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_TransactionCosts" xlink:to="bacq_TransactionCosts_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_PaymentsForUnderwritingExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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</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"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PaymentsForUnderwritingExpense_lbl0" xml:lang="en-US">Underwriters payable</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"/>   
    <loc xlink:type="locator" xlink:label="bacq_DeferredUnderwritingFee" xlink:href="bacq-20250930.xsd#bacq_DeferredUnderwritingFee"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_DeferredUnderwritingFee_lbl" xml:lang="en-US">Deferred underwriting fee</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_DeferredUnderwritingFee" xlink:to="bacq_DeferredUnderwritingFee_lbl"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_DeferredOfferingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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">Other 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_BusinessCombinationStepAcquisitionEquityInterestInAcquireePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireePercentage"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireePercentage_lbl" xml:lang="en-US">Net balance percentage</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireePercentage" xlink:to="us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireePercentage_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_lbl" xml:lang="en-US">Voting interest acquired</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:to="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_lbl"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_lbl0" xml:lang="en-US">Percentage of voting interest</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:to="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_lbl0"/> 
    <loc xlink:type="locator" xlink:label="bacq_PercentageOfRedeemInitialBusinessCombination" xlink:href="bacq-20250930.xsd#bacq_PercentageOfRedeemInitialBusinessCombination"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_PercentageOfRedeemInitialBusinessCombination_lbl" xml:lang="en-US">Percentage of redeem initial business combination</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PercentageOfRedeemInitialBusinessCombination" xlink:to="bacq_PercentageOfRedeemInitialBusinessCombination_lbl"/>    
    <loc xlink:type="locator" xlink:label="bacq_InterestToPayDissolutionExpenses" xlink:href="bacq-20250930.xsd#bacq_InterestToPayDissolutionExpenses"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_InterestToPayDissolutionExpenses_lbl" xml:lang="en-US">Interest to pay dissolution expenses</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_InterestToPayDissolutionExpenses" xlink:to="bacq_InterestToPayDissolutionExpenses_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_SharePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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">Trust account per public share (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"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_SharePrice_lbl0" xml:lang="en-US">Fair value 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_SharePrice" xlink:to="us-gaap_SharePrice_lbl0"/>   
    <loc xlink:type="locator" xlink:label="bacq_ConvertiblePromissoryNotes" xlink:href="bacq-20250930.xsd#bacq_ConvertiblePromissoryNotes"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_ConvertiblePromissoryNotes_lbl" xml:lang="en-US">Convertible promissory notes</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ConvertiblePromissoryNotes" xlink:to="bacq_ConvertiblePromissoryNotes_lbl"/>   
    <loc xlink:type="locator" xlink:label="bacq_CommonStockPurchasePrice" xlink:href="bacq-20250930.xsd#bacq_CommonStockPurchasePrice"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_CommonStockPurchasePrice_lbl" xml:lang="en-US">Common stock purchase price</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_CommonStockPurchasePrice" xlink:to="bacq_CommonStockPurchasePrice_lbl"/>    
    <loc xlink:type="locator" xlink:label="bacq_PercentageOfNumberOfShares" xlink:href="bacq-20250930.xsd#bacq_PercentageOfNumberOfShares"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_PercentageOfNumberOfShares_lbl" xml:lang="en-US">Percentage of number of shares</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PercentageOfNumberOfShares" xlink:to="bacq_PercentageOfNumberOfShares_lbl"/>   
    <loc xlink:type="locator" xlink:label="bacq_AggregatePurchasePrice" xlink:href="bacq-20250930.xsd#bacq_AggregatePurchasePrice"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_AggregatePurchasePrice_lbl" xml:lang="en-US">Aggregate purchase price</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_AggregatePurchasePrice" xlink:to="bacq_AggregatePurchasePrice_lbl"/>     
    <loc xlink:type="locator" xlink:label="bacq_InvestmentsMaximumMaturityTerm" xlink:href="bacq-20250930.xsd#bacq_InvestmentsMaximumMaturityTerm"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_InvestmentsMaximumMaturityTerm_lbl" xml:lang="en-US">Maturity term of U.S government securities</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_InvestmentsMaximumMaturityTerm" xlink:to="bacq_InvestmentsMaximumMaturityTerm_lbl"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_InterestExpenseOther" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseOther"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InterestExpenseOther_lbl" xml:lang="en-US">Interest dissolution expenses</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestExpenseOther" xlink:to="us-gaap_InterestExpenseOther_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_WorkingCapitalDeficit" xlink:href="bacq-20250930.xsd#bacq_WorkingCapitalDeficit"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_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="bacq_WorkingCapitalDeficit" xlink:to="bacq_WorkingCapitalDeficit_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_CashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashEquivalentsAtCarryingValue"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashEquivalentsAtCarryingValue_lbl" xml:lang="en-US">Cash equivalents</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashEquivalentsAtCarryingValue" xlink:to="us-gaap_CashEquivalentsAtCarryingValue_lbl"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_CashFDICInsuredAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashFDICInsuredAmount"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashFDICInsuredAmount_lbl" xml:lang="en-US">FDIC limit amount</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashFDICInsuredAmount" xlink:to="us-gaap_CashFDICInsuredAmount_lbl"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_UnrecognizedTaxBenefits" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrecognizedTaxBenefits"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xml:lang="en-US">Unrecognized tax benefits</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_UnrecognizedTaxBenefits" xlink:to="us-gaap_UnrecognizedTaxBenefits_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued_lbl" xml:lang="en-US">Accrued for interest and penalties</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued" xlink:to="us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xml:lang="en-US">Purchase of exercisable shares (in Shares)</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised" xlink:to="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_WeightedAverageNumberOfSharesForfeited" xlink:href="bacq-20250930.xsd#bacq_WeightedAverageNumberOfSharesForfeited"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_WeightedAverageNumberOfSharesForfeited_lbl" xml:lang="en-US">Weighted average number of shares forfeited (in Shares)</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_WeightedAverageNumberOfSharesForfeited" xlink:to="bacq_WeightedAverageNumberOfSharesForfeited_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_NumberOfOrdinaryShares" xlink:href="bacq-20250930.xsd#bacq_NumberOfOrdinaryShares"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_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="bacq_NumberOfOrdinaryShares" xlink:to="bacq_NumberOfOrdinaryShares_lbl"/>     
    <loc xlink:type="locator" xlink:label="bacq_PublicSharesRedemptionPercentage" xlink:href="bacq-20250930.xsd#bacq_PublicSharesRedemptionPercentage"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_PublicSharesRedemptionPercentage_lbl" xml:lang="en-US">Public shares redemption percentage</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PublicSharesRedemptionPercentage" xlink:to="bacq_PublicSharesRedemptionPercentage_lbl"/>     
    <loc xlink:type="locator" xlink:label="bacq_AdditionalSharesIssued" xlink:href="bacq-20250930.xsd#bacq_AdditionalSharesIssued"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_AdditionalSharesIssued_lbl" xml:lang="en-US">Additional shares issued</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_AdditionalSharesIssued" xlink:to="bacq_AdditionalSharesIssued_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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 to 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="bacq_PercentageOfIssuedAndOutstandingShares" xlink:href="bacq-20250930.xsd#bacq_PercentageOfIssuedAndOutstandingShares"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_PercentageOfIssuedAndOutstandingShares_lbl" xml:lang="en-US">Percentage of issued and outstanding</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PercentageOfIssuedAndOutstandingShares" xlink:to="bacq_PercentageOfIssuedAndOutstandingShares_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_RestrictionsOnTransferPeriodOfTimeAfterBusinessCombinationCompletion" xlink:href="bacq-20250930.xsd#bacq_RestrictionsOnTransferPeriodOfTimeAfterBusinessCombinationCompletion"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_RestrictionsOnTransferPeriodOfTimeAfterBusinessCombinationCompletion_lbl" xml:lang="en-US">Restrictions on transfer period of time after business combination completion</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_RestrictionsOnTransferPeriodOfTimeAfterBusinessCombinationCompletion" xlink:to="bacq_RestrictionsOnTransferPeriodOfTimeAfterBusinessCombinationCompletion_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_NumberOfTradingDays" xlink:href="bacq-20250930.xsd#bacq_NumberOfTradingDays"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_NumberOfTradingDays_lbl" xml:lang="en-US">Trading days</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_NumberOfTradingDays" xlink:to="bacq_NumberOfTradingDays_lbl"/>    
    <loc xlink:type="locator" xlink:label="bacq_ThresholdPeriodAfterBusinessCombinationInWhichSpecifiedTradingDaysWithinAnySpecifiedTradingDayPeriodCommences" xlink:href="bacq-20250930.xsd#bacq_ThresholdPeriodAfterBusinessCombinationInWhichSpecifiedTradingDaysWithinAnySpecifiedTradingDayPeriodCommences"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_ThresholdPeriodAfterBusinessCombinationInWhichSpecifiedTradingDaysWithinAnySpecifiedTradingDayPeriodCommences_lbl" xml:lang="en-US">Threshold period after business combination.</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ThresholdPeriodAfterBusinessCombinationInWhichSpecifiedTradingDaysWithinAnySpecifiedTradingDayPeriodCommences" xlink:to="bacq_ThresholdPeriodAfterBusinessCombinationInWhichSpecifiedTradingDaysWithinAnySpecifiedTradingDayPeriodCommences_lbl"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SaleOfStockConsiderationReceivedOnTransaction"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SaleOfStockConsiderationReceivedOnTransaction_lbl" xml:lang="en-US">Aggregate amount (in Dollars)</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:to="us-gaap_SaleOfStockConsiderationReceivedOnTransaction_lbl"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_NotesPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NotesPayable"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NotesPayable_lbl" xml:lang="en-US">Note payable (in Dollars)</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NotesPayable" xlink:to="us-gaap_NotesPayable_lbl"/> 
    <loc xlink:type="locator" xlink:label="bacq_WorkingCapitalLoanAmount" xlink:href="bacq-20250930.xsd#bacq_WorkingCapitalLoanAmount"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_WorkingCapitalLoanAmount_lbl" xml:lang="en-US">Working capital loan amount (in Dollars)</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_WorkingCapitalLoanAmount" xlink:to="bacq_WorkingCapitalLoanAmount_lbl"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_BusinessAcquisitionSharePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionSharePrice"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessAcquisitionSharePrice_lbl" xml:lang="en-US">Business combination price (in Dollars per share)</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionSharePrice" xlink:to="us-gaap_BusinessAcquisitionSharePrice_lbl"/>     
    <loc xlink:type="locator" xlink:label="bacq_WorkingCapitalOutstandingLoans" xlink:href="bacq-20250930.xsd#bacq_WorkingCapitalOutstandingLoans"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_WorkingCapitalOutstandingLoans_lbl" xml:lang="en-US">Working capital outstanding loans (in Dollars)</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_WorkingCapitalOutstandingLoans" xlink:to="bacq_WorkingCapitalOutstandingLoans_lbl"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_StockIssuedDuringPeriodSharesOther" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesOther"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockIssuedDuringPeriodSharesOther_lbl" xml:lang="en-US">Additional founder shares</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesOther" xlink:to="us-gaap_StockIssuedDuringPeriodSharesOther_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentOwnershipPercentage"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EquityMethodInvestmentOwnershipPercentage_lbl" xml:lang="en-US">Ownership percentage</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:to="us-gaap_EquityMethodInvestmentOwnershipPercentage_lbl"/>    
    <loc xlink:type="locator" xlink:label="bacq_OverAllotmentOptionPeriod" xlink:href="bacq-20250930.xsd#bacq_OverAllotmentOptionPeriod"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_OverAllotmentOptionPeriod_lbl" xml:lang="en-US">Over allotment option period</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_OverAllotmentOptionPeriod" xlink:to="bacq_OverAllotmentOptionPeriod_lbl"/> 
    <loc xlink:type="locator" xlink:label="bacq_UnderwritingCashDiscountPerUnit" xlink:href="bacq-20250930.xsd#bacq_UnderwritingCashDiscountPerUnit"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_UnderwritingCashDiscountPerUnit_lbl" xml:lang="en-US">Underwriting cash discount per unit (in Dollars per share)</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnderwritingCashDiscountPerUnit" xlink:to="bacq_UnderwritingCashDiscountPerUnit_lbl"/>   
    <loc xlink:type="locator" xlink:label="bacq_UnderwriterCashDiscount" xlink:href="bacq-20250930.xsd#bacq_UnderwriterCashDiscount"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_UnderwriterCashDiscount_lbl" xml:lang="en-US">Underwriter cash discount</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnderwriterCashDiscount" xlink:to="bacq_UnderwriterCashDiscount_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_DeferredFeePerUnit" xlink:href="bacq-20250930.xsd#bacq_DeferredFeePerUnit"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_DeferredFeePerUnit_lbl" xml:lang="en-US">Deferred fee per unit (in Dollars per share)</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_DeferredFeePerUnit" xlink:to="bacq_DeferredFeePerUnit_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_AggregateShareIssuedPercentage" xlink:href="bacq-20250930.xsd#bacq_AggregateShareIssuedPercentage"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_AggregateShareIssuedPercentage_lbl" xml:lang="en-US">Aggregate share issued percentage</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_AggregateShareIssuedPercentage" xlink:to="bacq_AggregateShareIssuedPercentage_lbl"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_CommonStockVotingRights" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockVotingRights"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonStockVotingRights_lbl" xml:lang="en-US">Voted on by shareholders</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockVotingRights" xlink:to="us-gaap_CommonStockVotingRights_lbl"/>   
    <loc xlink:type="locator" xlink:label="bacq_BusinessCombinationConsiderationsTransferredEquityInterestsIssuedAndIssuable" xlink:href="bacq-20250930.xsd#bacq_BusinessCombinationConsiderationsTransferredEquityInterestsIssuedAndIssuable"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_BusinessCombinationConsiderationsTransferredEquityInterestsIssuedAndIssuable_lbl" xml:lang="en-US">Holder rights of shares</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_BusinessCombinationConsiderationsTransferredEquityInterestsIssuedAndIssuable" xlink:to="bacq_BusinessCombinationConsiderationsTransferredEquityInterestsIssuedAndIssuable_lbl"/>   
    <loc xlink:type="locator" xlink:label="bacq_CommonStockShareIssued" xlink:href="bacq-20250930.xsd#bacq_CommonStockShareIssued"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_CommonStockShareIssued_lbl" xml:lang="en-US">Common stock share issued</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_CommonStockShareIssued" xlink:to="bacq_CommonStockShareIssued_lbl"/>     
    <loc xlink:type="locator" xlink:label="bacq_CommonStockShareOutstanding" xlink:href="bacq-20250930.xsd#bacq_CommonStockShareOutstanding"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_CommonStockShareOutstanding_lbl" xml:lang="en-US">Common stock share outstanding</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_CommonStockShareOutstanding" xlink:to="bacq_CommonStockShareOutstanding_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription_lbl" xml:lang="en-US">Segment description</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription" xlink:to="us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription_lbl"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration_lbl" xml:lang="en-US">Segment Reporting, CODM, Individual Title and Position or Group Name [Extensible Enumeration]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration" xlink:to="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_NumberOfReportableSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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">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_BasisOfAccountingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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="bacq_LiquidityCapitalResourcesAndGoingConcernPolicyTextBlock" xlink:href="bacq-20250930.xsd#bacq_LiquidityCapitalResourcesAndGoingConcernPolicyTextBlock"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_LiquidityCapitalResourcesAndGoingConcernPolicyTextBlock_lbl" xml:lang="en-US">Liquidity, Capital Resources and Going Concern</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_LiquidityCapitalResourcesAndGoingConcernPolicyTextBlock" xlink:to="bacq_LiquidityCapitalResourcesAndGoingConcernPolicyTextBlock_lbl"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_ConsolidationPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConsolidationPolicyTextBlock"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConsolidationPolicyTextBlock_lbl" xml:lang="en-US">Principles of Consolidation</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConsolidationPolicyTextBlock" xlink:to="us-gaap_ConsolidationPolicyTextBlock_lbl"/>   
    <loc xlink:type="locator" xlink:label="bacq_EmergingGrowthCompanyPolicyTextBlock" xlink:href="bacq-20250930.xsd#bacq_EmergingGrowthCompanyPolicyTextBlock"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_EmergingGrowthCompanyPolicyTextBlock_lbl" xml:lang="en-US">Emerging Growth Company</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_EmergingGrowthCompanyPolicyTextBlock" xlink:to="bacq_EmergingGrowthCompanyPolicyTextBlock_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_UseOfEstimates" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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_CashAndCashEquivalentsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsPolicyTextBlock"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashAndCashEquivalentsPolicyTextBlock_lbl" xml:lang="en-US">Cash and Cash Equivalents</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:to="us-gaap_CashAndCashEquivalentsPolicyTextBlock_lbl"/> 
    <loc xlink:type="locator" xlink:label="bacq_InvestmentsHeldInTrustAccountPolicyTextBlock" xlink:href="bacq-20250930.xsd#bacq_InvestmentsHeldInTrustAccountPolicyTextBlock"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_InvestmentsHeldInTrustAccountPolicyTextBlock_lbl" xml:lang="en-US">Investments Held in Trust Account</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_InvestmentsHeldInTrustAccountPolicyTextBlock" xlink:to="bacq_InvestmentsHeldInTrustAccountPolicyTextBlock_lbl"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_ConcentrationRiskCreditRisk" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskCreditRisk"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConcentrationRiskCreditRisk_lbl" xml:lang="en-US">Concentration of Credit Risk</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskCreditRisk" xlink:to="us-gaap_ConcentrationRiskCreditRisk_lbl"/> 
    <loc xlink:type="locator" xlink:label="bacq_OfferingCostsPolicyTextBlock" xlink:href="bacq-20250930.xsd#bacq_OfferingCostsPolicyTextBlock"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_OfferingCostsPolicyTextBlock_lbl" xml:lang="en-US">Offering Costs</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_OfferingCostsPolicyTextBlock" xlink:to="bacq_OfferingCostsPolicyTextBlock_lbl"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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_IncomeTaxPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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="bacq_RightsPolicyTextBlock" xlink:href="bacq-20250930.xsd#bacq_RightsPolicyTextBlock"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_RightsPolicyTextBlock_lbl" xml:lang="en-US">Rights</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_RightsPolicyTextBlock" xlink:to="bacq_RightsPolicyTextBlock_lbl"/>   
    <loc xlink:type="locator" xlink:label="bacq_ClassARedeemableShareClassificationPolicyTextBlock" xlink:href="bacq-20250930.xsd#bacq_ClassARedeemableShareClassificationPolicyTextBlock"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_ClassARedeemableShareClassificationPolicyTextBlock_lbl" xml:lang="en-US">Class A Ordinary Shares Subject to Possible Redemption</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ClassARedeemableShareClassificationPolicyTextBlock" xlink:to="bacq_ClassARedeemableShareClassificationPolicyTextBlock_lbl"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_EarningsPerSharePolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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 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_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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="bacq_LiquidityAndCapitalResourcesPolicyTextBlock" xlink:href="bacq-20250930.xsd#bacq_LiquidityAndCapitalResourcesPolicyTextBlock"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_LiquidityAndCapitalResourcesPolicyTextBlock_lbl" xml:lang="en-US">Liquidity, Capital Resources and Going Concern</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_LiquidityAndCapitalResourcesPolicyTextBlock" xlink:to="bacq_LiquidityAndCapitalResourcesPolicyTextBlock_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_CashHeldInTrustAccountPolicyTextBlock" xlink:href="bacq-20250930.xsd#bacq_CashHeldInTrustAccountPolicyTextBlock"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_CashHeldInTrustAccountPolicyTextBlock_lbl" xml:lang="en-US">Investments Held in Trust Account</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_CashHeldInTrustAccountPolicyTextBlock" xlink:to="bacq_CashHeldInTrustAccountPolicyTextBlock_lbl"/>     
    <loc xlink:type="locator" xlink:label="spac_CommonSharesMember" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_CommonSharesMember"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_CommonSharesMember_lbl" xml:lang="en-US">Common Shares [Member]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_CommonSharesMember" xlink:to="spac_CommonSharesMember_lbl"/>  
    <loc xlink:type="locator" xlink:label="spac_FounderSharesMember" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_FounderSharesMember"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_FounderSharesMember_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="spac_FounderSharesMember" xlink:to="spac_FounderSharesMember_lbl"/>    
    <loc xlink:type="locator" xlink:label="spac_NoRedemptionMember" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_NoRedemptionMember"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_NoRedemptionMember_lbl" xml:lang="en-US">No Redemption [Member]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_NoRedemptionMember" xlink:to="spac_NoRedemptionMember_lbl"/>  
    <loc xlink:type="locator" xlink:label="spac_RedemptionAt50PercentOfMaximumMember" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_RedemptionAt50PercentOfMaximumMember"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_RedemptionAt50PercentOfMaximumMember_lbl" xml:lang="en-US">Redemption at 50 Percent of Maximum [Member]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_RedemptionAt50PercentOfMaximumMember" xlink:to="spac_RedemptionAt50PercentOfMaximumMember_lbl"/>   
    <loc xlink:type="locator" xlink:label="spac_RedemptionAt100PercentOfMaximumMember" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_RedemptionAt100PercentOfMaximumMember"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_RedemptionAt100PercentOfMaximumMember_lbl" xml:lang="en-US">Redemption at 100 Percent of Maximum [Member]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_RedemptionAt100PercentOfMaximumMember" xlink:to="spac_RedemptionAt100PercentOfMaximumMember_lbl"/>     
    <loc xlink:type="locator" xlink:label="spac_PublicUnitsMember" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_PublicUnitsMember"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="spac_PublicUnitsMember_lbl" xml:lang="en-US">Public Units [Member]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_PublicUnitsMember" xlink:to="spac_PublicUnitsMember_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_RightsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RightsMember"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RightsMember_lbl" xml:lang="en-US">Rights [Member]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RightsMember" xlink:to="us-gaap_RightsMember_lbl"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember_lbl" xml:lang="en-US">Business Combination [Member]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember" xlink:to="us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember_lbl"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember_lbl0" xml:lang="en-US">Business Combination, Series of Individually Immaterial Business Combinations [Member]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember" xlink:to="us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember_lbl0"/>     
    <loc xlink:type="locator" xlink:label="bacq_PostBusinessCombinationMember" xlink:href="bacq-20250930.xsd#bacq_PostBusinessCombinationMember"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_PostBusinessCombinationMember_lbl" xml:lang="en-US">Post-Business Combination [Member]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PostBusinessCombinationMember" xlink:to="bacq_PostBusinessCombinationMember_lbl"/>    
    <loc xlink:type="locator" xlink:label="bacq_BusinessCombinationAgreementMember" xlink:href="bacq-20250930.xsd#bacq_BusinessCombinationAgreementMember"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_BusinessCombinationAgreementMember_lbl" xml:lang="en-US">Business Combination Agreement [Member]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_BusinessCombinationAgreementMember" xlink:to="bacq_BusinessCombinationAgreementMember_lbl"/>    
    <loc xlink:type="locator" xlink:label="bacq_PublicShareMember" xlink:href="bacq-20250930.xsd#bacq_PublicShareMember"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_PublicShareMember_lbl" xml:lang="en-US">Public Share [Member]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PublicShareMember" xlink:to="bacq_PublicShareMember_lbl"/>     
    <loc xlink:type="locator" xlink:label="bacq_NewMerlinLabsMember" xlink:href="bacq-20250930.xsd#bacq_NewMerlinLabsMember"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_NewMerlinLabsMember_lbl" xml:lang="en-US">New Merlin Labs [Member]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_NewMerlinLabsMember" xlink:to="bacq_NewMerlinLabsMember_lbl"/>    
    <loc xlink:type="locator" xlink:label="bacq_SeriesACumulativeConvertiblePreferredStockMember" xlink:href="bacq-20250930.xsd#bacq_SeriesACumulativeConvertiblePreferredStockMember"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_SeriesACumulativeConvertiblePreferredStockMember_lbl" xml:lang="en-US">Series A Cumulative Convertible Preferred Stock [Member]</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_SeriesACumulativeConvertiblePreferredStockMember" xlink:to="bacq_SeriesACumulativeConvertiblePreferredStockMember_lbl"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_SeriesAPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SeriesAPreferredStockMember"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SeriesAPreferredStockMember_lbl" xml:lang="en-US">Series A Preferred Stock [Member]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SeriesAPreferredStockMember" xlink:to="us-gaap_SeriesAPreferredStockMember_lbl"/> 
    <loc xlink:type="locator" xlink:label="bacq_SeriesAPreferredStockInvestmentMember" xlink:href="bacq-20250930.xsd#bacq_SeriesAPreferredStockInvestmentMember"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_SeriesAPreferredStockInvestmentMember_lbl" xml:lang="en-US">Series A Preferred Stock Investment [Member]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_SeriesAPreferredStockInvestmentMember" xlink:to="bacq_SeriesAPreferredStockInvestmentMember_lbl"/>     
    <loc xlink:type="locator" xlink:label="bacq_PublicSharesMember" xlink:href="bacq-20250930.xsd#bacq_PublicSharesMember"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_PublicSharesMember_lbl" xml:lang="en-US">Public Shares [Member]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PublicSharesMember" xlink:to="bacq_PublicSharesMember_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_FounderShareMember" xlink:href="bacq-20250930.xsd#bacq_FounderShareMember"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_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="bacq_FounderShareMember" xlink:to="bacq_FounderShareMember_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_FounderShares1Member" xlink:href="bacq-20250930.xsd#bacq_FounderShares1Member"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_FounderShares1Member_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="bacq_FounderShares1Member" xlink:to="bacq_FounderShares1Member_lbl"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_OverAllotmentOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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="srt_MinimumMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MinimumMember"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_MinimumMember_lbl" xml:lang="en-US">Minimum [Member]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MinimumMember" xlink:to="srt_MinimumMember_lbl"/>     
    <loc xlink:type="locator" xlink:label="srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_MaximumMember_lbl" xml:lang="en-US">Maximum [Member]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MaximumMember" xlink:to="srt_MaximumMember_lbl"/>     
    <loc xlink:type="locator" xlink:label="bacq_UnderwritingAgreementMember" xlink:href="bacq-20250930.xsd#bacq_UnderwritingAgreementMember"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_UnderwritingAgreementMember_lbl" xml:lang="en-US">Underwriting Agreement [Member]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnderwritingAgreementMember" xlink:to="bacq_UnderwritingAgreementMember_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_ClassOfStockDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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/2025/elts/us-gaap-2025.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/2025/elts/us-gaap-2025.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/2025/elts/us-gaap-2025.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_TemporaryEquityByClassOfStockTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityByClassOfStockTable"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TemporaryEquityByClassOfStockTable_lbl" xml:lang="en-US">Temporary Equity, by Class of Stock [Table]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityByClassOfStockTable" xlink:to="us-gaap_TemporaryEquityByClassOfStockTable_lbl"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_TemporaryEquityLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TemporaryEquityLineItems"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TemporaryEquityLineItems_lbl" xml:lang="en-US">Temporary Equity [Line Items]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityLineItems" xlink:to="us-gaap_TemporaryEquityLineItems_lbl"/>     
    <loc xlink:type="locator" xlink:label="bacq_SignificantAccountingPoliciesScheduleofBasicandDilutedNetIncomePerOrdinaryShareDetailsTable" xlink:href="bacq-20250930.xsd#bacq_SignificantAccountingPoliciesScheduleofBasicandDilutedNetIncomePerOrdinaryShareDetailsTable"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_SignificantAccountingPoliciesScheduleofBasicandDilutedNetIncomePerOrdinaryShareDetailsTable_lbl" xml:lang="en-US">Significant Accounting Policies - Schedule of Basic and Diluted Net Income Per Ordinary Share (Details) [Table]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_SignificantAccountingPoliciesScheduleofBasicandDilutedNetIncomePerOrdinaryShareDetailsTable" xlink:to="bacq_SignificantAccountingPoliciesScheduleofBasicandDilutedNetIncomePerOrdinaryShareDetailsTable_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_EarningsPerShareDilutedLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareDilutedLineItems"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EarningsPerShareDilutedLineItems_lbl" xml:lang="en-US">Schedule of Basic and Diluted Net Income Per Ordinary Share [Line Items]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerShareDilutedLineItems" xlink:to="us-gaap_EarningsPerShareDilutedLineItems_lbl"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_FairValueMeasurementsScheduleofCompanysAssetsandLiabilitiesDetailsTable" xlink:href="bacq-20250930.xsd#bacq_FairValueMeasurementsScheduleofCompanysAssetsandLiabilitiesDetailsTable"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_FairValueMeasurementsScheduleofCompanysAssetsandLiabilitiesDetailsTable_lbl" xml:lang="en-US">Fair Value Measurements - Schedule of Company&#8217;s Assets and Liabilities (Details) [Table]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_FairValueMeasurementsScheduleofCompanysAssetsandLiabilitiesDetailsTable" xlink:to="bacq_FairValueMeasurementsScheduleofCompanysAssetsandLiabilitiesDetailsTable_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xml:lang="en-US">Schedule of Company&#8217;s Assets and Liabilities [Line Items]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl"/> 
    <loc xlink:type="locator" xlink:label="bacq_SummaryofSignificantAccountingPoliciesScheduleofBasicandDilutedNetIncomeDetailsTable" xlink:href="bacq-20250930.xsd#bacq_SummaryofSignificantAccountingPoliciesScheduleofBasicandDilutedNetIncomeDetailsTable"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_SummaryofSignificantAccountingPoliciesScheduleofBasicandDilutedNetIncomeDetailsTable_lbl" xml:lang="en-US">Summary of Significant Accounting Policies - Schedule of Basic and Diluted Net Income (Details) [Table]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_SummaryofSignificantAccountingPoliciesScheduleofBasicandDilutedNetIncomeDetailsTable" xlink:to="bacq_SummaryofSignificantAccountingPoliciesScheduleofBasicandDilutedNetIncomeDetailsTable_lbl"/>    
    <loc xlink:type="locator" xlink:label="bacq_SummaryofSignificantAccountingPoliciesScheduleofBasicandDilutedNetIncomeDetailsLineItems" xlink:href="bacq-20250930.xsd#bacq_SummaryofSignificantAccountingPoliciesScheduleofBasicandDilutedNetIncomeDetailsLineItems"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_SummaryofSignificantAccountingPoliciesScheduleofBasicandDilutedNetIncomeDetailsLineItems_lbl" xml:lang="en-US">Schedule of Basic and Diluted Net Income [Line Items]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_SummaryofSignificantAccountingPoliciesScheduleofBasicandDilutedNetIncomeDetailsLineItems" xlink:to="bacq_SummaryofSignificantAccountingPoliciesScheduleofBasicandDilutedNetIncomeDetailsLineItems_lbl"/>  
    <loc xlink:type="locator" xlink:label="bacq_FairValueMeasurementsScheduleofCompanysAssetsandLiabilitiesDetailsLineItems" xlink:href="bacq-20250930.xsd#bacq_FairValueMeasurementsScheduleofCompanysAssetsandLiabilitiesDetailsLineItems"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="bacq_FairValueMeasurementsScheduleofCompanysAssetsandLiabilitiesDetailsLineItems_lbl" xml:lang="en-US">Schedule of Company&#8217;s Assets and Liabilities [Line Items]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_FairValueMeasurementsScheduleofCompanysAssetsandLiabilitiesDetailsLineItems" xlink:to="bacq_FairValueMeasurementsScheduleofCompanysAssetsandLiabilitiesDetailsLineItems_lbl"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_SegmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentDomain_lbl" xml:lang="en-US">Segments [Domain]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentDomain" xlink:to="us-gaap_SegmentDomain_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_lbl" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:to="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_lbl"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_SegmentReportingInformationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingInformationLineItems"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentReportingInformationLineItems_lbl" xml:lang="en-US">Segment Reporting Information [Line Items]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingInformationLineItems" xlink:to="us-gaap_SegmentReportingInformationLineItems_lbl"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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_BusinessAcquisitionAcquireeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionAcquireeDomain_lbl" xml:lang="en-US">Business Combination [Domain]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionAcquireeDomain" xlink:to="us-gaap_BusinessAcquisitionAcquireeDomain_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_RelatedPartyTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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_RelatedPartyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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_ArrangementsAndNonarrangementTransactionsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ArrangementsAndNonarrangementTransactionsMember"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ArrangementsAndNonarrangementTransactionsMember_lbl" xml:lang="en-US">Collaborative Arrangement and Arrangement Other than Collaborative [Domain]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:to="us-gaap_ArrangementsAndNonarrangementTransactionsMember_lbl"/> 
    <loc xlink:type="locator" xlink:label="us-gaap_ClassOfWarrantOrRightDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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="us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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="bacq_DescriptionofOrganizationandBusinessOperationsDetailsTable" xlink:href="bacq-20250930.xsd#bacq_DescriptionofOrganizationandBusinessOperationsDetailsTable"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_DescriptionofOrganizationandBusinessOperationsDetailsTable_lbl" xml:lang="en-US">Description of Organization and Business Operations (Details) [Table]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_DescriptionofOrganizationandBusinessOperationsDetailsTable" xlink:to="bacq_DescriptionofOrganizationandBusinessOperationsDetailsTable_lbl"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_CollaborativeArrangementsAndNoncollaborativeArrangementTransactionsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CollaborativeArrangementsAndNoncollaborativeArrangementTransactionsLineItems"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CollaborativeArrangementsAndNoncollaborativeArrangementTransactionsLineItems_lbl" xml:lang="en-US">Description of Organization and Business Operations [Line Items]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CollaborativeArrangementsAndNoncollaborativeArrangementTransactionsLineItems" xlink:to="us-gaap_CollaborativeArrangementsAndNoncollaborativeArrangementTransactionsLineItems_lbl"/>    
    <loc xlink:type="locator" xlink:label="bacq_InitialPublicOfferingDetailsTable" xlink:href="bacq-20250930.xsd#bacq_InitialPublicOfferingDetailsTable"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_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="bacq_InitialPublicOfferingDetailsTable" xlink:to="bacq_InitialPublicOfferingDetailsTable_lbl"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_ClassOfStockLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfStockLineItems"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ClassOfStockLineItems_lbl" xml:lang="en-US">Initial Public Offering [Line Items]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ClassOfStockLineItems" xlink:to="us-gaap_ClassOfStockLineItems_lbl"/>    
    <loc xlink:type="locator" xlink:label="bacq_PrivatePlacementDetailsTable" xlink:href="bacq-20250930.xsd#bacq_PrivatePlacementDetailsTable"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_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="bacq_PrivatePlacementDetailsTable" xlink:to="bacq_PrivatePlacementDetailsTable_lbl"/>  
    <loc xlink:type="locator" xlink:label="us-gaap_SubsidiarySaleOfStockLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsidiarySaleOfStockLineItems"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsidiarySaleOfStockLineItems_lbl" xml:lang="en-US">Private Placement [Line Items]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_SubsidiarySaleOfStockLineItems_lbl"/>  
    <loc xlink:type="locator" xlink:label="srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RangeMember_lbl" xml:lang="en-US">Statistical Measurement [Domain]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RangeMember" xlink:to="srt_RangeMember_lbl"/> 
    <loc xlink:type="locator" xlink:label="srt_EquityMethodInvesteeNameDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EquityMethodInvesteeNameDomain"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_EquityMethodInvesteeNameDomain_lbl" xml:lang="en-US">Investment, Name [Domain]</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_EquityMethodInvesteeNameDomain" xlink:to="srt_EquityMethodInvesteeNameDomain_lbl"/>    
    <loc xlink:type="locator" xlink:label="bacq_RelatedPartyTransactionsDetailsTable" xlink:href="bacq-20250930.xsd#bacq_RelatedPartyTransactionsDetailsTable"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_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="bacq_RelatedPartyTransactionsDetailsTable" xlink:to="bacq_RelatedPartyTransactionsDetailsTable_lbl"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_RelatedPartyTransactionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionLineItems"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionLineItems_lbl" xml:lang="en-US">Related Party Transactions [Line Items]</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_RelatedPartyTransactionLineItems_lbl"/> 
    <loc xlink:type="locator" xlink:label="bacq_CommitmentsandContingenciesDetailsTable" xlink:href="bacq-20250930.xsd#bacq_CommitmentsandContingenciesDetailsTable"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_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="bacq_CommitmentsandContingenciesDetailsTable" xlink:to="bacq_CommitmentsandContingenciesDetailsTable_lbl"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_LossContingenciesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LossContingenciesLineItems"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LossContingenciesLineItems_lbl" xml:lang="en-US">Commitments and Contingencies [Line Items]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="us-gaap_LossContingenciesLineItems_lbl"/>    
    <loc xlink:type="locator" xlink:label="bacq_ShareholdersDeficitDetailsTable" xlink:href="bacq-20250930.xsd#bacq_ShareholdersDeficitDetailsTable"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_ShareholdersDeficitDetailsTable_lbl" xml:lang="en-US">Shareholders&#8217; Deficit (Details) [Table]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ShareholdersDeficitDetailsTable" xlink:to="bacq_ShareholdersDeficitDetailsTable_lbl"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ClassOfStockLineItems_lbl0" xml:lang="en-US">Shareholders&#8217; Deficit [Line Items]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ClassOfStockLineItems" xlink:to="us-gaap_ClassOfStockLineItems_lbl0"/>     
    <loc xlink:type="locator" xlink:label="spac_AllSecurityClassesMember" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_AllSecurityClassesMember"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_AllSecurityClassesMember_lbl" xml:lang="en-US">All Security Classes [Member]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_AllSecurityClassesMember" xlink:to="spac_AllSecurityClassesMember_lbl"/>    
    <loc xlink:type="locator" xlink:label="spac_AllSpacSponsorsAffiliatesOrPromotersMember" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_AllSpacSponsorsAffiliatesOrPromotersMember"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_AllSpacSponsorsAffiliatesOrPromotersMember_lbl" xml:lang="en-US">All SPAC Sponsors, Affiliates, or Promoters [Member]</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_AllSpacSponsorsAffiliatesOrPromotersMember" xlink:to="spac_AllSpacSponsorsAffiliatesOrPromotersMember_lbl"/>     
    <loc xlink:type="locator" xlink:label="spac_DeSpacForepartSponsorCompensationTable" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacForepartSponsorCompensationTable"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacForepartSponsorCompensationTable_lbl" xml:lang="en-US">De-SPAC Forepart, Sponsor Compensation [Table]</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacForepartSponsorCompensationTable" xlink:to="spac_DeSpacForepartSponsorCompensationTable_lbl"/>  
    <loc xlink:type="locator" xlink:label="spac_DeSpacForepartSponsorCompensationLineItems" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacForepartSponsorCompensationLineItems"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacForepartSponsorCompensationLineItems_lbl" xml:lang="en-US">De-SPAC Forepart, Sponsor Compensation [Line Items]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacForepartSponsorCompensationLineItems" xlink:to="spac_DeSpacForepartSponsorCompensationLineItems_lbl"/>     
    <loc xlink:type="locator" xlink:label="spac_AllDilutionSourcesMember" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_AllDilutionSourcesMember"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_AllDilutionSourcesMember_lbl" xml:lang="en-US">All Dilution Sources [Member]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_AllDilutionSourcesMember" xlink:to="spac_AllDilutionSourcesMember_lbl"/>    
    <loc xlink:type="locator" xlink:label="spac_AllRedemptionLevelsMember" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_AllRedemptionLevelsMember"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_AllRedemptionLevelsMember_lbl" xml:lang="en-US">All Redemption Levels [Member]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_AllRedemptionLevelsMember" xlink:to="spac_AllRedemptionLevelsMember_lbl"/> 
    <loc xlink:type="locator" xlink:label="spac_DeSpacAdjustedNetTangibleBookValuePerShareWithSourcesOfDilutionTable" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacAdjustedNetTangibleBookValuePerShareWithSourcesOfDilutionTable"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacAdjustedNetTangibleBookValuePerShareWithSourcesOfDilutionTable_lbl" xml:lang="en-US">De-SPAC, Adjusted Net Tangible Book Value Per Share with Sources of Dilution [Table]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacAdjustedNetTangibleBookValuePerShareWithSourcesOfDilutionTable" xlink:to="spac_DeSpacAdjustedNetTangibleBookValuePerShareWithSourcesOfDilutionTable_lbl"/>  
    <loc xlink:type="locator" xlink:label="spac_DeSpacNetTangibleBookValueLineItems" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacNetTangibleBookValueLineItems"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacNetTangibleBookValueLineItems_lbl" xml:lang="en-US">De-SPAC, Net Tangible Book Value [Line Items]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacNetTangibleBookValueLineItems" xlink:to="spac_DeSpacNetTangibleBookValueLineItems_lbl"/> 
    <loc xlink:type="locator" xlink:label="spac_AllDeSpacAndRelatedFinancingTransactionsAffectedPartiesMember" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_AllDeSpacAndRelatedFinancingTransactionsAffectedPartiesMember"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_AllDeSpacAndRelatedFinancingTransactionsAffectedPartiesMember_lbl" xml:lang="en-US">All De-SPAC and Related Financing Transactions Affected Parties [Member]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_AllDeSpacAndRelatedFinancingTransactionsAffectedPartiesMember" xlink:to="spac_AllDeSpacAndRelatedFinancingTransactionsAffectedPartiesMember_lbl"/>   
    <loc xlink:type="locator" xlink:label="spac_DeSpacAndRelatedFinancingTransactionsEffectsTable" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacAndRelatedFinancingTransactionsEffectsTable"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacAndRelatedFinancingTransactionsEffectsTable_lbl" xml:lang="en-US">De-SPAC and Related Financing Transactions, Effects [Table]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacAndRelatedFinancingTransactionsEffectsTable" xlink:to="spac_DeSpacAndRelatedFinancingTransactionsEffectsTable_lbl"/>    
    <loc xlink:type="locator" xlink:label="spac_EffectsOfTheDeSpacAndRelatedFinancingTransactionsLineItems" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_EffectsOfTheDeSpacAndRelatedFinancingTransactionsLineItems"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_EffectsOfTheDeSpacAndRelatedFinancingTransactionsLineItems_lbl" xml:lang="en-US">Effects of the de-SPAC and Related Financing Transactions [Line Items]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_EffectsOfTheDeSpacAndRelatedFinancingTransactionsLineItems" xlink:to="spac_EffectsOfTheDeSpacAndRelatedFinancingTransactionsLineItems_lbl"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_AccruedOfferingCostsCurrent_lbl0" xml:lang="en-US">The amount of accrued offering costs.</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_AccruedOfferingCostsCurrent" xlink:to="bacq_AccruedOfferingCostsCurrent_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_AdditionalSharesIssued_lbl0" xml:lang="en-US">Represents the number of additional shares issued.</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_AdditionalSharesIssued" xlink:to="bacq_AdditionalSharesIssued_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_AggregatePurchasePrice_lbl0" xml:lang="en-US">Represents the value of aggregate purchase price.</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_AggregatePurchasePrice" xlink:to="bacq_AggregatePurchasePrice_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_AggregateShareIssuedPercentage_lbl0" xml:lang="en-US">Aggregate share issued percentage.</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_AggregateShareIssuedPercentage" xlink:to="bacq_AggregateShareIssuedPercentage_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_BusinessCombinationConsiderationsTransferredEquityInterestsIssuedAndIssuable_lbl0" xml:lang="en-US">Business combination considerations transferred equity interests issued and issuable.</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_BusinessCombinationConsiderationsTransferredEquityInterestsIssuedAndIssuable" xlink:to="bacq_BusinessCombinationConsiderationsTransferredEquityInterestsIssuedAndIssuable_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_CashHeldInTrustAccountPolicyTextBlock_lbl0" xml:lang="en-US">The disclosure of cash held in trust account.</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_CashHeldInTrustAccountPolicyTextBlock" xlink:to="bacq_CashHeldInTrustAccountPolicyTextBlock_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_CashUnderwritingFeePayable_lbl0" xml:lang="en-US">The amount of cash underwriting fee payable.</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_CashUnderwritingFeePayable" xlink:to="bacq_CashUnderwritingFeePayable_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_ClassARedeemableShareClassificationPolicyTextBlock_lbl0" xml:lang="en-US">The disclosure of class a redeemable share classification.</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ClassARedeemableShareClassificationPolicyTextBlock" xlink:to="bacq_ClassARedeemableShareClassificationPolicyTextBlock_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_CommonStockPurchasePrice_lbl0" xml:lang="en-US">Represents the value of common stock purchase price.</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_CommonStockPurchasePrice" xlink:to="bacq_CommonStockPurchasePrice_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_CommonStockShareIssued_lbl0" xml:lang="en-US">Number of common stock share issued.</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_CommonStockShareIssued" xlink:to="bacq_CommonStockShareIssued_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_CommonStockShareOutstanding_lbl0" xml:lang="en-US">Number of common stock share outstanding.</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_CommonStockShareOutstanding" xlink:to="bacq_CommonStockShareOutstanding_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_ConvertiblePromissoryNotes_lbl0" xml:lang="en-US">Represents the value of convertible promissory notes.</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ConvertiblePromissoryNotes" xlink:to="bacq_ConvertiblePromissoryNotes_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_DeferredFeePerUnit_lbl0" xml:lang="en-US">Deferred fee per unit.</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_DeferredFeePerUnit" xlink:to="bacq_DeferredFeePerUnit_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_DeferredOfferingCostsIncludedInAccruedOfferingCosts_lbl0" xml:lang="en-US">Represents the value 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="bacq_DeferredOfferingCostsIncludedInAccruedOfferingCosts" xlink:to="bacq_DeferredOfferingCostsIncludedInAccruedOfferingCosts_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_DeferredUnderwritingFee_lbl0" xml:lang="en-US">Deferred underwriting fee.</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_DeferredUnderwritingFee" xlink:to="bacq_DeferredUnderwritingFee_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_DeferredUnderwritingFeePayable_lbl0" xml:lang="en-US">The amount of deferred underwriting fee payable.</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_DeferredUnderwritingFeePayable" xlink:to="bacq_DeferredUnderwritingFeePayable_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_DeferredUnderwritingFeePayableNoncurrent_lbl0" xml:lang="en-US">Represents the amount of deferred underwriting fee payable.</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_DeferredUnderwritingFeePayableNoncurrent" xlink:to="bacq_DeferredUnderwritingFeePayableNoncurrent_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_EmergingGrowthCompanyPolicyTextBlock_lbl0" xml:lang="en-US">Emerging growth company.</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_EmergingGrowthCompanyPolicyTextBlock" xlink:to="bacq_EmergingGrowthCompanyPolicyTextBlock_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_FairValuePerShareRight_lbl0" xml:lang="en-US">The price of fair value per share right.</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_FairValuePerShareRight" xlink:to="bacq_FairValuePerShareRight_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_FormationCosts_lbl0" xml:lang="en-US">The amount of formation costs.</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_FormationCosts" xlink:to="bacq_FormationCosts_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_FormationCostsPaidBySponsorInExchangeForIssuanceOfClassBOrdinaryShares_lbl0" xml:lang="en-US">The amount of formation costs paid by sponsor in exchange for issuance.</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_FormationCostsPaidBySponsorInExchangeForIssuanceOfClassBOrdinaryShares" xlink:to="bacq_FormationCostsPaidBySponsorInExchangeForIssuanceOfClassBOrdinaryShares_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_InitialPublicOfferingTextBlock_lbl0" xml:lang="en-US">The entire disclosure on information about initial public offering.</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_InitialPublicOfferingTextBlock" xlink:to="bacq_InitialPublicOfferingTextBlock_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_InterestIncomeOnInvestmentsHeldInTrustAccount_lbl2" xml:lang="en-US">Amount before accretion (amortization) of purchase discount (premium) of interest income on non operating securities.</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_InterestIncomeOnInvestmentsHeldInTrustAccount" xlink:to="bacq_InterestIncomeOnInvestmentsHeldInTrustAccount_lbl2"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_InterestToPayDissolutionExpenses_lbl0" xml:lang="en-US">Represents the amount of interest to pay dissolution expenses.</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_InterestToPayDissolutionExpenses" xlink:to="bacq_InterestToPayDissolutionExpenses_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_InvestmentsHeldInTrustAccountPolicyTextBlock_lbl0" xml:lang="en-US">Investments held in trust account.</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_InvestmentsHeldInTrustAccountPolicyTextBlock" xlink:to="bacq_InvestmentsHeldInTrustAccountPolicyTextBlock_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_InvestmentsMaximumMaturityTerm_lbl0" xml:lang="en-US">Investments Maximum Maturity Term.</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_InvestmentsMaximumMaturityTerm" xlink:to="bacq_InvestmentsMaximumMaturityTerm_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_LiquidityAndCapitalResourcesPolicyTextBlock_lbl0" 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="bacq_LiquidityAndCapitalResourcesPolicyTextBlock" xlink:to="bacq_LiquidityAndCapitalResourcesPolicyTextBlock_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_LiquidityCapitalResourcesAndGoingConcernPolicyTextBlock_lbl0" xml:lang="en-US">Liquidity, Capital Resources and Going Concern.</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_LiquidityCapitalResourcesAndGoingConcernPolicyTextBlock" xlink:to="bacq_LiquidityCapitalResourcesAndGoingConcernPolicyTextBlock_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_MarketAdjustment_lbl0" xml:lang="en-US">The percentage of market adjustment.</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_MarketAdjustment" xlink:to="bacq_MarketAdjustment_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_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="bacq_NumberOfOrdinaryShares" xlink:to="bacq_NumberOfOrdinaryShares_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_NumberOfSharesIssuedPerUnit_lbl2" xml:lang="en-US">The number of shares in a unit.</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_NumberOfSharesIssuedPerUnit" xlink:to="bacq_NumberOfSharesIssuedPerUnit_lbl2"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_NumberOfTradingDays_lbl0" xml:lang="en-US">Number of trading days.</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_NumberOfTradingDays" xlink:to="bacq_NumberOfTradingDays_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_OfferingCostsPolicyTextBlock_lbl0" xml:lang="en-US">Disclosure of accounting policy for offering costs.</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_OfferingCostsPolicyTextBlock" xlink:to="bacq_OfferingCostsPolicyTextBlock_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_OverAllotmentOptionPeriod_lbl0" xml:lang="en-US">Over allotment option period.</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_OverAllotmentOptionPeriod" xlink:to="bacq_OverAllotmentOptionPeriod_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_PaymentOfOperationCostsThroughPromissoryNote_lbl0" xml:lang="en-US">Represents the amount of payment of operation costs through promissory note.</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PaymentOfOperationCostsThroughPromissoryNote" xlink:to="bacq_PaymentOfOperationCostsThroughPromissoryNote_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_PercentageOfIssuedAndOutstandingShares_lbl0" xml:lang="en-US">Percentage of issued and outstanding shares.</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PercentageOfIssuedAndOutstandingShares" xlink:to="bacq_PercentageOfIssuedAndOutstandingShares_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_PercentageOfNumberOfShares_lbl0" xml:lang="en-US">Represents the number of shares.</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PercentageOfNumberOfShares" xlink:to="bacq_PercentageOfNumberOfShares_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_PercentageOfRedeemInitialBusinessCombination_lbl0" xml:lang="en-US">Percentage of redeem initial business combination.</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PercentageOfRedeemInitialBusinessCombination" xlink:to="bacq_PercentageOfRedeemInitialBusinessCombination_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_PreadjustedValuePerShareRight_lbl0" xml:lang="en-US">The price of pre-adjusted value per share right.</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PreadjustedValuePerShareRight" xlink:to="bacq_PreadjustedValuePerShareRight_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_PrepaidServicesPaidBySponsorThroughThePromissoryNoteRelatedParty_lbl0" xml:lang="en-US">Represents the value of  prepaid services paid by Sponsor through the promissory note &#8211; related party.</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PrepaidServicesPaidBySponsorThroughThePromissoryNoteRelatedParty" xlink:to="bacq_PrepaidServicesPaidBySponsorThroughThePromissoryNoteRelatedParty_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_PrivatePlacementTextBlock_lbl0" xml:lang="en-US">Private placement text block.</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PrivatePlacementTextBlock" xlink:to="bacq_PrivatePlacementTextBlock_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_ProceedsAllocatedToPublicRights_lbl0" xml:lang="en-US">The amount of proceeds allocated to public rights.</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ProceedsAllocatedToPublicRights" xlink:to="bacq_ProceedsAllocatedToPublicRights_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_PublicSharesRedemptionPercentage_lbl0" xml:lang="en-US">Public shares redemption percentage.</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PublicSharesRedemptionPercentage" xlink:to="bacq_PublicSharesRedemptionPercentage_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_RestrictionsOnTransferPeriodOfTimeAfterBusinessCombinationCompletion_lbl0" xml:lang="en-US">Restrictions on transfer period of time after business combination completion.</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_RestrictionsOnTransferPeriodOfTimeAfterBusinessCombinationCompletion" xlink:to="bacq_RestrictionsOnTransferPeriodOfTimeAfterBusinessCombinationCompletion_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_RightsPolicyTextBlock_lbl0" xml:lang="en-US">Rights policy text clock.</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_RightsPolicyTextBlock" xlink:to="bacq_RightsPolicyTextBlock_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_ScheduleOfMarketAssumptionsInValuationOfPublicRightsTableTextBlock_lbl1" xml:lang="en-US">The tabular disclosure of market assumptions in valuation of public rights.</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ScheduleOfMarketAssumptionsInValuationOfPublicRightsTableTextBlock" xlink:to="bacq_ScheduleOfMarketAssumptionsInValuationOfPublicRightsTableTextBlock_lbl1"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_ShortTermPrepaidInsurance_lbl0" xml:lang="en-US">The amount of short term prepaid insurance.</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ShortTermPrepaidInsurance" xlink:to="bacq_ShortTermPrepaidInsurance_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_StockIssuedDuringPeriodSharesSaleOfPrivatePlacementUnits_lbl0" xml:lang="en-US">Represent the shares value of sale of private placement units.</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_StockIssuedDuringPeriodSharesSaleOfPrivatePlacementUnits" xlink:to="bacq_StockIssuedDuringPeriodSharesSaleOfPrivatePlacementUnits_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_StockIssuedDuringPeriodValueSaleOfPrivatePlacementUnits_lbl0" xml:lang="en-US">Represent the amount of sale of private placement units.</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_StockIssuedDuringPeriodValueSaleOfPrivatePlacementUnits" xlink:to="bacq_StockIssuedDuringPeriodValueSaleOfPrivatePlacementUnits_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_ThresholdPeriodAfterBusinessCombinationInWhichSpecifiedTradingDaysWithinAnySpecifiedTradingDayPeriodCommences_lbl0" xml:lang="en-US">Threshold period after business combination.</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ThresholdPeriodAfterBusinessCombinationInWhichSpecifiedTradingDaysWithinAnySpecifiedTradingDayPeriodCommences" xlink:to="bacq_ThresholdPeriodAfterBusinessCombinationInWhichSpecifiedTradingDaysWithinAnySpecifiedTradingDayPeriodCommences_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_TransactionCosts_lbl0" xml:lang="en-US">Transaction costs.</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_TransactionCosts" xlink:to="bacq_TransactionCosts_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_UnderlyingSharePrice_lbl0" xml:lang="en-US">The price of underlying share.</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnderlyingSharePrice" xlink:to="bacq_UnderlyingSharePrice_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_UnderwriterCashDiscount_lbl0" xml:lang="en-US">Represents the cash underwriting discount per unit.</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnderwriterCashDiscount" xlink:to="bacq_UnderwriterCashDiscount_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_UnderwritingCashDiscountPerUnit_lbl0" xml:lang="en-US">Underwriting cash discount per unit</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnderwritingCashDiscountPerUnit" xlink:to="bacq_UnderwritingCashDiscountPerUnit_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_UnitsIssuedDuringPeriodSharesNewIssues_lbl2" xml:lang="en-US">Represent the units issued during period shares new issues.</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnitsIssuedDuringPeriodSharesNewIssues" xlink:to="bacq_UnitsIssuedDuringPeriodSharesNewIssues_lbl2"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_WeightedAverageNumberOfSharesForfeited_lbl0" xml:lang="en-US">The number of weighted average forfeited shares.</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_WeightedAverageNumberOfSharesForfeited" xlink:to="bacq_WeightedAverageNumberOfSharesForfeited_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_WorkingCapitalDeficit_lbl0" xml:lang="en-US">Working capital deficit.</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_WorkingCapitalDeficit" xlink:to="bacq_WorkingCapitalDeficit_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_WorkingCapitalLoanAmount_lbl0" xml:lang="en-US">Amount of working capital loan.</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_WorkingCapitalLoanAmount" xlink:to="bacq_WorkingCapitalLoanAmount_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="bacq_WorkingCapitalOutstandingLoans_lbl0" xml:lang="en-US">The amount of working capital outstanding loans.</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_WorkingCapitalOutstandingLoans" xlink:to="bacq_WorkingCapitalOutstandingLoans_lbl0"/>  
    <loc xlink:type="locator" xlink:label="srt_ChiefExecutiveOfficerMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ChiefExecutiveOfficerMember"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ChiefExecutiveOfficerMember_lbl" xml:lang="en-US">Chief Executive Officer</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ChiefExecutiveOfficerMember" xlink:to="srt_ChiefExecutiveOfficerMember_lbl"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SeriesAPreferredStockMember_lbl0" xml:lang="en-US">Series A Preferred Stock [Member]</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SeriesAPreferredStockMember" xlink:to="us-gaap_SeriesAPreferredStockMember_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="us-gaap_OtherAssetsAbstract_lbl0" xml:lang="en-US">Other Assets [Abstract]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherAssetsAbstract" xlink:to="us-gaap_OtherAssetsAbstract_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EarningsPerShareDiluted_lbl2" 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_lbl2"/>    
    <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="bacq_WeightedAverageNumberOfSharesForfeited_lbl1" xml:lang="en-US">Weighted Average Number Of Shares Forfeited</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_WeightedAverageNumberOfSharesForfeited" xlink:to="bacq_WeightedAverageNumberOfSharesForfeited_lbl1"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_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="bacq_AccruedOfferingCostsCurrent" xlink:to="bacq_AccruedOfferingCostsCurrent_lbl1"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_ShortTermPrepaidInsurance_lbl1" xml:lang="en-US">Short Term Prepaid Insurance</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ShortTermPrepaidInsurance" xlink:to="bacq_ShortTermPrepaidInsurance_lbl1"/>  
    <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="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_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued_lbl0" xml:lang="en-US">Unrecognized Tax Benefits, Income Tax Penalties and Interest Accrued</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued" xlink:to="us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacTransactionAccountingTreatmentTextBlock_lbl0" xml:lang="en-US">De-SPAC Transaction, Accounting Treatment [Text Block]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacTransactionAccountingTreatmentTextBlock" xlink:to="spac_DeSpacTransactionAccountingTreatmentTextBlock_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract_lbl0" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic [Abstract]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:to="us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsAbstract_lbl1" 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_lbl1"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacNumberOfSharesUsedAdjustment_lbl0" xml:lang="en-US">De-SPAC, Number of Shares Used, Adjustment</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacNumberOfSharesUsedAdjustment" xlink:to="spac_DeSpacNumberOfSharesUsedAdjustment_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl2" 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_lbl2"/>   
    <loc xlink:type="locator" xlink:label="bacq_ScheduleOfBasicAndDilutedNetIncomeAbstract" xlink:href="bacq-20250930.xsd#bacq_ScheduleOfBasicAndDilutedNetIncomeAbstract"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_ScheduleOfBasicAndDilutedNetIncomeAbstract_lbl" xml:lang="en-US">Schedule Of Basic And Diluted Net Income Abstract</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ScheduleOfBasicAndDilutedNetIncomeAbstract" xlink:to="bacq_ScheduleOfBasicAndDilutedNetIncomeAbstract_lbl"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_PublicUnitsMember_lbl0" xml:lang="en-US">Public Units [Member]</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_PublicUnitsMember" xlink:to="spac_PublicUnitsMember_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_NewMerlinMember_lbl0" xml:lang="en-US">New Merlin Member</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_NewMerlinMember" xlink:to="bacq_NewMerlinMember_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_InflectionPointMember_lbl0" xml:lang="en-US">Inflection Point Member</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_InflectionPointMember" xlink:to="bacq_InflectionPointMember_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl0" xml:lang="en-US">Increase (Decrease) in Prepaid Expense and Other Assets</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:to="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_SeriesAPreferredStockInvestmentMember_lbl0" xml:lang="en-US">Series APreferred Stock Investment Member</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_SeriesAPreferredStockInvestmentMember" xlink:to="bacq_SeriesAPreferredStockInvestmentMember_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration_lbl0" xml:lang="en-US">Segment Reporting, CODM, Individual Title and Position or Group Name [Extensible Enumeration]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration" xlink:to="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IPOMember_lbl1" 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_lbl1"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_NumberOfSharesIssuedPerUnit_lbl3" xml:lang="en-US">Number Of Shares Issued Per Unit</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_NumberOfSharesIssuedPerUnit" xlink:to="bacq_NumberOfSharesIssuedPerUnit_lbl3"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsForUnderwritingExpense_lbl1" 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_lbl1"/>   
    <loc xlink:type="locator" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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="bacq_FairValueMeasurementsScheduleofCompanysAssetsandLiabilitiesDetailsLineItems_lbl0" xml:lang="en-US">Fair Value Measurements Scheduleof Companys Assetsand Liabilities Details Line Items</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_FairValueMeasurementsScheduleofCompanysAssetsandLiabilitiesDetailsLineItems" xlink:to="bacq_FairValueMeasurementsScheduleofCompanysAssetsandLiabilitiesDetailsLineItems_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityIncorporationDateOfIncorporation_lbl0" xml:lang="en-US">Entity Incorporation, Date of Incorporation</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityIncorporationDateOfIncorporation" xlink:to="dei_EntityIncorporationDateOfIncorporation_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="bacq_UnderwritingCashDiscountPerUnit_lbl1" xml:lang="en-US">Underwriting Cash Discount Per Unit</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnderwritingCashDiscountPerUnit" xlink:to="bacq_UnderwritingCashDiscountPerUnit_lbl1"/>    
    <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="us-gaap_NotesIssued1_lbl0" xml:lang="en-US">Notes Issued</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NotesIssued1" xlink:to="us-gaap_NotesIssued1_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_CommonStockShareOutstanding_lbl1" xml:lang="en-US">Common Stock Share Outstanding</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_CommonStockShareOutstanding" xlink:to="bacq_CommonStockShareOutstanding_lbl1"/> 
    <loc xlink:type="locator" xlink:label="spac_DeSpacAdjustedNetTangibleBookValuePerShareWithSourcesOfDilutionAbstract" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacAdjustedNetTangibleBookValuePerShareWithSourcesOfDilutionAbstract"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacAdjustedNetTangibleBookValuePerShareWithSourcesOfDilutionAbstract_lbl" xml:lang="en-US">De-SPAC, Adjusted Net Tangible Book Value Per Share with Sources of Dilution [Abstract]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacAdjustedNetTangibleBookValuePerShareWithSourcesOfDilutionAbstract" xlink:to="spac_DeSpacAdjustedNetTangibleBookValuePerShareWithSourcesOfDilutionAbstract_lbl"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_InvestmentsHeldInTrustAccountPolicyTextBlock_lbl1" xml:lang="en-US">Investments Held In Trust Account Policy Text Block</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_InvestmentsHeldInTrustAccountPolicyTextBlock" xlink:to="bacq_InvestmentsHeldInTrustAccountPolicyTextBlock_lbl1"/>     
    <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"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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_InvestmentIncomeInterest_lbl0" xml:lang="en-US">Investment Income, Interest</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InvestmentIncomeInterest" xlink:to="us-gaap_InvestmentIncomeInterest_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl0" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [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="bacq_PercentageOfNumberOfShares_lbl1" xml:lang="en-US">Percentage Of Number Of Shares</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PercentageOfNumberOfShares" xlink:to="bacq_PercentageOfNumberOfShares_lbl1"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_FounderShares1Member_lbl0" xml:lang="en-US">Founder Shares1 Member</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_FounderShares1Member" xlink:to="bacq_FounderShares1Member_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TemporaryEquityRedemptionPricePerShare_lbl0" xml:lang="en-US">Temporary Equity, Redemption Price Per Share</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityRedemptionPricePerShare" xlink:to="us-gaap_TemporaryEquityRedemptionPricePerShare_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_OverAllotmentOptionPeriod_lbl1" xml:lang="en-US">Over Allotment Option Period</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_OverAllotmentOptionPeriod" xlink:to="bacq_OverAllotmentOptionPeriod_lbl1"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_ClassARedeemableShareClassificationPolicyTextBlock_lbl1" xml:lang="en-US">Class ARedeemable Share Classification Policy Text Block</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ClassARedeemableShareClassificationPolicyTextBlock" xlink:to="bacq_ClassARedeemableShareClassificationPolicyTextBlock_lbl1"/>  
    <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_lbl2" 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_lbl2"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_BusinessCombinationAgreementMember_lbl0" xml:lang="en-US">Business Combination Agreement Member</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_BusinessCombinationAgreementMember" xlink:to="bacq_BusinessCombinationAgreementMember_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsToAcquireInvestments_lbl0" xml:lang="en-US">Payments to Acquire Investments</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquireInvestments" xlink:to="us-gaap_PaymentsToAcquireInvestments_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_Liabilities_lbl0" xml:lang="en-US">Liabilities</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_Liabilities_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquityAbstract_lbl1" 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_lbl1"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacNetTangibleBookValuePerShare_lbl0" xml:lang="en-US">De-SPAC, Net Tangible Book Value, Per Share</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacNetTangibleBookValuePerShare" xlink:to="spac_DeSpacNetTangibleBookValuePerShare_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacForepartMaterialFinancingTransactionsOccurredDescriptionTextBlock_lbl0" xml:lang="en-US">De-SPAC Forepart, Material Financing Transactions Occurred, Description [Text Block]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacForepartMaterialFinancingTransactionsOccurredDescriptionTextBlock" xlink:to="spac_DeSpacForepartMaterialFinancingTransactionsOccurredDescriptionTextBlock_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockVotingRights_lbl0" xml:lang="en-US">Common Stock, Voting Rights</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonStockVotingRights" xlink:to="us-gaap_CommonStockVotingRights_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="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment_lbl0" xml:lang="en-US">Temporary Equity, Accretion to Redemption Value, Adjustment</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment" xlink:to="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssued1_lbl0" xml:lang="en-US">Stock Issued</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssued1" xlink:to="us-gaap_StockIssued1_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="spac_DeSpacSecurityHoldersAreEntitledToAppraisalRightsFlag_lbl0" xml:lang="en-US">De-SPAC, Security Holders are Entitled to Appraisal Rights [Flag]</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacSecurityHoldersAreEntitledToAppraisalRightsFlag" xlink:to="spac_DeSpacSecurityHoldersAreEntitledToAppraisalRightsFlag_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_CashHeldInTrustAccountPolicyTextBlock_lbl1" xml:lang="en-US">Cash Held In Trust Account Policy Text Block</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_CashHeldInTrustAccountPolicyTextBlock" xlink:to="bacq_CashHeldInTrustAccountPolicyTextBlock_lbl1"/> 
    <loc xlink:type="locator" xlink:label="spac_DeSpacTransactionsEffectsLineItems" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacTransactionsEffectsLineItems"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacTransactionsEffectsLineItems_lbl" xml:lang="en-US">De-SPAC Transactions, Effects [Line Items]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacTransactionsEffectsLineItems" xlink:to="spac_DeSpacTransactionsEffectsLineItems_lbl"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacSecurityHoldersRedemptionRightsSummaryTextBlock_lbl0" xml:lang="en-US">De-SPAC, Security Holders Redemption Rights Summary [Text Block]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacSecurityHoldersRedemptionRightsSummaryTextBlock" xlink:to="spac_DeSpacSecurityHoldersRedemptionRightsSummaryTextBlock_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_DeferredUnderwritingFeePayableNoncurrent_lbl1" xml:lang="en-US">Deferred Underwriting Fee Payable Noncurrent</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_DeferredUnderwritingFeePayableNoncurrent" xlink:to="bacq_DeferredUnderwritingFeePayableNoncurrent_lbl1"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacNetTangibleBookValueAmountOfDilutionPerShare_lbl0" xml:lang="en-US">De-SPAC, Net Tangible Book Value, Amount of Dilution Per Share</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacNetTangibleBookValueAmountOfDilutionPerShare" xlink:to="spac_DeSpacNetTangibleBookValueAmountOfDilutionPerShare_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_PercentageOfIssuedAndOutstandingShares_lbl1" xml:lang="en-US">Percentage Of Issued And Outstanding Shares</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PercentageOfIssuedAndOutstandingShares" xlink:to="bacq_PercentageOfIssuedAndOutstandingShares_lbl1"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_LiquidityAndCapitalResourcesPolicyTextBlock_lbl1" xml:lang="en-US">Liquidity And Capital Resources Policy Text Block</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_LiquidityAndCapitalResourcesPolicyTextBlock" xlink:to="bacq_LiquidityAndCapitalResourcesPolicyTextBlock_lbl1"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl1" 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_lbl1"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherIncomeAbstract_lbl1" xml:lang="en-US">Component of Operating Income [Abstract]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherIncomeAbstract" xlink:to="us-gaap_OtherIncomeAbstract_lbl1"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_UnderlyingSharePrice_lbl1" xml:lang="en-US">Underlying Share Price</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnderlyingSharePrice" xlink:to="bacq_UnderlyingSharePrice_lbl1"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_AggregateShareIssuedPercentage_lbl1" xml:lang="en-US">Aggregate Share Issued Percentage</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_AggregateShareIssuedPercentage" xlink:to="bacq_AggregateShareIssuedPercentage_lbl1"/>  
    <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>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xlink:to="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl0" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_NoRedemptionMember_lbl0" xml:lang="en-US">No Redemption [Member]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_NoRedemptionMember" xlink:to="spac_NoRedemptionMember_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_StockIssuedDuringPeriodSharesSaleOfPrivatePlacementUnits_lbl1" xml:lang="en-US">Stock Issued During Period Shares Sale Of Private Placement Units</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_StockIssuedDuringPeriodSharesSaleOfPrivatePlacementUnits" xlink:to="bacq_StockIssuedDuringPeriodSharesSaleOfPrivatePlacementUnits_lbl1"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PrepaidExpenseNoncurrent_lbl0" xml:lang="en-US">Prepaid Expense, Noncurrent</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PrepaidExpenseNoncurrent" xlink:to="us-gaap_PrepaidExpenseNoncurrent_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_MinimumMember_lbl0" xml:lang="en-US">Minimum [Member]</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MinimumMember" xlink:to="srt_MinimumMember_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_UnderwriterCashDiscount_lbl1" xml:lang="en-US">Underwriter Cash Discount</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnderwriterCashDiscount" xlink:to="bacq_UnderwriterCashDiscount_lbl1"/>   
    <loc xlink:type="locator" xlink:label="spac_DeSpacCompensationProspectusSummaryAbstract" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacCompensationProspectusSummaryAbstract"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacCompensationProspectusSummaryAbstract_lbl" xml:lang="en-US">De-SPAC, Compensation, Prospectus Summary [Abstract]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacCompensationProspectusSummaryAbstract" xlink:to="spac_DeSpacCompensationProspectusSummaryAbstract_lbl"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_BusinessCombinationConsiderationsTransferredEquityInterestsIssuedAndIssuable_lbl1" xml:lang="en-US">Business Combination Considerations Transferred Equity Interests Issued And Issuable</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_BusinessCombinationConsiderationsTransferredEquityInterestsIssuedAndIssuable" xlink:to="bacq_BusinessCombinationConsiderationsTransferredEquityInterestsIssuedAndIssuable_lbl1"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NotesPayable_lbl0" xml:lang="en-US">Notes Payable</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NotesPayable" xlink:to="us-gaap_NotesPayable_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract_lbl0" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic [Abstract]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:to="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_FounderSharesMember_lbl0" xml:lang="en-US">Founder Shares [Member]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_FounderSharesMember" xlink:to="spac_FounderSharesMember_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_PublicShareMember_lbl0" xml:lang="en-US">Public Share Member</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PublicShareMember" xlink:to="bacq_PublicShareMember_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TemporaryEquityParOrStatedValuePerShare_lbl0" xml:lang="en-US">Temporary Equity, Par or Stated Value Per Share</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityParOrStatedValuePerShare" xlink:to="us-gaap_TemporaryEquityParOrStatedValuePerShare_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl0" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacForepartPricePaidOrToBePaidForSecuritiesPerShare_lbl0" xml:lang="en-US">De-SPAC Forepart, Price Paid or to be Paid for Securities, Per Share</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacForepartPricePaidOrToBePaidForSecuritiesPerShare" xlink:to="spac_DeSpacForepartPricePaidOrToBePaidForSecuritiesPerShare_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_CommonStockPurchasePrice_lbl1" xml:lang="en-US">Common Stock Purchase Price</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_CommonStockPurchasePrice" xlink:to="bacq_CommonStockPurchasePrice_lbl1"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl2" 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_lbl2"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionSharePrice_lbl0" xml:lang="en-US">Business Combination, Price Per Share</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionSharePrice" xlink:to="us-gaap_BusinessAcquisitionSharePrice_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_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="us-gaap_RepaymentsOfRelatedPartyDebt_lbl1" xml:lang="en-US">Repayments of Related Party Debt</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RepaymentsOfRelatedPartyDebt" xlink:to="us-gaap_RepaymentsOfRelatedPartyDebt_lbl1"/>    
    <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="spac_RedemptionAt100PercentOfMaximumMember_lbl0" xml:lang="en-US">Redemption at 100 Percent of Maximum [Member]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_RedemptionAt100PercentOfMaximumMember" xlink:to="spac_RedemptionAt100PercentOfMaximumMember_lbl0"/> 
    <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="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_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="bacq_AssetAbstract_lbl0" xml:lang="en-US">Asset Abstract</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_AssetAbstract" xlink:to="bacq_AssetAbstract_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_MaximumMember_lbl0" xml:lang="en-US">Maximum [Member]</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MaximumMember" xlink:to="srt_MaximumMember_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_RestrictionsOnTransferPeriodOfTimeAfterBusinessCombinationCompletion_lbl1" xml:lang="en-US">Restrictions On Transfer Period Of Time After Business Combination Completion</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_RestrictionsOnTransferPeriodOfTimeAfterBusinessCombinationCompletion" xlink:to="bacq_RestrictionsOnTransferPeriodOfTimeAfterBusinessCombinationCompletion_lbl1"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacBoardDeterminationProspectusSummaryTextBlock_lbl0" xml:lang="en-US">De-SPAC, Board Determination, Prospectus Summary [Text Block]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacBoardDeterminationProspectusSummaryTextBlock" xlink:to="spac_DeSpacBoardDeterminationProspectusSummaryTextBlock_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_InterestIncomeOnInvestmentsHeldInTrustAccount_lbl3" xml:lang="en-US">Interest Income On Investments Held In Trust Account</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_InterestIncomeOnInvestmentsHeldInTrustAccount" xlink:to="bacq_InterestIncomeOnInvestmentsHeldInTrustAccount_lbl3"/>  
    <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="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="bacq_MarketAdjustment_lbl1" xml:lang="en-US">Market Adjustment</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_MarketAdjustment" xlink:to="bacq_MarketAdjustment_lbl1"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingIncomeLoss_lbl0" xml:lang="en-US">Operating Income (Loss)</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingIncomeLoss" xlink:to="us-gaap_OperatingIncomeLoss_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_AggregatePurchasePrice_lbl1" xml:lang="en-US">Aggregate Purchase Price</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_AggregatePurchasePrice" xlink:to="bacq_AggregatePurchasePrice_lbl1"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacBoardDeterminationDisclosureTextBlock_lbl0" xml:lang="en-US">De-SPAC, Board Determination Disclosure [Text Block]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacBoardDeterminationDisclosureTextBlock" xlink:to="spac_DeSpacBoardDeterminationDisclosureTextBlock_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TemporaryEquityCarryingAmountAttributableToParent_lbl2" xml:lang="en-US">Temporary Equity, Carrying Amount, Attributable to Parent</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:to="us-gaap_TemporaryEquityCarryingAmountAttributableToParent_lbl2"/> 
    <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_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl0" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskCreditRisk_lbl0" xml:lang="en-US">Concentration Risk, Credit Risk, Policy [Policy Text Block]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskCreditRisk" xlink:to="us-gaap_ConcentrationRiskCreditRisk_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SaleOfStockConsiderationReceivedOnTransaction_lbl0" xml:lang="en-US">Sale of Stock, Consideration Received on Transaction</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:to="us-gaap_SaleOfStockConsiderationReceivedOnTransaction_lbl0"/>   
    <loc xlink:type="locator" xlink:label="spac_DeSpacBoardDeterminationFactorsConsideredLineItems" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacBoardDeterminationFactorsConsideredLineItems"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacBoardDeterminationFactorsConsideredLineItems_lbl" xml:lang="en-US">De-SPAC, Board Determination, Factors Considered [Line Items]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacBoardDeterminationFactorsConsideredLineItems" xlink:to="spac_DeSpacBoardDeterminationFactorsConsideredLineItems_lbl"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TemporaryEquityAccretionToRedemptionValue_lbl0" xml:lang="en-US">Temporary Equity, Accretion to Redemption Value</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityAccretionToRedemptionValue" xlink:to="us-gaap_TemporaryEquityAccretionToRedemptionValue_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_PIPEInvestmentProceedsMember_lbl0" xml:lang="en-US">PIPEInvestment Proceeds Member</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PIPEInvestmentProceedsMember" xlink:to="bacq_PIPEInvestmentProceedsMember_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>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityCentralIndexKey" xlink:to="dei_EntityCentralIndexKey_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacSecurityHoldersAreEntitledToRedemptionRightsFlag_lbl0" xml:lang="en-US">De-SPAC, Security Holders are Entitled to Redemption Rights [Flag]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacSecurityHoldersAreEntitledToRedemptionRightsFlag" xlink:to="spac_DeSpacSecurityHoldersAreEntitledToRedemptionRightsFlag_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_PrepaidServicesPaidBySponsorThroughThePromissoryNoteRelatedParty_lbl1" xml:lang="en-US">Prepaid Services Paid By Sponsor Through The Promissory Note Related Party</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PrepaidServicesPaidBySponsorThroughThePromissoryNoteRelatedParty" xlink:to="bacq_PrepaidServicesPaidBySponsorThroughThePromissoryNoteRelatedParty_lbl1"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl0" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_DenominatorAbstract_lbl0" xml:lang="en-US">Denominator Abstract</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_DenominatorAbstract" xlink:to="bacq_DenominatorAbstract_lbl0"/>     
    <loc xlink:type="locator" xlink:label="spac_DeSpacTransactionsDilutionLineItems" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_DeSpacTransactionsDilutionLineItems"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacTransactionsDilutionLineItems_lbl" xml:lang="en-US">De-SPAC Transactions, Dilution [Line Items]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacTransactionsDilutionLineItems" xlink:to="spac_DeSpacTransactionsDilutionLineItems_lbl"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_AmendmentDescription_lbl0" xml:lang="en-US">Amendment Description</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_AmendmentDescription" xlink:to="dei_AmendmentDescription_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_UnderwritingAgreementMember_lbl0" xml:lang="en-US">Underwriting Agreement Member</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnderwritingAgreementMember" xlink:to="bacq_UnderwritingAgreementMember_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_TransactionCosts_lbl1" xml:lang="en-US">Transaction Costs</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_TransactionCosts" xlink:to="bacq_TransactionCosts_lbl1"/>    
    <loc xlink:type="locator" xlink:label="spac_EffectsOfTheDeSpacAndRelatedFinancingTransactionsAbstract" xlink:href="https://xbrl.sec.gov/spac/2025/spac-2025.xsd#spac_EffectsOfTheDeSpacAndRelatedFinancingTransactionsAbstract"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_EffectsOfTheDeSpacAndRelatedFinancingTransactionsAbstract_lbl" xml:lang="en-US">Effects of the de-SPAC and Related Financing Transactions [Abstract]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_EffectsOfTheDeSpacAndRelatedFinancingTransactionsAbstract" xlink:to="spac_EffectsOfTheDeSpacAndRelatedFinancingTransactionsAbstract_lbl"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_PercentageOfRedeemInitialBusinessCombination_lbl1" xml:lang="en-US">Percentage Of Redeem Initial Business Combination</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PercentageOfRedeemInitialBusinessCombination" xlink:to="bacq_PercentageOfRedeemInitialBusinessCombination_lbl1"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacCompensationProspectusSummaryTableTextBlock_lbl0" xml:lang="en-US">De-SPAC, Compensation, Prospectus Summary [Table Text Block]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacCompensationProspectusSummaryTableTextBlock" xlink:to="spac_DeSpacCompensationProspectusSummaryTableTextBlock_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_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="bacq_DeferredOfferingCostsIncludedInAccruedOfferingCosts" xlink:to="bacq_DeferredOfferingCostsIncludedInAccruedOfferingCosts_lbl1"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_RedemptionAt50PercentOfMaximumMember_lbl0" xml:lang="en-US">Redemption at 50 Percent of Maximum [Member]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_RedemptionAt50PercentOfMaximumMember" xlink:to="spac_RedemptionAt50PercentOfMaximumMember_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_LessAbstract_lbl0" xml:lang="en-US">Less Abstract</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_LessAbstract" xlink:to="bacq_LessAbstract_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireePercentage_lbl0" xml:lang="en-US">Business Combination, Achieved in Stages, Preacquisition Equity Interest in Acquiree, Percentage</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireePercentage" xlink:to="us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireePercentage_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_FormationCostsPaidBySponsorInExchangeForIssuanceOfClassBOrdinaryShares_lbl1" xml:lang="en-US">Formation Costs Paid By Sponsor In Exchange For Issuance Of Class BOrdinary Shares</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_FormationCostsPaidBySponsorInExchangeForIssuanceOfClassBOrdinaryShares" xlink:to="bacq_FormationCostsPaidBySponsorInExchangeForIssuanceOfClassBOrdinaryShares_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="bacq_FairValuePerShareRight_lbl1" xml:lang="en-US">Fair Value Per Share Right</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_FairValuePerShareRight" xlink:to="bacq_FairValuePerShareRight_lbl1"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_NumberOfOrdinaryShares_lbl1" 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="bacq_NumberOfOrdinaryShares" xlink:to="bacq_NumberOfOrdinaryShares_lbl1"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_DeferredUnderwritingFeePayable_lbl1" xml:lang="en-US">Deferred Underwriting Fee Payable</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_DeferredUnderwritingFeePayable" xlink:to="bacq_DeferredUnderwritingFeePayable_lbl1"/>  
    <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>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="us-gaap_RetainedEarningsAccumulatedDeficit_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CorporateMember_lbl0" xml:lang="en-US">Corporate Segment [Member]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CorporateMember" xlink:to="us-gaap_CorporateMember_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl1" xml:lang="en-US">Sale of Stock, Price 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_lbl1"/> 
    <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>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityRegistrantName" xlink:to="dei_EntityRegistrantName_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_StockIssuedDuringPeriodValueSaleOfPrivatePlacementUnits_lbl1" xml:lang="en-US">Stock Issued During Period Value Sale Of Private Placement Units</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_StockIssuedDuringPeriodValueSaleOfPrivatePlacementUnits" xlink:to="bacq_StockIssuedDuringPeriodValueSaleOfPrivatePlacementUnits_lbl1"/>  
    <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>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommitmentsAndContingencies" xlink:to="us-gaap_CommitmentsAndContingencies_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TemporaryEquityTableTextBlock_lbl1" xml:lang="en-US">Temporary Equity [Table Text Block]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquityTableTextBlock" xlink:to="us-gaap_TemporaryEquityTableTextBlock_lbl1"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_AdditionalSharesIssued_lbl1" xml:lang="en-US">Additional Shares Issued</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_AdditionalSharesIssued" xlink:to="bacq_AdditionalSharesIssued_lbl1"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_UnlabeledAbstract3_lbl0" xml:lang="en-US">Unlabeled Abstract3</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnlabeledAbstract3" xlink:to="bacq_UnlabeledAbstract3_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_UnlabeledAbstract2_lbl0" xml:lang="en-US">Unlabeled Abstract2</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnlabeledAbstract2" xlink:to="bacq_UnlabeledAbstract2_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromIssuanceInitialPublicOffering_lbl0" 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_lbl0"/>     
    <loc xlink:type="locator" xlink:label="us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementOfCashFlowsAbstract" xlink:to="us-gaap_StatementOfCashFlowsAbstract_lbl"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_UnlabeledAbstract1_lbl0" xml:lang="en-US">Unlabeled Abstract1</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnlabeledAbstract1" xlink:to="bacq_UnlabeledAbstract1_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_UnlabeledAbstract0_lbl0" xml:lang="en-US">Unlabeled Abstract0</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnlabeledAbstract0" xlink:to="bacq_UnlabeledAbstract0_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_RedemptionsFromTrustAccountMember_lbl0" xml:lang="en-US">Redemptions From Trust Account Member</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_RedemptionsFromTrustAccountMember" xlink:to="bacq_RedemptionsFromTrustAccountMember_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_WorkingCapitalOutstandingLoans_lbl1" xml:lang="en-US">Working Capital Outstanding Loans</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_WorkingCapitalOutstandingLoans" xlink:to="bacq_WorkingCapitalOutstandingLoans_lbl1"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_UnaffiliatedInflectionPointPublicShareholdersMember_lbl0" xml:lang="en-US">Unaffiliated Inflection Point Public Shareholders Member</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnaffiliatedInflectionPointPublicShareholdersMember" xlink:to="bacq_UnaffiliatedInflectionPointPublicShareholdersMember_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl0" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercises in Period</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised" xlink:to="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl0"/>   
    <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>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:to="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodValueShareBasedCompensationForfeited_lbl0" xml:lang="en-US">Shares Issued, Value, Share-Based Payment Arrangement, Forfeited</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodValueShareBasedCompensationForfeited" xlink:to="us-gaap_StockIssuedDuringPeriodValueShareBasedCompensationForfeited_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalWarrantIssued_lbl0" xml:lang="en-US">Adjustments to Additional Paid in Capital, Warrant Issued</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdjustmentsToAdditionalPaidInCapitalWarrantIssued" xlink:to="us-gaap_AdjustmentsToAdditionalPaidInCapitalWarrantIssued_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock_lbl0" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis [Table Text Block]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock" xlink:to="us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacSecurityHoldersAppraisalRightsSummaryTextBlock_lbl0" xml:lang="en-US">De-SPAC, Security Holders Appraisal Rights Summary [Text Block]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacSecurityHoldersAppraisalRightsSummaryTextBlock" xlink:to="spac_DeSpacSecurityHoldersAppraisalRightsSummaryTextBlock_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EquityMethodInvestmentOwnershipPercentage_lbl0" xml:lang="en-US">Equity Method Investment, Ownership Percentage</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:to="us-gaap_EquityMethodInvestmentOwnershipPercentage_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_SeriesACumulativeConvertiblePreferredStockMember_lbl0" xml:lang="en-US">Series ACumulative Convertible Preferred Stock Member</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_SeriesACumulativeConvertiblePreferredStockMember" xlink:to="bacq_SeriesACumulativeConvertiblePreferredStockMember_lbl0"/>   
    <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>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesCurrentAbstract" xlink:to="us-gaap_LiabilitiesCurrentAbstract_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_RightsPolicyTextBlock_lbl1" xml:lang="en-US">Rights Policy Text Block</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_RightsPolicyTextBlock" xlink:to="bacq_RightsPolicyTextBlock_lbl1"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TemporaryEquitySharesAuthorized_lbl0" xml:lang="en-US">Temporary Equity, Shares Authorized</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquitySharesAuthorized" xlink:to="us-gaap_TemporaryEquitySharesAuthorized_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_PIPEInvestorsMember_lbl0" xml:lang="en-US">PIPEInvestors Member</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PIPEInvestorsMember" xlink:to="bacq_PIPEInvestorsMember_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_lbl1" xml:lang="en-US">Cash Flow, Noncash Investing and Financing Activities Disclosure [Abstract]</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_lbl1"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_AnticipatedTransactionExpensesMember_lbl0" xml:lang="en-US">Anticipated Transaction Expenses Member</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_AnticipatedTransactionExpensesMember" xlink:to="bacq_AnticipatedTransactionExpensesMember_lbl0"/>    
    <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="spac_DeSpacNumberOfSharesUsedToDetermineNetTangibleBookValueAdjusted_lbl0" xml:lang="en-US">De-SPAC, Number of Shares Used to Determine Net Tangible Book Value, Adjusted</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacNumberOfSharesUsedToDetermineNetTangibleBookValueAdjusted" xlink:to="spac_DeSpacNumberOfSharesUsedToDetermineNetTangibleBookValueAdjusted_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_WorkingCapitalDeficit_lbl1" xml:lang="en-US">Working Capital Deficit</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_WorkingCapitalDeficit" xlink:to="bacq_WorkingCapitalDeficit_lbl1"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_CommonStockShareIssued_lbl1" xml:lang="en-US">Common Stock Share Issued</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_CommonStockShareIssued" xlink:to="bacq_CommonStockShareIssued_lbl1"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestExpenseOther_lbl0" xml:lang="en-US">Interest Expense, Other</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestExpenseOther" xlink:to="us-gaap_InterestExpenseOther_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_PlusAbstract3_lbl0" xml:lang="en-US">Plus Abstract3</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PlusAbstract3" xlink:to="bacq_PlusAbstract3_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_PlusAbstract2_lbl0" xml:lang="en-US">Plus Abstract2</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PlusAbstract2" xlink:to="bacq_PlusAbstract2_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacNetTangibleBookValueAdjustedPerShare_lbl0" xml:lang="en-US">De-SPAC, Net Tangible Book Value, Adjusted, Per Share</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacNetTangibleBookValueAdjustedPerShare" xlink:to="spac_DeSpacNetTangibleBookValueAdjustedPerShare_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_ThresholdPeriodAfterBusinessCombinationInWhichSpecifiedTradingDaysWithinAnySpecifiedTradingDayPeriodCommences_lbl1" xml:lang="en-US">Threshold Period After Business Combination In Which Specified Trading Days Within Any Specified Trading Day Period Commences</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ThresholdPeriodAfterBusinessCombinationInWhichSpecifiedTradingDaysWithinAnySpecifiedTradingDayPeriodCommences" xlink:to="bacq_ThresholdPeriodAfterBusinessCombinationInWhichSpecifiedTradingDaysWithinAnySpecifiedTradingDayPeriodCommences_lbl1"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_PlusAbstract1_lbl0" xml:lang="en-US">Plus Abstract1</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PlusAbstract1" xlink:to="bacq_PlusAbstract1_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_PlusAbstract0_lbl0" xml:lang="en-US">Plus Abstract0</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PlusAbstract0" xlink:to="bacq_PlusAbstract0_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TemporaryEquitySharesOutstanding_lbl1" xml:lang="en-US">Temporary Equity, Shares Outstanding</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TemporaryEquitySharesOutstanding" xlink:to="us-gaap_TemporaryEquitySharesOutstanding_lbl1"/>  
    <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_PaymentsOfStockIssuanceCosts_lbl0" xml:lang="en-US">Payments of Stock Issuance Costs</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsOfStockIssuanceCosts" xlink:to="us-gaap_PaymentsOfStockIssuanceCosts_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockIssuedDuringPeriodSharesOther_lbl0" xml:lang="en-US">Stock Issued During Period, Shares, Other</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockIssuedDuringPeriodSharesOther" xlink:to="us-gaap_StockIssuedDuringPeriodSharesOther_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_PublicSharesRedemptionPercentage_lbl1" xml:lang="en-US">Public Shares Redemption Percentage</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PublicSharesRedemptionPercentage" xlink:to="bacq_PublicSharesRedemptionPercentage_lbl1"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl1" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueInputsLevel1Member" xlink:to="us-gaap_FairValueInputsLevel1Member_lbl1"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInPrepaidInsurance_lbl0" xml:lang="en-US">Increase (Decrease) in Prepaid Insurance</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInPrepaidInsurance" xlink:to="us-gaap_IncreaseDecreaseInPrepaidInsurance_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_PlusAbstract_lbl0" xml:lang="en-US">Plus Abstract</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PlusAbstract" xlink:to="bacq_PlusAbstract_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_ProceedsAllocatedToPublicRights_lbl1" xml:lang="en-US">Proceeds Allocated To Public Rights</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ProceedsAllocatedToPublicRights" xlink:to="bacq_ProceedsAllocatedToPublicRights_lbl1"/>    
    <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>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_StockholdersEquity_lbl2"/>    
    <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>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityExTransitionPeriod" xlink:to="dei_EntityExTransitionPeriod_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_InitialPublicOfferingTextBlock_lbl1" xml:lang="en-US">Initial Public Offering Text Block</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_InitialPublicOfferingTextBlock" xlink:to="bacq_InitialPublicOfferingTextBlock_lbl1"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_lbl1" xml:lang="en-US">Business Combination, Voting Equity Interest Acquired, Percentage</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired" xlink:to="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_lbl1"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_UnitsIssuedDuringPeriodSharesNewIssues_lbl3" xml:lang="en-US">Units Issued During Period Shares New Issues</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnitsIssuedDuringPeriodSharesNewIssues" xlink:to="bacq_UnitsIssuedDuringPeriodSharesNewIssues_lbl3"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SharePrice_lbl1" xml:lang="en-US">Share Price</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_lbl1"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_ConvertiblePromissoryNotes_lbl1" xml:lang="en-US">Convertible Promissory Notes</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ConvertiblePromissoryNotes" xlink:to="bacq_ConvertiblePromissoryNotes_lbl1"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashAndCashEquivalentsPolicyTextBlock_lbl0" xml:lang="en-US">Cash and Cash Equivalents, Policy [Policy Text Block]</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:to="us-gaap_CashAndCashEquivalentsPolicyTextBlock_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RightsMember_lbl0" xml:lang="en-US">Rights [Member]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RightsMember" xlink:to="us-gaap_RightsMember_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacBackgroundProspectusSummaryTextBlock_lbl0" xml:lang="en-US">De-SPAC, Background, Prospectus Summary [Text Block]</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacBackgroundProspectusSummaryTextBlock" xlink:to="spac_DeSpacBackgroundProspectusSummaryTextBlock_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl0" xml:lang="en-US">Unrecognized Tax Benefits</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_UnrecognizedTaxBenefits" xlink:to="us-gaap_UnrecognizedTaxBenefits_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_BasicAndDilutedNetIncomeLossPerOrdinaryShareAbstract_lbl0" xml:lang="en-US">Basic And Diluted Net Income Loss Per Ordinary Share Abstract</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_BasicAndDilutedNetIncomeLossPerOrdinaryShareAbstract" xlink:to="bacq_BasicAndDilutedNetIncomeLossPerOrdinaryShareAbstract_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_OfferingCostsPolicyTextBlock_lbl1" xml:lang="en-US">Offering Costs Policy Text Block</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_OfferingCostsPolicyTextBlock" xlink:to="bacq_OfferingCostsPolicyTextBlock_lbl1"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_DeSpacForepartSponsorCompensationMaterialDilutionFlag_lbl0" xml:lang="en-US">De-SPAC Forepart, Sponsor Compensation, Material Dilution [Flag]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacForepartSponsorCompensationMaterialDilutionFlag" xlink:to="spac_DeSpacForepartSponsorCompensationMaterialDilutionFlag_lbl0"/>   
    <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> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GeneralAndAdministrativeExpense" xlink:to="us-gaap_GeneralAndAdministrativeExpense_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_PrivatePlacementTextBlock_lbl1" xml:lang="en-US">Private Placement Text Block</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PrivatePlacementTextBlock" xlink:to="bacq_PrivatePlacementTextBlock_lbl1"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_CashUnderwritingFeePayable_lbl1" xml:lang="en-US">Cash Underwriting Fee Payable</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_CashUnderwritingFeePayable" xlink:to="bacq_CashUnderwritingFeePayable_lbl1"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl1" xml:lang="en-US">Common Stock, Par or Stated Value 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_lbl1"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_UnlabeledAbstract_lbl0" xml:lang="en-US">Unlabeled Abstract</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_UnlabeledAbstract" xlink:to="bacq_UnlabeledAbstract_lbl0"/> 
    <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 Disclosure [Text Block]</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_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EarningsPerSharePolicyTextBlock_lbl0" xml:lang="en-US">Earnings Per Share, Policy [Policy Text Block]</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_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_LiabilitiesClassAOrdinarySharesSubjectToPossibleRedemptionAndShareholdersDeficitAbstract_lbl0" xml:lang="en-US">Liabilities Class AOrdinary Shares Subject To Possible Redemption And Shareholders Deficit Abstract</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_LiabilitiesClassAOrdinarySharesSubjectToPossibleRedemptionAndShareholdersDeficitAbstract" xlink:to="bacq_LiabilitiesClassAOrdinarySharesSubjectToPossibleRedemptionAndShareholdersDeficitAbstract_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromIssuanceOfPrivatePlacement_lbl2" xml:lang="en-US">Proceeds from Issuance of Private Placement</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_lbl2"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonStockSharesIssued_lbl1" xml:lang="en-US">Common Stock, Shares, Issued</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_lbl1"/>    
    <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>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityEmergingGrowthCompany" xlink:to="dei_EntityEmergingGrowthCompany_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentOfFinancingAndStockIssuanceCosts_lbl0" xml:lang="en-US">Payment of Financing and Stock Issuance Costs</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentOfFinancingAndStockIssuanceCosts" xlink:to="us-gaap_PaymentOfFinancingAndStockIssuanceCosts_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_PostBusinessCombinationMember_lbl0" xml:lang="en-US">Post Business Combination Member</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PostBusinessCombinationMember" xlink:to="bacq_PostBusinessCombinationMember_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_NetTangibleBookValueMember_lbl0" xml:lang="en-US">Net Tangible Book Value Member</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_NetTangibleBookValueMember" xlink:to="bacq_NetTangibleBookValueMember_lbl0"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_SponsorMember_lbl0" xml:lang="en-US">Sponsor Member</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_SponsorMember" xlink:to="bacq_SponsorMember_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl1" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl1"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl0" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted</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_lbl0"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PreferredStockSharesIssued_lbl1" xml:lang="en-US">Preferred Stock, Shares Issued</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_lbl1"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_FounderShareMember_lbl0" xml:lang="en-US">Founder Share Member</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_FounderShareMember" xlink:to="bacq_FounderShareMember_lbl0"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PrivatePlacementMember_lbl1" 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_lbl1"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_InterestToPayDissolutionExpenses_lbl1" xml:lang="en-US">Interest To Pay Dissolution Expenses</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_InterestToPayDissolutionExpenses" xlink:to="bacq_InterestToPayDissolutionExpenses_lbl1"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl1" xml:lang="en-US">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:to="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl1"/>   
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_LiabilitiesClassAOrdinarySharesSubjectToPossibleRedemptionAndShareholdersDeficitAbstract0_lbl0" xml:lang="en-US">Liabilities Class AOrdinary Shares Subject To Possible Redemption And Shareholders Deficit Abstract0</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_LiabilitiesClassAOrdinarySharesSubjectToPossibleRedemptionAndShareholdersDeficitAbstract0" xlink:to="bacq_LiabilitiesClassAOrdinarySharesSubjectToPossibleRedemptionAndShareholdersDeficitAbstract0_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember_lbl1" xml:lang="en-US">Business Combination, Series of Individually Immaterial Business Combinations [Member]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember" xlink:to="us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember_lbl1"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl0" xml:lang="en-US">Fair Value Disclosures [Text Block]</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueDisclosuresTextBlock" xlink:to="us-gaap_FairValueDisclosuresTextBlock_lbl0"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_PaymentOfOperationCostsThroughPromissoryNote_lbl1" xml:lang="en-US">Payment Of Operation Costs Through Promissory Note</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_PaymentOfOperationCostsThroughPromissoryNote" xlink:to="bacq_PaymentOfOperationCostsThroughPromissoryNote_lbl1"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashFDICInsuredAmount_lbl0" xml:lang="en-US">Cash, FDIC Insured Amount</label>  
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashFDICInsuredAmount" xlink:to="us-gaap_CashFDICInsuredAmount_lbl0"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_WorkingCapitalLoanAmount_lbl1" xml:lang="en-US">Working Capital Loan Amount</label>    
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_WorkingCapitalLoanAmount" xlink:to="bacq_WorkingCapitalLoanAmount_lbl1"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetIncomeLoss_lbl1" xml:lang="en-US">Net Income (Loss) Attributable to Parent</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_lbl1"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl2" 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_lbl2"/> 
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_DeferredUnderwritingFee_lbl1" xml:lang="en-US">Deferred Underwriting Fee</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_DeferredUnderwritingFee" xlink:to="bacq_DeferredUnderwritingFee_lbl1"/>   
    <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="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_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="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_lbl0" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements Disclosure [Text Block]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:to="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_lbl0"/>   
    <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"/>    
    <loc xlink:type="locator" xlink:label="us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.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="spac_DeSpacForepartSecuritiesIssuedOrToBeIssuedShares_lbl0" xml:lang="en-US">De-SPAC Forepart, Securities Issued or To Be Issued, Shares</label>     
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_DeSpacForepartSecuritiesIssuedOrToBeIssuedShares" xlink:to="spac_DeSpacForepartSecuritiesIssuedOrToBeIssuedShares_lbl0"/>   
    <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="bacq_ScheduleOfMarketAssumptionsInValuationOfPublicRightsTableTextBlock_lbl2" xml:lang="en-US">Schedule Of Market Assumptions In Valuation Of Public Rights Table Text Block</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_ScheduleOfMarketAssumptionsInValuationOfPublicRightsTableTextBlock" xlink:to="bacq_ScheduleOfMarketAssumptionsInValuationOfPublicRightsTableTextBlock_lbl2"/>    
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_LiquidityCapitalResourcesAndGoingConcernPolicyTextBlock_lbl1" xml:lang="en-US">Liquidity Capital Resources And Going Concern Policy Text Block</label> 
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="bacq_LiquidityCapitalResourcesAndGoingConcernPolicyTextBlock" xlink:to="bacq_LiquidityCapitalResourcesAndGoingConcernPolicyTextBlock_lbl1"/>  
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl2" 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_lbl2"/>     
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="spac_CommonSharesMember_lbl0" xml:lang="en-US">Common Shares [Member]</label>   
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="spac_CommonSharesMember" xlink:to="spac_CommonSharesMember_lbl0"/>   
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_InvestmentsMaximumMaturityTerm_lbl1" xml:lang="en-US">Investments Maximum Maturity Term</label> 
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="bacq_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_DeferredOfferingCosts_lbl0" xml:lang="en-US">Deferred Offering Costs</label>     
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