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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationAcquisitionRelatedCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Transaction costs related to acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationAcquisitionRelatedCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Acquisition-Related Cost, Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BuildingImprovementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Building Improvements [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BuildingImprovementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Buildings and Improvements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EnvironmentalCostsPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Environmental Costs, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EnvironmentalCostsPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Environmental Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ContributionsDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Contributions [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ContributionsDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Contributions.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskByTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DemandRegistrationMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Demand Registration [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DemandRegistrationMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Demand registration.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DemandRegistrationMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Demand Registration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonUnitOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Unit, Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonUnitOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Units, Ending Balances</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonUnitOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Units, Beginning Balances</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Present value of lease payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis with Unobservable Inputs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis with Unobservable Inputs, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Fair Value, Net Derivative Asset (Liability) Measured on Recurring Basis with Unobservable Inputs, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueNetDerivativeAssetLiabilityMeasuredOnRecurringBasisWithUnobservableInputs_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair value of financial Instruments measured on recurring basis using significant unobservable inputs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Related Party Transactions [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Activities of USPH Class A Units and Subscription Notes Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityIncorporationStateCountryCode_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Incorporation, State or Country Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityIncorporationStateCountryCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Incorporation, State or Country Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, to be Paid, Year Four</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2030</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BalanceSheetLocationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Financial Position Location, Balance [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConvertiblePreferredStockNonredeemableOrRedeemableIssuerOptionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Convertible Preferred Stock, Nonredeemable or Redeemable, Issuer Option, Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConvertiblePreferredStockNonredeemableOrRedeemableIssuerOptionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred units aggregate value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConvertiblePreferredStockNonredeemableOrRedeemableIssuerOptionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Conversion of redeemable noncontrolling interest to noncontrolling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Increase (Decrease) in Accounts Payable, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Accounts Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Due within one year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, Year One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Excluding Current Maturities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term debt, net of current maturities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Long-term portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCurrentReportingStatus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Current Reporting Status</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCurrentReportingStatus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Current Reporting Status</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentOfNotesReceivableFromRelatedParties_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Repayment of Notes Receivable from Related Parties</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentOfNotesReceivableFromRelatedParties_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Repayment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentOfNotesReceivableFromRelatedParties_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Repayment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpensesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating expenses:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpensesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Expenses [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Level 2</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 2 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitments and Contingencies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheThreeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Tranche Three [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheThreeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Vesting Upon Four Year Anniversary</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheThreeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Investor Return Equal To or Greater Than 3.0</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PartnersCapitalAccountUnitBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Partners' Capital Account, Unit-Based Payment Arrangement, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PartnersCapitalAccountUnitBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unit-based compensation expense, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Asset, Expected Amortization, Year Four</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated net amortization expense, 2030</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Temporary equity stated value per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Stated Value per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetRetirementObligationsPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Retirement Obligation [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetRetirementObligationsPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset Retirement Obligations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ContributionTwoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Contribution Two [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ContributionTwoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Contribution two.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ContributionTwoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Safe Harbor Contribution of 50% of Employees' Contribution</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ProductOrServiceAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Product and Service</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ProductOrServiceAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Product and Service [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalPeriodFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Fiscal Period Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalPeriodFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Period Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, to be Paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total future undiscounted lease payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassPUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class P Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassPUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class P Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassPUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Class P Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Interest Rate, Stated Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateStatedPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument, interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue from Contract with Customer [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityShellCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Shell Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityShellCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Shell Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Other accrued liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Accrued Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other accruals</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DescriptionOfDefinedContributionPensionAndOtherPostretirementPlans_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Defined Contribution Plan, Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DescriptionOfDefinedContributionPensionAndOtherPostretirementPlans_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Defined contribution plan, description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash and Cash Equivalents, at Carrying Value, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Cash and Cash Equivalents, at Carrying Value, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Cash and Cash Equivalents, at Carrying Value, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total cash and cash equivalents, carrying value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MembersCapital_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Members' Capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MembersCapital_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Members capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Schedule of Maturities of Long-Term Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Maturities of Long-Term Debt [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CommitmentsAndContingenciesDisclosureLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitments And Contingencies Disclosure [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CommitmentsAndContingenciesDisclosureLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments And Contingencies Disclosure [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CommitmentsAndContingenciesDisclosureLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Commitments and contingencies disclosure.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, Conversion of Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock upon settlement of restricted stock units, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Common Stock, Shares, Issued, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsEquityValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement by Share Based Payment Award Fair Value Assumptions Equity Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsEquityValue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangement by share based payment award fair value assumptions equity value.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsEquityValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset Class</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Class [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statement [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EmployeeTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EmployeeTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Employee type.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncontrollingInterestInNetIncomeLossPreferredUnitHoldersRedeemable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accretion on CLHI Corporate's redeemable noncontrolling interest's preferred shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncontrollingInterestInNetIncomeLossPreferredUnitHoldersRedeemable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncontrolling Interest in Net Income (Loss) Preferred Unit Holders, Redeemable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Right-of-Use Asset Obtained in Exchange for Operating Lease Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EscrowAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Escrow Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EscrowAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Escrow Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EscrowAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Escrow agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average grant date fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Weighted Average Grant Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Businesses, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Business acquisition, cash payment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesGross_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total cash consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetRetirementObligation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Retirement Obligation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetRetirementObligation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Asset Retirement Obligation, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetRetirementObligation_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetRetirementObligation_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statement [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionAcquireeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFilerCategory_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Filer Category</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFilerCategory_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Filer Category</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TaxReturnOpenForExamination_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tax Return Open For Examination</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TaxReturnOpenForExamination_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tax return open for examination.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TaxReturnOpenForExamination_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tax return open for examination</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities and Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities, members' equity, and stockholders' equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Term loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Term Loan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Term Loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Current Maturities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Long-Term Debt, Current Maturities, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current maturities of long- term debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Maturity, Year Three</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">2028</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2029</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationCostsOfGoodsSold_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchase price per Asset Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationCostsOfGoodsSold_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Costs of Goods Sold</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Lived Tangible Asset [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, to be Paid, Year Three</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2029</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign currency translation adjustment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax, Portion Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax, Portion Attributable to Parent, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_USSaltIntermediateHoldingsLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">US Salt Intermediate Holdings, LLC [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_USSaltIntermediateHoldingsLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">US Salt Intermediate Holdings, LLC.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_USSaltIntermediateHoldingsLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">US Salt Intermediate Holdings, LLC</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpensesAndOtherCurrentAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Expenses and Other Current Assets [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpensesAndOtherCurrentAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid and Other Current Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionPercentageOfVotingInterestsAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Voting equity interest acquired, percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TradeNamesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tradename</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TradeNamesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Trade Names [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PercentageOfQuarterlyManagementFee_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of quarterly management fee</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PercentageOfQuarterlyManagementFee_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage of Quarterly Management Fee</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PercentageOfQuarterlyManagementFee_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage of Quarterly Management Fee.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalents, Fair Value Disclosure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total cash and cash equivalents, fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lease and other liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Other Liabilities, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Assets, Remaining Amortization Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Remaining useful lives for the intangible assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, at Federal Statutory Income Tax Rate, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">U.S. statutory rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MembersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Members' Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MembersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Members' equity (Predecessor)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BasisOfPresentationAndConsolidationPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Basis of Presentation and Consolidation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BasisOfPresentationAndConsolidationPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Basis Of Presentation And Consolidation Policy [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BasisOfPresentationAndConsolidationPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Basis of presentation and consolidation.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LossContingencyNumberOfCasesDismissedByPlaintiff_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of cases dismissed by plaintiff</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LossContingencyNumberOfCasesDismissedByPlaintiff_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loss Contingency Number Of Cases Dismissed By Plaintiff</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LossContingencyNumberOfCasesDismissedByPlaintiff_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Loss contingency number of cases dismissed by plaintiff.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Goodwill, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Goodwill, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Goodwill, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNoncashIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNoncashIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Noncash Income (Expense)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNoncashIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Noncash Income (Expense), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Effective Income Tax Rate Reconciliation, Percent, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Benefit for income taxes, percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeStockOptionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Common Stock Options Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash paid for income taxes, net of refunds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Taxes Paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, to be Paid, Remainder of Fiscal Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxAuthorityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Jurisdiction [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetRetirementObligationAccretionExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Retirement Obligation, Accretion Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetRetirementObligationAccretionExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accretion of expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_SegmentGeographicalDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Geographical [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite Lived Intangible Assets Amortization Expense After Year Four</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Finite lived intangible assets amortization expense after year four.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated net amortization expense, thereafter</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InventoryFinishedGoods_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finished Goods</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InventoryFinishedGoods_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Inventory, Finished Goods, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FinanceLeaseExpiringYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Expiring Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FinanceLeaseExpiringYear_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Finance lease, expiring year.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FinanceLeaseExpiringYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance lease expiring year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Defined Contribution Plan, Employer Matching Contribution, Percent of Employees' Gross Pay</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of employee's eligible gross compensation each year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationRefundsLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Refunds liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationRefundsLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Refunds Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationRefundsLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal group, including discontinued operation, refunds liability.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NoncashLeaseExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncash Lease Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NoncashLeaseExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Noncash lease expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NoncashLeaseExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Noncash lease expense.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfInventoryCurrentTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Inventory</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfInventoryCurrentTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Inventory, Current [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Receivable, Allowance for Credit Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCapitalLeaseObligation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lease liabilities, non-current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCapitalLeaseObligation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Liability Assumed, Lease Obligation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Debt issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Issuance Costs, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Debt Issuance Costs, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ContributionOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Contribution One [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ContributionOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Contribution One.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ContributionOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Safe Harbor Contribution of 100% of Employees' Contribution</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetUsefulLife_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Asset, Useful Life</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetUsefulLife_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finite lived intangible asset useful lives</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetUsefulLife_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Estimated Useful Life</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Cash and Cash Equivalents [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Breakdown of Cash and Cash Equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VestingDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Vesting [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PercentageOfAnnualManagementFee_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of annual management fee</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PercentageOfAnnualManagementFee_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage of Annual Management Fee</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PercentageOfAnnualManagementFee_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage of annual management fee.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of Options, Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisaggregationOfRevenueTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Disaggregation Of Revenue [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisaggregationOfRevenueTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disaggregation of Revenue [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Computation of Basic and Diluted Net Loss Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TrademarksAndTradeNamesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trade Names and Trademark</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TrademarksAndTradeNamesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Trademarks and Trade Names [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Earnings Per Share, Basic, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss per share attributable to common stockholders, basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net income per share attributable to common stockholders, basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisaggregationOfRevenueTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Disaggregated Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisaggregationOfRevenueTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disaggregation of Revenue [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SubscriptionReceivableMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subscription Receivable [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SubscriptionReceivableMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Subscription Receivable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SubscriptionReceivableMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subscription Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ScheduleOfLeaseTermAndDiscountRateInformationRelatedToLeaseTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Lease Term and Discount Rate Information Related To Lease [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ScheduleOfLeaseTermAndDiscountRateInformationRelatedToLeaseTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule of lease term and discount rate information related to lease.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ScheduleOfLeaseTermAndDiscountRateInformationRelatedToLeaseTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Lease Term and Discount Rate Information</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments for Repurchase of Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Payments for Repurchase of Equity, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Repurchase of units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRepurchaseOfEquity_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Repurchase of units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Retirement Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retirement Benefits [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Number of Options, Beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Number of Options, Ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IndefinitelivedIntangibleAssetsAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Indefinite-Lived Intangible Assets Acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IndefinitelivedIntangibleAssetsAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Acquired intangible assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NetAssetsOfDisposalGroupIncludingDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NetAssetsOfDisposalGroupIncludingDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Assets Of Disposal Group Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NetAssetsOfDisposalGroupIncludingDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Net assets of disposal group including discontinued operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestIncomeExpenseNonoperatingNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Income (Expense), Nonoperating</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestIncomeExpenseNonoperatingNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest and other expense, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestIncomeExpenseNonoperatingNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Interest Income (Expense), Nonoperating, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestIncomeExpenseNonoperatingNet_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net interest and other income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevolvingCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revolving Credit Facility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevolvingCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revolving Credit Facility [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevolvingCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Revolving line of credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationRightOfUseAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Right-of-use assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationRightOfUseAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Right-of-Use Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationRightOfUseAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal group, including discontinued operation, right-of-use assets.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Accounts Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts receivable, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Accounts Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Accounts receivable, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Adjustments to reconcile net income to net cash (used in) provided by operating activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Customer1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Customer 1 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Customer1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Customer 1.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Customer1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">One Customer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ContributionsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Contributions [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ContributionsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Contributions.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IssuanceOfNoncontrollingInterestUSSaltAcquisition_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of Noncontrolling interest - US Salt Acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IssuanceOfNoncontrollingInterestUSSaltAcquisition_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Issuance of Noncontrolling interest US Salt Acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IssuanceOfNoncontrollingInterestUSSaltAcquisition_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Issuance of noncontrolling interest US salt acquisition.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DomesticCountryMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Domestic Tax Jurisdiction [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DomesticCountryMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Federal Authorities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RoyaltyAgreementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Royalty Agreements [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RoyaltyAgreementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Permits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Fair Value, Fiscal Year Maturity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationFundsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal group, including discontinued operation, funds receivable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationFundsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Funds receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationFundsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Funds Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Payment of debt issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments of Debt Issuance Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_USPHClassAUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">USPH Class A Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_USPHClassAUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">USPH Class A Units.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_USPHClassAUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">USPH Class A Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PackagedMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Packaged member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PackagedMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Packaged</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Parent [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stockholders' equity (Successor)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Small Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Small Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityCommitmentFeeAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Commitment Fee Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityCommitmentFeeAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unused amount of credit available</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Accrued Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Increase (Decrease) in Accrued Liabilities, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketApproachValuationTechniqueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Valuation, Market Approach [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketApproachValuationTechniqueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Market Approach</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Retained Earnings (Accumulated Deficit), Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Retained Earnings (Accumulated Deficit), Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Retained Earnings (Accumulated Deficit), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings (Accumulated Deficit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated deficit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Preferred Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeographicConcentrationRiskMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Geographic Concentration Risk [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeographicConcentrationRiskMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Geographic Concentration Risk</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SellersRepresentativeExpenseFund_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sellers representative expense fund</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SellersRepresentativeExpenseFund_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sellers Representative Expense Fund</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SellersRepresentativeExpenseFund_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Sellers representative expense fund</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Number of Options, Forfeited or cancelled</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Forfeitures in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock, Price Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sale of stock, price per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BusinessAcquisitionsProFormaNetLossAttributableToNon-ControllingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pro forma net loss attributable to noncontrolling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BusinessAcquisitionsProFormaNetLossAttributableToNon-ControllingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Acquisitions Pro Forma Net Loss attributable to Non-Controlling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BusinessAcquisitionsProFormaNetLossAttributableToNon-ControllingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business acquisitions pro forma net loss attributable to non-controlling interest.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Time-BasedClassPUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Time-based Class P Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Time-BasedClassPUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Time-Based Class P Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Time-BasedClassPUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Time-based Class P Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedInsuranceCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued insurance services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedInsuranceCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Insurance, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DefinedContributionPlanTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Defined Contribution Plan [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeasesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Leases [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonClassAMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class A Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonClassAMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Class A [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonClassAMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Class A</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CollectionOfSubscriptionNoteReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collection of Subscription Note Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CollectionOfSubscriptionNoteReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Collection of subscription note receivable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CollectionOfSubscriptionNoteReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Collection of subscription note receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfGoodsAndServiceExcludingDepreciationDepletionAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cost of Goods and Service, Excluding Depreciation, Depletion, and Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfGoodsAndServiceExcludingDepreciationDepletionAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cost of Goods and Service, Excluding Depreciation, Depletion, and Amortization, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfGoodsAndServiceExcludingDepreciationDepletionAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cost of sales</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ProductsAndServicesDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Product and Service</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ProductsAndServicesDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Product and Service [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AbramsCapitalPartnersILPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Abrams Capital Partners I LP [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AbramsCapitalPartnersILPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Abrams capital partners I, LP.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AbramsCapitalPartnersILPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">ACP I</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IssuanceOfSubsidiaryMembershipUnitsRightsOfferingBackstop_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Issuance of Subsidiary Membership Units Rights Offering Backstop</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IssuanceOfSubsidiaryMembershipUnitsRightsOfferingBackstop_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Issuance of subsidiary membership units rights offering backstop.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IssuanceOfSubsidiaryMembershipUnitsRightsOfferingBackstop_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of subsidiary membership units - Rights Offering backstop</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TransactionExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Transaction expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TransactionExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Transaction Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TransactionExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Transaction expense.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TransactionExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Transaction expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SaltReservesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Salt Reserves [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SaltReservesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Salt reserves.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SaltReservesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Salt Reserves</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InventoryDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Inventories</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InventoryDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Inventory Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_InvestmentAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investment Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_InvestmentAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_InvestmentAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Investment agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CollectivelyOwnedPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Collectively owned percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CollectivelyOwnedPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collectively owned percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AccruedAndUnpaidDistributionsPerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued and Unpaid Distributions Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AccruedAndUnpaidDistributionsPerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accrued and unpaid distributions per share.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AccruedAndUnpaidDistributionsPerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued and unpaid distributions per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of subscription rights to purchase</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Warrant or Right, Number of Securities Called by Warrants or Rights</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ChiefExecutiveOfficerMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">David Sugarman</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ChiefExecutiveOfficerMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Chief Executive Officer [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OrganizationConsolidationBasisOfPresentationBusinessDescriptionAndAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Overview, Basis of Presentation and Significant Accounting Policies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OrganizationConsolidationBasisOfPresentationBusinessDescriptionAndAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Organization, Consolidation, Basis of Presentation, Business Description and Accounting Policies [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationNetAssetsSoldPursuantToTheAssetSale_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation Net Assets Sold Pursuant To The Asset Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationNetAssetsSoldPursuantToTheAssetSale_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal group, including discontinued operation net assets sold pursuant to the asset sale.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationNetAssetsSoldPursuantToTheAssetSale_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net assets sold pursuant to the Asset Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationNetAssetsSoldPursuantToTheAssetSale_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: Net assets sold pursuant to the Asset Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerSharePolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerSharePolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net Income Per Unit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities and Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Liabilities, Members' Equity and Stockholders' Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressPostalZipCode_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, Postal Zip Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressPostalZipCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Postal Zip Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TradeAndOtherAccountsReceivablePolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Receivable [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TradeAndOtherAccountsReceivablePolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts Receivable, Net and Allowance for Expected Credit Losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash (used in) provided by operating activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Operating Lease Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SupplementalCashFlowInformationRelatedToLeasesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Supplemental Cash Flow Information</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SupplementalCashFlowInformationRelatedToLeasesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Supplemental cash flow information related to leases.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, CODM, Profit (Loss) Measure, How Used, Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Common Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedInventory_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired, Inventory, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedInventory_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Inventory</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CreditAgreementExcessCashFlowPercentageDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Agreement Excess Cash Flow Percentage Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CreditAgreementExcessCashFlowPercentageDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Credit agreement excess cash flow percentage description.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CreditAgreementExcessCashFlowPercentageDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">ECF percentage description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Maturity, Year One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2027</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-Average Exercise Price, Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Grants in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year Three</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2029</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Accumulated depreciation and depletion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CommitmentsAndContingenciesDisclosureTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitments And Contingencies Disclosure [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CommitmentsAndContingenciesDisclosureTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments And Contingencies Disclosure [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CommitmentsAndContingenciesDisclosureTable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Commitments and contingencies disclosure.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EscrowDeposit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Escrow Deposit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EscrowDeposit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Escrow fund</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LossContingencyNumberOfCasesCoordinatedAndConsolidated_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of cases coordinated and consolidated</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LossContingencyNumberOfCasesCoordinatedAndConsolidated_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loss Contingency Number Of Cases Coordinated and Consolidated</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LossContingencyNumberOfCasesCoordinatedAndConsolidated_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Loss contingency number of cases coordinated and consolidated.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateEffectivePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Interest Rate, Effective Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateEffectivePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, Address Line One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Address Line One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateImmaterialEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Change in Accounting Principle, Accounting Standards Update, Immaterial Effect [true false]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Share-Based Payment Award, Stock Options, Valuation Assumptions [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Valuation Assumptions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BusinessCombinationPaymentOfUnitBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Payment of Unit Based Compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BusinessCombinationPaymentOfUnitBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business combination payment of unit based compensation.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BusinessCombinationPaymentOfUnitBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unit-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AccretionOfStockIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accretion of Stock Issuance Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AccretionOfStockIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accretion of stock issuance costs.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AccretionOfStockIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accretion to adjust redemption value of subsidiary's Preferred Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Hierarchy and NAV</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Foreign Currency Transactions and Translations Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign Currency Transactions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AdditionalUnitsIssuableForFutureInvestment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Units Issuable For Future Investment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AdditionalUnitsIssuableForFutureInvestment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional units issuable for future investment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AdditionalUnitsIssuableForFutureInvestment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Additional units issuable for future investment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill and Intangible Assets Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Goodwill and Intangible Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BalanceSheetLocationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Financial Position Location, Balance [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ManagementFeeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Management Fee Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ManagementFeeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Management Fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_USPHClassBUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">USPH Class B Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_USPHClassBUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">USPH Class B Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_USPHClassBUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">USPH Class B Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PaymentsForRepaymentOfPrincipalOnTermLoan_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Repayment of principal on term loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PaymentsForRepaymentOfPrincipalOnTermLoan_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments For Repayment of Principal on Term Loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PaymentsForRepaymentOfPrincipalOnTermLoan_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Repayment of principal on term loan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PaymentsForRepaymentOfPrincipalOnTermLoan_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Repayment of principal on term loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease right-of-use assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Right-of-Use Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, Undiscounted Excess Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Imputed interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Imputed interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EquityExchangedForOwnershipInUSSalt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Exchanged For Ownership In US Salt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EquityExchangedForOwnershipInUSSalt_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Equity exchanged for ownership in us Salt.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EquityExchangedForOwnershipInUSSalt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity exchanged for ownership in US Salt (Note 2)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Purchases of marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Debt Securities, Available-for-Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InventoryDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Inventory Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DistributionsMadeToLimitedPartnerTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Distributions Made to Limited Partner [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GrossProfit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Gross profit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GrossProfit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gross Profit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TypeOfArrangementAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Collaborative Arrangement and Arrangement Other than Collaborative</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TypeOfArrangementAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collaborative Arrangement and Arrangement Other than Collaborative [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RailCarRepairAccrualCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Rail Car Repair Accrual, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RailCarRepairAccrualCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Rail car repair accrual, current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RailCarRepairAccrualCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Rail car repair accrual</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByParent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsidiary, Ownership Percentage, Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByParent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of ownership interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ArrangementsAndNonarrangementTransactionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Collaborative Arrangement and Arrangement Other than Collaborative</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ArrangementsAndNonarrangementTransactionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collaborative Arrangement and Arrangement Other than Collaborative [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Receivable, Allowance for Credit Loss, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less: allowance for expected credit losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: allowance for expected credit losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Assets [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RightsOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Rights Offering [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RightsOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Rights offering.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RightsOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Rights Offering</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrimeRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prime Rate [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrimeRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Prime Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ValuationTechniqueAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Valuation Approach and Technique [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Including Exchange Rate Effect and Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net (decrease) increase in cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Anti-dilutive securities excluded from computation of earnings per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Dilutive securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NonPackagedMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Non packaged member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NonPackagedMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Non Packaged</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BalanceSheetRelatedDisclosuresAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Balance Sheet Related Disclosures [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherNoncurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Other Assets, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRightOfUseAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Recognized Identifiable Assets Acquired and Liabilities Assumed Right of Use Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRightOfUseAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business combination recognized identifiable assets acquired and liabilities assumed right of use assets.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRightOfUseAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Right-of-use asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupClassificationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group Classification [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityInterestIssuedOrIssuableTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Consideration Transferred, Equity Interest, Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, par value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other comprehensive loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other comprehensive income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Tranche One [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Vesting Upon Later of Two Year Anniversary</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Investor Return Equal To or Greater Than 2.0</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BaseRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Alternative Base Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BaseRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Base Rate [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-Average Remaining Contractual Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Remaining Contractual Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdministrativeFeesExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Administrative expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdministrativeFeesExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Administrative Fees Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Amortized Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DefinedContributionPlanDisclosureLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Defined Contribution Plan Disclosure [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AbramsCapitalPartnersIILPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Abrams Capital Partners II LP [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AbramsCapitalPartnersIILPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Abrams capital partners II, LP.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AbramsCapitalPartnersIILPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">ACP II</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AttributedToClassBMembersUntilAllClassBCapitalContributionErodedMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Attributed to Class B Members Until All Class B Capital Contribution Eroded [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AttributedToClassBMembersUntilAllClassBCapitalContributionErodedMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Attributed to Class B Members until all Class B Capital Contribution eroded.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_MaintenanceMaterials_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Maintenance Materials</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_MaintenanceMaterials_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Maintenance materials</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_MaintenanceMaterials_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maintenance materials</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ScheduleOfLongTermAndDiscountRateInformationRelatedToLeasesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Long Term and Discount Rate Information</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ScheduleOfLongTermAndDiscountRateInformationRelatedToLeasesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Long Term And Discount Rate Information Related To Leases [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ScheduleOfLongTermAndDiscountRateInformationRelatedToLeasesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule of long term and discount rate information related to leases.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instruments [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Number of Options, Exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock upon exercise of options for cash, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercises in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherPrepaidExpenseCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other prepaid expenses and assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherPrepaidExpenseCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Prepaid Expense, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalCashFlowElementsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Supplemental cash flow disclosures:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalCashFlowElementsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Supplemental Cash Flow Elements [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableRollforward_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Receivable, Allowance for Credit Loss [Roll Forward]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RightOfUseAssetsObtainedInExchangeForLeaseLiabilitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Right of Use Assets Obtained In Exchange For Lease Liabilities [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RightOfUseAssetsObtainedInExchangeForLeaseLiabilitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Right-of-use assets obtained in exchange for lease liabilities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RightOfUseAssetsObtainedInExchangeForLeaseLiabilitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Right-of-use assets obtained in exchange for lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfSalesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cost of Sales [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfSalesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cost of Sales</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_OwnershipDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Ownership [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current Fiscal Year End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current Fiscal Year End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Long-Term Debt Instruments [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Intangible Asset, Acquired, Finite-Lived [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Identifiable Intangible Asset Estimated Useful Life and Asset Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentQuarterlyReport_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Quarterly Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentQuarterlyReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Quarterly Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherNoncurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired, Other Asset, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherNoncurrentAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other noncurrent assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PercentageOfAnnualDiscretionaryBonus_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage of annual discretionary bonus.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PercentageOfAnnualDiscretionaryBonus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage of Annual Discretionary Bonus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PercentageOfAnnualDiscretionaryBonus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of annual discretionary bonus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReceivablesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Receivables [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CustomerRelationshipsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Customer Relationships [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CustomerRelationshipsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Customer Relationships</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, State or Province</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, State or Province</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Unvested share outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning balance of number of units nonvested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending balance of number of units nonvested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of non-vested units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Redeemable Noncontrolling Interest [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Preferred Stock, Shares Outstanding, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Preferred Stock, Shares Outstanding, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Comprehensive loss attributable to common stockholders</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BCPBackstopAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">BCP Backstop Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BCPBackstopAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">BCP Backstop Agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_StatementGeographicalAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Geographical [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PartnersCapitalAccountTreasuryUnitsPurchases_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Partners' Capital Account, Treasury Units, Purchased</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PartnersCapitalAccountTreasuryUnitsPurchases_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Repurchase of units, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PartnersCapitalAccountTreasuryUnitsPurchases_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Repurchase of units, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConversionOfStockSharesConverted1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Conversion of Stock, Shares Converted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConversionOfStockSharesConverted1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of shares exchanged for each share of Class A common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MembersEquityAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Members' Equity Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MembersEquityAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Noncontrolling parent interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Receivable [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetRetirementObligationDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Retirement Obligation Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Equity, Attributable to Noncontrolling Interest, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Equity, Attributable to Noncontrolling Interest, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Equity, Attributable to Noncontrolling Interest, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Noncontrolling interest (Note 14)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationCashAdjustmentPursuantToTheAssetSale_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: Cash adjustment pursuant to the Asset Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationCashAdjustmentPursuantToTheAssetSale_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash adjustment pursuant to the Asset Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationCashAdjustmentPursuantToTheAssetSale_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation Cash Adjustment Pursuant To The Asset Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationCashAdjustmentPursuantToTheAssetSale_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal group, including discontinued operation cash adjustment pursuant to the asset sale.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Stock-Based Compensation Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expensed and Capitalized, Amount [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_USSaltHoldingsLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">US Salt Holdings LLC [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_USSaltHoldingsLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">US salt holdings, LLC.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_USSaltHoldingsLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">US Salt Holdings, LLC</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestCostsCapitalized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Costs Capitalized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestCostsCapitalized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Capitalized interest costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomePolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomePolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Comprehensive Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationMerchantsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Merchants payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationMerchantsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Merchants Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationMerchantsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal group, including discontinued operation, merchants payable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PerformanceSharesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">PSUs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PerformanceSharesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Performance Stock Units ("PSUs")</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PerformanceSharesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Performance Shares [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RedeemableNoncontrollingInterestDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemable Non-controlling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RedeemableNoncontrollingInterestDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Redeemable Noncontrolling Interest Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RedeemableNoncontrollingInterestDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Redeemable noncontrolling interest disclosure.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Subsequent Event</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Maturity, Remainder of Fiscal Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Remaining 2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Unamortized Discount (Premium) and Debt Issuance Costs, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Debt Instrument, Unamortized Discount (Premium) and Debt Issuance Costs, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Unamortized debt discount and issuance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance of Convertible Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from issuance of redeemable convertible Preferred Units, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ColocationAndCloudServicesArrangementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Colocation and Cloud Services Arrangement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ColocationAndCloudServicesArrangementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Colocation And Cloud Services Arrangement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ColocationAndCloudServicesArrangementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Colocation and cloud services arrangement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Antidilutive Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsPrepaidExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired, Prepaid Expense and Other Asset, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsPrepaidExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of vesting of award</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Rights, Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpenseNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expense, after Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpenseNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total equity-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Sale of Debt Securities, Available-for-Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sales of marketable securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StateAndLocalJurisdictionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">State Authorities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StateAndLocalJurisdictionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">State and Local Jurisdiction [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinimumNetWorthRequiredForCompliance_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Minimum liquidity financial covenant</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinimumNetWorthRequiredForCompliance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Banking Regulation, Mortgage Banking, Net Worth, Minimum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated Other Comprehensive Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">AOCI Attributable to Parent [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_NameOfMajorCustomerDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Customer [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RegistrationPaymentArrangementArrangementDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Registration Payment Arrangement, Arrangement [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillImpairmentLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Impairment of goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillImpairmentLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill, Impairment Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherInventoryNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Inventory, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherInventoryNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other inventories</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherInventoryNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Inventories not expected to be consumed within the next twelve months</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalents [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Consideration Transferred</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Business acquisition, purchase price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Preliminary purchase consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Business acquisition, Total consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityPreferredCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Redeemable Noncontrolling Interest, Equity, Preferred, Carrying Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityPreferredCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Adjusted initial carrying value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Preferred Stock, Value, Issued, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Preferred Stock, Value, Issued, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Preferred Stock, Value, Issued, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Value, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, $0.0001 par value: 100,000 shares authorized as of March 31, 2026; No shares issued and outstanding as of March 31, 2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionEquityInterestIssuedOrIssuableValueAssigned_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair value of the equity consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionEquityInterestIssuedOrIssuableValueAssigned_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Consideration Transferred, Equity Interest, Share Issued, Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Finite-Lived</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Acquired intangible assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Intangible assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Maturity Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Debt instrument, maturity date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ScheduleOfPurchaseConsiderationTransferredTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Fair Value of Total Purchase Consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ScheduleOfPurchaseConsiderationTransferredTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Purchase Consideration Transferred [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ScheduleOfPurchaseConsiderationTransferredTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule of purchase consideration transferred.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AbramsBackstopAgreementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Abrams Backstop Agreements [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AbramsBackstopAgreementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Abrams backstop agreements.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Minimum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Minimum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average grant date fair value, granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period, Weighted Average Grant Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current assets:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassBUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class B Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassBUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Class b units member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassBUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class B Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Warrant or Right, Number of Securities Called by Each Warrant or Right</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of each subscription rights to purchase shares of common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AmortizationOfIntangibleAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortization expense of the finite-lived intangible assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AmortizationOfIntangibleAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amortization of Intangible Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonClassBMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class B</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonClassBMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Class B [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Level 3</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 3 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromLongTermLinesOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Borrowings under credit facility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromLongTermLinesOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Long-Term Lines of Credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired, Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PercentageOfCashCollateralizedRemainByBuyer_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of cash collateralized remain by buyer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PercentageOfCashCollateralizedRemainByBuyer_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage Of Cash Collateralized Remain By Buyer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PercentageOfCashCollateralizedRemainByBuyer_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage of cash collateralized remain by buyer.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_OperatingLeaseExpiringYear_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Operating Lease Expiring Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_OperatingLeaseExpiringYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating lease expiring year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseDecreaseInOtherInventories_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other inventories</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseDecreaseInOtherInventories_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase Decrease In Other Inventories</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseDecreaseInOtherInventories_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Increase decrease in other inventories.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseDecreaseInOtherInventories_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other inventories</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transactions [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityInterestIssuedOrIssuableByTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Consideration Transferred, Equity Interest, Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NetLossesWouldBePercentageAttributedToClassOfMembersAtHighLevelHoldingsInNetLossPosition_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Losses would be Percentage Attributed to Class of Members At High Level Holdings in Net Loss Position</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NetLossesWouldBePercentageAttributedToClassOfMembersAtHighLevelHoldingsInNetLossPosition_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Net losses would be percentage attributed to class of members at high level holdings in net loss position.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NetLossesWouldBePercentageAttributedToClassOfMembersAtHighLevelHoldingsInNetLossPosition_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net losses would be percentage attributed to class of members at high level holdings in net loss position</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares, Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning Balance, Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending Balance, Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LineOfCreditFacilityAdditionalBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate commitments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LineOfCreditFacilityAdditionalBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line Of Credit Facility Additional Borrowing Capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LineOfCreditFacilityAdditionalBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Line of credit facility, additional borrowing capacity.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Receivable, after Allowance for Credit Loss, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts receivable, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Accounts, Notes, Loans and Financing Receivable [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Accounts Receivable, Net of Allowance for Excepted Credit Losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Liabilities [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitments and contingencies (Note 13)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeLeasesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Leases [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeLeasesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending balance of weighted average grant date fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning balance of weighted average grant date fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average grant date fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareholdersEquityAndShareBasedPaymentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity Award Activity and Stock-Based Compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareholdersEquityAndShareBasedPaymentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shareholders' Equity and Share-Based Payments [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProvisionForDoubtfulAccounts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Receivable, Credit Loss Expense (Reversal)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProvisionForDoubtfulAccounts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Add: bad debt expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">General and Administrative</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">General and Administrative Expense [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">General and Administrative Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Present value of lease payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ConversionOfRedeemableNoncontrollingInterestToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Conversion of Redeemable Noncontrolling Interest to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ConversionOfRedeemableNoncontrollingInterestToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Conversion of redeemable noncontrolling interest to noncontrolling interest.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ConversionOfRedeemableNoncontrollingInterestToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Conversion of redeemable noncontrolling interest to noncontrolling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ConversionOfRedeemableNoncontrollingInterestToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Conversion of redeemable noncontrolling interest to noncontrolling interest (Note 14)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockPercentageOfOwnershipAfterTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of stock, percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revolving credit facility, variable interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Basis Spread on Variable Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Basis spread on variable rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableGrossCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Receivable, before Allowance for Credit Loss, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableGrossCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskByBenchmarkAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Benchmark [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_KClassPUnitAwardMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">600K Class P Unit Award [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_KClassPUnitAwardMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">600K class P unit award.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_KClassPUnitAwardMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">600K Class P Unit Award</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TotalMembersEquityAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Total Members Equity And Stockholders' Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TotalMembersEquityAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Total Members equity and stockholders' equity.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TotalMembersEquityAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total members' equity and stockholders' equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Maturity, Year Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">2027</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2028</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EstimatedNetAmortizationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Estimated Net Amortization Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EstimatedNetAmortizationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Estimated net amortization expense.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EstimatedNetAmortizationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated net amortization expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current portion of finance lease liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Weighted Average Discount Rate, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Foreign currency effects on cash, cash equivalents and restricted cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign currency effects on cash, cash equivalents and restricted cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effect of Exchange Rate on Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SubscriptionNoteReceivableMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subscription Note Receivable [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SubscriptionNoteReceivableMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Subscription Note Receivable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SubscriptionNoteReceivableMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subscription Note Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCollateralForBorrowedSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Collateral for Borrowed Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCollateralForBorrowedSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash collateral received</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired, Cash and Cash Equivalent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Operating Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationOperatingExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Add: Transaction costs paid by buyer on behalf of the Company at closing</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EstimatedTransactionCostsIncurredInExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Estimated Transaction Costs Incurred in Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EstimatedTransactionCostsIncurredInExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Estimated transaction costs incurred in expenses.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EstimatedTransactionCostsIncurredInExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated transaction costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongtermDebtTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term Debt, Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongtermDebtTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostApproachValuationTechniqueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Valuation, Cost Approach [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostApproachValuationTechniqueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cost Approach</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted Average Number of Shares Outstanding, Basic, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average shares used in computing net income per share attributable to common stockholders, basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LiborMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">LIBOR.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LiborMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">LIBOR [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LiborMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">LIBOR</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_StatementScenarioAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Scenario [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsVestedInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-Average Exercise Price, Vested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsVestedInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangements By Share Based Payment Award Options Vested In Period Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsVestedInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share-based compensation arrangements by share-based payment award, options, vested in period, weighted average exercise price.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentInformationLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Information [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentInformationLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Information [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortized Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Amortized Cost, Fiscal Year Maturity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Share Based Compensation Arrangements By Share Based Payment Award [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Lived Tangible Asset [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetRetirementObligationLiabilitiesIncurred_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Liabilities incurred</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetRetirementObligationLiabilitiesIncurred_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Retirement Obligation, Liabilities Incurred</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total maturities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related Party Transaction (Predecessor)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transactions Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Cash_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Cash_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Business cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">APIC, Share-based Payment Arrangement, Increase for Cost Recognition, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableRateDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Variable Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableRateDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Variable Rate [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BaseSalary_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Base Salary</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BaseSalary_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Base salary.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BaseSalary_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Base salary</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total stockholders' equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, par value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Stockholders' Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestByLegalEntityTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Redeemable Noncontrolling Interest [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheTwoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Tranche Two [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheTwoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Vesting Upon Later of Three Year Anniversary</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheTwoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Investor Return Equal To or Greater Than 2.5</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfSalesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cost of Goods and Service [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfSalesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cost of Sales</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionNameOfAcquiredEntity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Name of acquiree</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Asset, Expected Amortization, Remainder of Fiscal Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated net amortization expense, remainder of 2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ValuationTechniqueDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Valuation Approach and Technique [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UseOfEstimates_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Use of Estimates</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UseOfEstimates_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Use of Estimates, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfNonvestedShareActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Nonvested Share Activity [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfNonvestedShareActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Changes in Non-vested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property, plant and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired, Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Business Combination, Recognized Asset Acquired, Property, Plant, and Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncomeLossAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) Attributable to Redeemable Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncomeLossAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Income (Loss) Attributable to Redeemable Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncomeLossAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net (income) attributable to redeemable non-controlling interest (Note 7)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncomeLossAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Net (income) attributable to redeemable non-controlling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncomeLossAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Net (loss) attributable to noncontrolling interest (Note 14)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncomeLossAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net (loss) attributable to noncontrolling interest (Note 14)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingAndMarketingExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Selling and Marketing Expense [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingAndMarketingExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Selling expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingAndMarketingExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Selling Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Financial Instruments and Fair Value Measurement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Disclosures [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Future Maturities of Finance Lease Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, to be Paid, Maturity [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Service-BasedVestingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Service-Based Vesting</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Service-BasedVestingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Service-Based Vesting [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Service-BasedVestingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Service-based vesting.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="country_US_lbl" xlink:role="http://www.xbrl.org/2003/role/label">UNITED STATES</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="country_US_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Domestic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseInOperatingLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase in Operating Loss Carryforwards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseInOperatingLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Increase in operating loss carryforwards.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_IncreaseInOperatingLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Increase in operating loss carryforwards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncontrollingInterestMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncontrolling Interest [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncontrollingInterestMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Noncontrolling parent interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ScheduleOfConsiderationTransferredTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Consideration Transferred [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ScheduleOfConsiderationTransferredTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule of consideration transferred.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ScheduleOfConsiderationTransferredTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Fair Value of Total Consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityIncorporationDateOfIncorporation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity incorporation, date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityIncorporationDateOfIncorporation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Incorporation, Date of Incorporation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Accrued Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Accrued Liabilities [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RetainedEarningsAccumulatedDeficitMemberEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings Accumulated Deficit Member Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RetainedEarningsAccumulatedDeficitMemberEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Retained earnings accumulated deficit member equity.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RetainedEarningsAccumulatedDeficitMemberEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Retained earnings</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncashInvestingAndFinancingItemsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncash Investing and Financing Items [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncashInvestingAndFinancingItemsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Supplemental noncash investing and financing activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Maturity, Year Four</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">2029</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2030</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionEffectiveDateOfAcquisition1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective date of acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, CODM, Individual Title and Position or Group Name [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PercentageOfAcquiringBeneficialOwnership_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage of acquiring Beneficial ownership.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PercentageOfAcquiringBeneficialOwnership_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage of acquiring Beneficial ownership.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PercentageOfAcquiringBeneficialOwnership_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of acquiring beneficial ownership</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_UnreturnedCapitalOfClassAUnitholdersBeforeDistributions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unreturned Capital of Class A Unitholders Before Distributions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_UnreturnedCapitalOfClassAUnitholdersBeforeDistributions_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Unreturned capital of Class A unitholders before distributions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_UnreturnedCapitalOfClassAUnitholdersBeforeDistributions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unreturned capital of Class A unitholders before distributions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ProceedsFromIssuanceOfSubsidiaryMembershipUnitsPriorToConversion_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance of Subsidiary Membership Units Prior to Conversion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ProceedsFromIssuanceOfSubsidiaryMembershipUnitsPriorToConversion_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Proceeds from issuance of subsidiary membership units prior to conversion.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ProceedsFromIssuanceOfSubsidiaryMembershipUnitsPriorToConversion_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from issuance of subsidiary membership units, prior to conversion (Note 14)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingOtherItemAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, Other Segment Item, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingOtherItemAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other segment items</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetRetirementObligationDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset Retirement Obligations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetRetirementObligationDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Retirement Obligation Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Expense, Operating and Nonoperating</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Interest Expense, Operating and Nonoperating, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReceivablesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Receivable [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReceivablesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subscription Note Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity, Including Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Temporary Equity, Carrying Amount, Including Portion Attributable to Noncontrolling Interests, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Initial Carrying Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Balance, beginning of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Balance, end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityCarryingAmountIncludingPortionAttributableToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Redemption value of redeemable preferred stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ReferenceRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Reference Rate.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ReferenceRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Reference Rate [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ReferenceRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reference Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Credit Facility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Facility [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityMethodInvestmentOwnershipPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Method Investment, Ownership Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityMethodInvestmentOwnershipPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of ownership interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, to be Paid, Year One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2027</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingRights_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Rights</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingRights_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Incentive units vesting rights, description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term debt, net of current maturities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Liability Assumed, Long-Term Debt, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Warrant or Right, Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate number of rights to purchase</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassAConvertiblePreferredUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class A Convertible Preferred Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassAConvertiblePreferredUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Class A convertible preferred units.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassAConvertiblePreferredUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class A Convertible Preferred Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Fiscal Year Maturity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SettlementLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Settlement Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SettlementLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Agreement to settle liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related and Nonrelated Parties [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property, Plant and Equipment, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LimitedPartnersCapitalAccountUnitsIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Limited Partners' Capital Account, Units Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LimitedPartnersCapitalAccountUnitsIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Members' units issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountingStandardsUpdateExtensibleList_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounting Standards Update [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NumberOfPreferredUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Preferred Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NumberOfPreferredUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of preferred units.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NumberOfPreferredUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of preferred units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, City or Town</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, City or Town</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationContingentConsiderationLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Contingent costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationContingentConsiderationLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Contingent Consideration, Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationContingentConsiderationLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Business Combination, Contingent Consideration, Liability, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongtermPurchaseCommitmentPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchase commitment, period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongtermPurchaseCommitmentPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Purchase Commitment, Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of reportable segment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Reportable Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MemberUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Member Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MemberUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Member Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AttributedToClassAMembersMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Attributed to Class A Members [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AttributedToClassAMembersMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Attributed to Class A Members.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_UnpaidManagementFees_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unpaid Management Fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_UnpaidManagementFees_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Unpaid management fees.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_UnpaidManagementFees_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unpaid management fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_SecurityExchangeName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Security Exchange Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_SecurityExchangeName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Security Exchange Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Credit Facility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Facility [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentVariableInterestRateTypeExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Variable Interest Rate, Type [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FinanceLeaseLiabilityPaymentsDueAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease Liability Payments Due After Year Four</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FinanceLeaseLiabilityPaymentsDueAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Finance lease, liability, to be paid, after year four.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FinanceLeaseLiabilityPaymentsDueAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Thereafter</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionDateOfAcquisitionAgreement1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Acquisition agreement date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RevenueStream1AOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue stream 1A One [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RevenueStream1AOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Revenue stream 1A One.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RevenueStream1AOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenue stream 1A</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Long-term Debt, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Property, Plant and Equipment, Gross, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Property, Plant and Equipment, Gross, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Property, Plant and Equipment, Gross, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property, plant and equipment, gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityBankruptcyProceedingsReportingCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Bankruptcy Proceedings, Reporting Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityBankruptcyProceedingsReportingCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Bankruptcy Proceedings, Reporting Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PaymentsForBusinessCombinationCashConsideration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments for Business Combination Cash Consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PaymentsForBusinessCombinationCashConsideration_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Payments for business combination cash consideration.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PaymentsForBusinessCombinationCashConsideration_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_CounterpartyNameAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Counterparty Name [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">(Loss) income before benefit from income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Outstanding, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Vest upon the performance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TermLoanFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Term Loan Facility [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TermLoanFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Term loan facility.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TermLoanFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Term Loan Facility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Antidilutive Securities, Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities, Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InventoryNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Inventory, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InventoryNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Inventories</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InventoryNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BusinessCombinationRepaymentOfAcqurieeDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Repayment of US Salt debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BusinessCombinationRepaymentOfAcqurieeDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Repayment of Acquriee Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BusinessCombinationRepaymentOfAcqurieeDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business combination repayment of acquriee debt.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total cash, cash equivalents and restricted cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Cash and cash equivalents at beginning of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Cash and cash equivalents at end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Paid, Excluding Capitalized Interest, Operating Activity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash paid for interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statistical Measurement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Warrant or Right, Exercise Price of Warrants or Rights</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exercise price of rights per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share based compensation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Period End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Period End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_TitleOfIndividualAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title and Position [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Hierarchy and NAV</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityCommitmentFeePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitment fee percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityCommitmentFeePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Commitment Fee Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnSaleOfPropertyPlantEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) on Disposition of Property Plant Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnSaleOfPropertyPlantEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Gain (Loss) on Disposition of Property Plant Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnSaleOfPropertyPlantEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Losses recognized from disposal</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Long Term Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DefinedContributionPlanEmployersMatchingContributionAnnualVestingPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Defined Contribution Plan, Employers Matching Contribution, Annual Vesting Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DefinedContributionPlanEmployersMatchingContributionAnnualVestingPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Annual vesting percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfFinancialPositionAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Financial Position [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedStockUnitsRSUMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Unvested Restricted Stock Units Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedStockUnitsRSUMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Restricted Stock Units ("RSUs")</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedStockUnitsRSUMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restricted Stock Units (RSUs) [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueRecognitionPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenue Recognition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueRecognitionPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ExcessCashFlow_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Excess cash flow</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ExcessCashFlow_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Excess Cash Flow</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ExcessCashFlow_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Excess Cash Flow</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AggregateEnterpriseValueOfAcquisitionOfBusinessesOrAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Aggregate Enterprise Value of Acquisition of Businesses or Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AggregateEnterpriseValueOfAcquisitionOfBusinessesOrAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Aggregate Enterprise Value of Acquisition of Businesses or Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AggregateEnterpriseValueOfAcquisitionOfBusinessesOrAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate enterprise value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Antidilutive Securities Excluded From Computation Of Earnings Per Share [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VestingAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Vesting [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other comprehensive loss:</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementClassOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class of Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementClassOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ProfessionalServicesAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Professional Services Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ProfessionalServicesAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Professional Services Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ProfessionalServicesAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Professional Services agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PermitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Permits [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PermitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Permits.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PermitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Permits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Limited Partners' Capital Account, Units Outstanding</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CashPaidForAmountsIncludedInMeasurementOfLeaseLiabilitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cash paid for amounts included in measurement of lease liabilities..</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CashPaidForAmountsIncludedInMeasurementOfLeaseLiabilitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Paid For Amounts Included In Measurement Of Lease Liabilities [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CashPaidForAmountsIncludedInMeasurementOfLeaseLiabilitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash paid for amounts included in the measurement of lease liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, to be Paid, Fiscal Year Maturity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfChangeInAssetRetirementObligationTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Change in Asset Retirement Obligation [Table Text Block]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinessesNetOfCashDivested_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from Asset Sale, net of cash disposed</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinessesNetOfCashDivested_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Divestiture of Businesses, Net of Cash Divested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinessesNetOfCashDivested_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Proceeds from Divestiture of Businesses, Net of Cash Divested, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinessesNetOfCashDivested_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Cash disposed on Asset Sale, net of proceeds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Cash and Cash Equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PercentageOfNoncontrollingParentInterestRepresentedAggregator_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Noncontrolling parent interest represented aggregator</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PercentageOfNoncontrollingParentInterestRepresentedAggregator_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage of Noncontrolling Parent Interest Represented Aggregator</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PercentageOfNoncontrollingParentInterestRepresentedAggregator_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage of noncontrolling parent interest represented aggregator</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RevenueStream1BOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenue stream 1B</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RevenueStream1BOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue stream 1B One [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RevenueStream1BOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Revenue stream 1B One.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetRetirementObligationsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Retirement Obligations, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetRetirementObligationsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Asset Retirement Obligations, Noncurrent, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetRetirementObligationsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset retirement obligations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Requisite Service Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Incentive units vested requisite service period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LossContingencyEstimateOfPossibleLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loss Contingency, Estimate of Possible Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LossContingencyEstimateOfPossibleLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated potential loss from legal contingencies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2028</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Groups, Including Discontinued Operations [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableRateAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Variable Rate [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableRateAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Variable Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Indefinite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Assets, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Finite-Lived Intangible Assets, Gross, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Gross Carrying Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnDerivativesAndMarketableSecuritiesArisingDuringPeriodNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income Unrealized Holding Gain Loss On Derivatives And Marketable Securities Arising During Period Net Of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnDerivativesAndMarketableSecuritiesArisingDuringPeriodNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Other comprehensive income unrealized holding gain loss on derivatives and marketable securities arising during period net of tax.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnDerivativesAndMarketableSecuritiesArisingDuringPeriodNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrealized holding losses on derivatives and marketable securities, net of tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ProceedsFromIssuanceOfSubsidiaryMembershipUnitsFromBackstoppedRightsOffering_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance of Subsidiary Membership Units from Backstopped Rights Offering</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ProceedsFromIssuanceOfSubsidiaryMembershipUnitsFromBackstoppedRightsOffering_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Proceeds from issuance of subsidiary membership units from backstopped rights offering.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ProceedsFromIssuanceOfSubsidiaryMembershipUnitsFromBackstoppedRightsOffering_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from issuance of subsidiary membership units from the backstopped rights offering</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted Average Number of Shares Outstanding, Diluted, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average shares used in computing net income per share attributable to common stockholders, diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassAUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class A units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassAUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Class a units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassAUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class A Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFileNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity File Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFileNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Securities Act File Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LineOfCreditFacilityReducedPrincipalAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reduced revolving credit facility aggregate principal amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LineOfCreditFacilityReducedPrincipalAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Reduced Principal Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LineOfCreditFacilityReducedPrincipalAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Line of credit facility, reduced principal amount.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CoverAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cover [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Expense and Other Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Number of Restricted Stock Units, Forfeited or cancelled</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Forfeited in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Number of units, forfeited</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SalesRevenueNetMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SalesRevenueNetMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue Benchmark</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SalesRevenueNetMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net Sales</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ScenarioUnspecifiedDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Scenario [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_USTreasurySecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">US Treasury Securities [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_USTreasurySecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">U.S. Treasury Bills</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PaymentOfTaxesRelatedToRSUSettlement_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Payment of taxes related to RSU settlement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PaymentOfTaxesRelatedToRSUSettlement_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payment Of Taxes Related To R S U Settlement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PaymentOfTaxesRelatedToRSUSettlement_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Payment of taxes related to RSU settlement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Operating Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of operating segment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment Information</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">General and Administrative Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">General and administrative</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">General and Administrative Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Administrative expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EquityAndNon-ControllingInterestTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity and Non-Controlling Interest [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EquityAndNon-ControllingInterestTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Equity and Non-Controlling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EquityAndNon-ControllingInterestTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity and NonControlling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NoncontrollingInterestPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncontrolling Interest [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NoncontrollingInterestPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Noncontrolling interest.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NoncontrollingInterestPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesAcquisitions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, Acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesAcquisitions_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Aggregate proceeds shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesAcquisitions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock - US Salt Acquisition, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pro forma net (income) loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Pro Forma Information, Pro Forma Income (Loss), after Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Shares Issued in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares awarded as compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PurchaseCommitmentRemainingMinimumAmountCommitted_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchase obligations, remaining commitment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PurchaseCommitmentRemainingMinimumAmountCommitted_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Purchase Commitment, Remaining Minimum Amount Committed</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Liability Assumed, Accounts Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Pro Forma Information [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Assets, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Finite-Lived Intangible Assets, Net, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Finite-Lived Intangible Assets, Net, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated net amortization expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Estimated Asset Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ValueOfAdditionalUnitsIssuableForFutureInvestment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Value Of Additional Units Issuable For Future Investment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ValueOfAdditionalUnitsIssuableForFutureInvestment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Value of additional units issuable for future investment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ValueOfAdditionalUnitsIssuableForFutureInvestment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Value of additional units issuable for future investment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsDiscountForLackOfMarketability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Fair Value Assumptions Discount For Lack Of Marketability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsDiscountForLackOfMarketability_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangement by share based payment award fair value assumptions discount for lack of marketability.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsDiscountForLackOfMarketability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Discount for lack of marketability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TemporaryEquityAccruedDistributionsAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity Accrued Distributions Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TemporaryEquityAccruedDistributionsAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Temporary equity accrued distributions amount.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TemporaryEquityAccruedDistributionsAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued distributions amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TemporaryEquityAccruedDistributionsAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Accrued Distributions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLife_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Useful lives of assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLife_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Useful Life</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLife_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Property, Plant and Equipment, Estimated Useful life</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Recently Adopted Accounting Pronouncements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Future Maturities of Operating Lease Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Maturity [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Antidilutive Securities Excluded From Computation Of Earnings Per Share [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_UnionEmployeesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Union Employees [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_UnionEmployeesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Union employees.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_UnionEmployeesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Union Employees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Recognized Identifiable Assets Acquired and Liabilities Assumed Current Liabilities Accrued Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business combination recognized identifiable assets acquired and liabilities assumed current liabilities accrued liabilities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_OwnershipAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Ownership [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Sharebasedcompensationarrangementbysharebasedpaymentawardoptionsgrantdatefairvalue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantDateFairValue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Sharebasedcompensationarrangementbysharebasedpaymentawardoptionsgrantdatefairvalue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangement by share based payment award options grant date fair value.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Sharebasedcompensationarrangementbysharebasedpaymentawardoptionsgrantdatefairvalue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Options, Grant date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NonUnionEmployeesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-Union Employees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NonUnionEmployeesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Non Union Employees [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NonUnionEmployeesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Non union employees.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Depreciation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Depreciation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Depreciation, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Depreciation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance of Long-Term Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Proceeds from Issuance of Long-Term Debt, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net borrowing proceeds from initial term loans</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Proceeds from issuance of long-term debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrecognized tax benefits, interest and penalties</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrecognized Tax Benefits, Income Tax Penalties and Interest Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Unrecognized Tax Benefits, Income Tax Penalties and Interest Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending balance, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning balance, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares, Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current portion of operating lease liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Depreciation, Depletion and Amortization, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation, Depletion and Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Depreciation, depletion, and amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentTransitionReport_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Transition Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentTransitionReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Transition Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total operating expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Liabilities, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipmentNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and equipment, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationPropertyPlantAndEquipmentNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Property, Plant and Equipment, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RedeemableNoncontrollingInterestPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Redeemable Noncontrolling Interest [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RedeemableNoncontrollingInterestPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Redeemable noncontrolling interest.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RedeemableNoncontrollingInterestPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redeemable Non-Controlling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cost of Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Cost of sales</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total net sales</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sales</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PackagingAndSupplies_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Packaging And Supplies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PackagingAndSupplies_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Packaging and supplies.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PackagingAndSupplies_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Packaging and supplies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_NoTradingSymbolFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">No Trading Symbol Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income (Loss), Net of Tax, Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total comprehensive loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfCashFlowsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Cash Flows [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NewYorkFederalReserveBankRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">NYFRB</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NewYorkFederalReserveBankRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">New York Federal Reserve Bank Rate [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NewYorkFederalReserveBankRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">New York Federal Reserve Bank Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, New Issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchase price of shares sold</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Businesses, Net of Cash Acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Payments to Acquire Businesses, Net of Cash Acquired, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Acquisition of US Salt, net of cash acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Acquisition of US Salt, net of cash acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Assets [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net Income Per Share (Successor) and Per Unit (Predecessor)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operations and Disposal Groups [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermPurchaseCommitmentAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchase commitment amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermPurchaseCommitmentAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Purchase Commitment, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InventoryWriteDown_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Inventory Write-down</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InventoryWriteDown_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Inventory obsolescence</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInInventories_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Inventories</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInInventories_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Increase (Decrease) in Inventories, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInInventories_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Inventory</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInInventories_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Inventory</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeAmountsAttributableToNoncontrollingInterestDisclosuresAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Amounts Attributable to Noncontrolling Interest, Disclosures [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DavidSugarmanEmploymentAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sugarman Employment Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DavidSugarmanEmploymentAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">David Sugarman Employment Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DavidSugarmanEmploymentAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">David Sugarman Employment Agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AccruedDividendsAndAccretionToAdjustRedemptionValueOfSubsidiarysPreferredUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Dividends and Accretion to Adjust Redemption Value of Subsidiary's Preferred Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AccruedDividendsAndAccretionToAdjustRedemptionValueOfSubsidiarysPreferredUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accrued dividends and accretion to adjust redemption value of subsidiary's preferred units.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AccruedDividendsAndAccretionToAdjustRedemptionValueOfSubsidiarysPreferredUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued distributions and accretion to adjust redemption value of subsidiary's preferred units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AccruedDividendsAndAccretionToAdjustRedemptionValueOfSubsidiarysPreferredUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Accrued distributions and accretion to adjust redemption value of subsidiary's Preferred Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BusinessAcquisitionsProFormaNetIncomeAttributableToNon-ControllingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Acquisitions Pro Forma Net Income attributable to Non-Controlling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BusinessAcquisitionsProFormaNetIncomeAttributableToNon-ControllingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business acquisitions pro forma net income attributable to non-controlling interest.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BusinessAcquisitionsProFormaNetIncomeAttributableToNon-ControllingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pro forma net (income) attributable to controlling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PartnersCapitalAccountDistributions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Members' distributions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PartnersCapitalAccountDistributions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Partners' Capital Account, Distributions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PartnersCapitalAccountDistributions_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Partners' Capital Account, Distributions, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PartnersCapitalAccountDistributions_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Members' distributions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockConvertibleSharesIssuable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Convertible, Shares Issuable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockConvertibleSharesIssuable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred shares issuable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationShareBasedArrangementsLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Compensation Share-Based Arrangements, Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationShareBasedArrangementsLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Compensation expense to be recognized related to vesting of award</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from (Payment for) Other Financing Activity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Intangibles, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Assets, Net (Excluding Goodwill)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Intangible Assets, Net (Excluding Goodwill), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Roll Forward of Allowance for Expected Credit Losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Receivable, Allowance for Credit Loss [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassBMemberUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class B Member Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassBMemberUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class B Member Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassBMemberUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Class B Member Units.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PurchaseObligation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchase obligation for asset sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PurchaseObligation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Purchase Obligation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PurchaseObligation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Purchase Obligation, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeasePayments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating cash flows from operating leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeasePayments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeasePayments_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Cash paid for operating leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinesses_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net proceeds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinesses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Divestiture of Businesses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromDivestitureOfBusinesses_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from Asset Sale, net of cash disposed</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetRetirementObligationRevisionOfEstimate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Retirement Obligation, Revision of Estimate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetRetirementObligationRevisionOfEstimate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Changes in estimated obligations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SeniorSecuredDebtMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Senior Secured Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SeniorSecuredDebtMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Senior Secured Debt [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SeniorSecuredDebtMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Senior secured debt.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Risk free interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Risk Free Interest Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Risk-free interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConstructionInProgressMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Construction in Progress [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConstructionInProgressMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Construction in Process</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Increase (Decrease) in Prepaid Expense and Other Assets, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Prepaid Expense and Other Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Paid off the credit agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Repayments of Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtByMaturityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Fiscal Year Maturity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromRightsConcentrationRiskMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue from Rights Concentration Risk</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Fiscal Year Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Year Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ScheduleOfDepreciationAndDepletionExpenseIncludedInStatementsOfOperationsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Depreciation And Depletion Expense Included In Statements Of Operations [table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ScheduleOfDepreciationAndDepletionExpenseIncludedInStatementsOfOperationsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule of depreciation and depletion expense included in statements of operations.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ScheduleOfDepreciationAndDepletionExpenseIncludedInStatementsOfOperationsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Depreciation and Depletion Expense Included in Statements of Operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentMeasurementInput_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Measurement Input</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TemporaryEquityIssuanceOfSubsidiaryToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity Issuance of Subsidiary to Noncontrolling Interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TemporaryEquityIssuanceOfSubsidiaryToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Temporary equity issuance of subsidiary to noncontrolling interests.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TemporaryEquityIssuanceOfSubsidiaryToNoncontrollingInterests_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Adjusted issuance of subsidiary's Preferred Units to redeemable non-controlling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskBenchmarkDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk Benchmark [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_MembersEquitySubscriptionNoteReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Members' Equity Subscription Note Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_MembersEquitySubscriptionNoteReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Members' equity subscription note receivable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_MembersEquitySubscriptionNoteReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subscription note receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EmploymentAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employment Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EmploymentAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Employment agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EmploymentAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Employment Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash flows from investing activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SaleOfStockConsiderationReceivableOnTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock Consideration Receivable on Transaction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SaleOfStockConsiderationReceivableOnTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Sale of stock consideration receivable on transaction.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SaleOfStockConsiderationReceivableOnTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate purchase price receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CompensationAndRetirementDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retirement Benefits [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accounts Payable, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LeasesOperatingAndFinanceLeasesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Leases Operating and Finance Leases [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LeasesOperatingAndFinanceLeasesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Leases Operating and Finance Leases.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LeasesOperatingAndFinanceLeasesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireeFairValue1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Achieved in Stages, Preacquisition Equity Interest in Acquiree, Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireeFairValue1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Business combination fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityPreferredFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Redeemable Noncontrolling Interest, Equity, Preferred, Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RedeemableNoncontrollingInterestEquityPreferredFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Mezzanine equity and initially recognized at fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Thereafter</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long Term Debt Maturities Repayments Of Principal After Year Four</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Long term debt maturities repayments of principal after year four.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Product Development</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Research and Development Expense [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationExcludedCashAtClosing_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation Excluded Cash At Closing</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationExcludedCashAtClosing_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disposal group, including discontinued operation excluded cash at closing.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationExcludedCashAtClosing_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Excluded cash at closing</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DisposalGroupIncludingDiscontinuedOperationExcludedCashAtClosing_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: Excluded cash at closing</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SummaryOfNoncontrollingInterestComponentOfTheCompanysCondensedConsolidatedStatementsOfOperationsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Summary of Noncontrolling Interest Component of the Company's Condensed Consolidated Statements of Operations [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SummaryOfNoncontrollingInterestComponentOfTheCompanysCondensedConsolidatedStatementsOfOperationsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Summary of Noncontrolling Interest Component of the Company's Condensed Consolidated Statements of Operations [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnSaleOfBusiness_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Gain on Asset Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnSaleOfBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Gain on Asset Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnSaleOfBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Gain on asset sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnSaleOfBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Gain on Asset Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnSaleOfBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) on Disposition of Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestDecreaseFromRedemptions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncontrolling Interest, Decrease from Redemptions or Purchase of Interests</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestDecreaseFromRedemptions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reduced cost of issuing value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PartnersCapitalAccountUnitsUnitbasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Partners' Capital Account, Unit-Based Payment Arrangement, Number of Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PartnersCapitalAccountUnitsUnitbasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unit-based compensation expense, Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated net amortization expense, 2027</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Asset, Expected Amortization, Year One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BusinessCombinationPaymentOfOutstandingDebtAndRelatedFeesAndBalances_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Payment of Outstanding Debt and Related Fees and Balances</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BusinessCombinationPaymentOfOutstandingDebtAndRelatedFeesAndBalances_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business combination payment of outstanding debt and related fees and balances.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BusinessCombinationPaymentOfOutstandingDebtAndRelatedFeesAndBalances_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Payment of outstanding debt and related fees and balances</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RevenueStream1AMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue stream 1A [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RevenueStream1AMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Revenue stream 1A.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_RevenueStream1AMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenue stream 1A</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Disclosures [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies Disclosure [Abstract]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueAcquisitions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock - US Salt Acquisition, Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TransactionExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Transaction Expenses [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TransactionExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Transaction expenses.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TransactionExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Transaction expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BCPSpecialOpportunitiesFundIIIOriginationsLPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">BCP Special Opportunities Fund III Originations LP [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BCPSpecialOpportunitiesFundIIIOriginationsLPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">BCP Special Opportunities Fund III Originations LP</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BCPSpecialOpportunitiesFundIIIOriginationsLPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">BCP Special Opportunities Fund III Originations LP</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BCPSpecialOpportunitiesFundIIIOriginationsLPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">BCP</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_NorthAmericaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">North America</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_NorthAmericaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">North America [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2027</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfIndefiniteLivedIntangibleAssetsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Asset, Indefinite-Lived [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MembersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total Members Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MembersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Members' Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockConsiderationReceivedOnTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate purchase price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockConsiderationReceivedOnTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock, Consideration Received on Transaction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockConsiderationReceivedOnTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Aggregate purchase amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss attributable to common stockholders</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net income attributable to common stockholders</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired to Liability Assumed, Excess (Less)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net assets acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities held-for-sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Income (Loss) Attributable to Redeemable Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net Income (Loss) Attributable to Redeemable Noncontrolling Interest, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net (income) attributable to redeemable non-controlling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net income attributable to redeemable non-controlling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLossAttributableToRedeemableNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Net (income) attributable to redeemable non-controlling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Line of Credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Long-Term Line of Credit, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Outstanding borrowings</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionProFormaInformationTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Pro Forma Information [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionProFormaInformationTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Unaudited Pro Forma Information</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Share-based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrecognized compensation expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDeferredTaxLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Liability Assumed, Deferred Tax Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedDeferredTaxLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred tax liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskPercentage1_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Concentration risk percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskPercentage1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskPercentage1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage of net sales</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionEquityInterestIssuedOrIssuableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Consideration Transferred, Equity Interest [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionEquityInterestIssuedOrIssuableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Fair Value of Equity Consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Weighted Average Remaining Lease Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance leases</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Performance-BasedClassPUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Performance-Based Class P Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Performance-BasedClassPUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Performance-based Class P Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_Performance-BasedClassPUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Performance-based Class P Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LesseeOperatingAndFinanceLeaseLiabilityMaturityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee Operating and Finance Lease Liability Maturity [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LesseeOperatingAndFinanceLeaseLiabilityMaturityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lessee operating and finance lease liability maturity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LesseeOperatingAndFinanceLeaseLiabilityMaturityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Future Maturities of Lease Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-Average Exercise Price, Forfeited or cancelled</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Forfeitures in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average grant date fair value, forfeited</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Forfeitures, Weighted Average Grant Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_WellCappingAccrualCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Well Capping Accrual Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_WellCappingAccrualCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Well capping accrual current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_WellCappingAccrualCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Well capping accrual</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MoneyMarketFundsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Money Market Funds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MoneyMarketFundsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Money Market Funds [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related and Nonrelated Parties [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Accrued Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Remainder of Fiscal Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentInformationTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Information [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentInformationTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Information [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NumberOfMajorCustomer_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Major Customer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NumberOfMajorCustomer_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of major customer.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NumberOfMajorCustomer_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of major customer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Right-of-Use Asset, after Accumulated Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Finance Lease, Right-of-Use Asset, after Accumulated Amortization, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance lease right-of-use assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Selling expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Selling Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Changes in operating assets and liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Increase (Decrease) in Operating Capital [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionSharePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Price Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionSharePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares issued at per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionSharePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Price per share issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Property, Plant and Equipment, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Weighted-Average Exercise Price, Beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Weighted-Average Exercise Price, Ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average grant date fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Recurring and Nonrecurring [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Business Combinations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Unrecognized Tax Benefits, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Unrecognized Tax Benefits, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrecognized Tax Benefits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrecognized tax benefits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional Paid-in Capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid-in Capital [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueIssuedForServices_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, Issued for Services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueIssuedForServices_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock - Rights Offering, Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_WeightedAverageDiscountRateAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Discount Rate [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_WeightedAverageDiscountRateAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Weighted Average Discount Rate.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_WeightedAverageDiscountRateAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average discount rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementFrequencyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Measurement Frequency</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementFrequencyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Measurement Frequency [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementLocationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Statement Location</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementLocationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Income Location, Balance [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FundsToTheSellersRepresentativeAdjustedFromEscrowAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Funds to the Sellers Representative Adjusted from Escrow Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FundsToTheSellersRepresentativeAdjustedFromEscrowAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Funds to the sellers representative adjusted from escrow amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_FundsToTheSellersRepresentativeAdjustedFromEscrowAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Funds to the sellers representative adjusted from escrow amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_TradingSymbol_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trading Symbol</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_TradingSymbol_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Trading Symbol</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Asset, Finite-Lived [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property, Plant and Equipment, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Due within one year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, Year One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PreferredStockPurchaseRightsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred Stock Purchase Rights</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PreferredStockPurchaseRightsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock Purchase Rights [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PreferredStockPurchaseRightsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Preferred stock purchase rights.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationPrepaidAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupIncludingDiscontinuedOperationPrepaidAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Prepaid and Other Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued payroll, bonus, and employee benefits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee-related Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Employee-related Liabilities, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TaxDistributions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tax Distributions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TaxDistributions_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tax distributions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TaxDistributions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tax distributions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash flows from financing activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitment fee percentage on unused portion of aggregate commitments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Unused Capacity, Commitment Fee Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Commitment fee percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Expected term (in years)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Expected time to a liquidity event</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsRecurringMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Recurring</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsRecurringMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Recurring [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PurchaseObligationPayableTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchase obligations, payable period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PurchaseObligationPayableTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Purchase Obligation Payable Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PurchaseObligationPayableTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Purchase obligation payable term.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total future undiscounted lease payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Imputed interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Imputed interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingAndMarketingExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Selling and Marketing Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingAndMarketingExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Selling and Marketing Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingAndMarketingExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Selling expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Components [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityComponentDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity Component</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityComponentDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Component [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Activity Under Equity Plans and Related Information</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Activity [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByAssetClassAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset Class</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByAssetClassAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Class [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassAMemberUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class A Member Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassAMemberUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Class A Member Units.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ClassAMemberUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class A Member Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill and Intangible Assets Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Asset Acquired and Liability Assumed [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Preliminary Acquisition Date Fair Value of Tangible and Intangible Assets Acquired, Net of Liabilities Assumed</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DebtIssuanceCostsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Issuance Costs [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DebtIssuanceCostsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt issuance costs.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DebtIssuanceCostsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt Issuance Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EligibleLong-TermIncentiveProgramVestingPerformancePeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Eligible Long-term Incentive Program Vesting Performance Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EligibleLong-TermIncentiveProgramVestingPerformancePeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Eligible long-term incentive program vesting performance period.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EligibleLong-TermIncentiveProgramVestingPerformancePeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Eligible long-term incentive program vesting performance period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidInsurance_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid insurance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidInsurance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Insurance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MachineryAndEquipmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Machinery and Equipment [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MachineryAndEquipmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Machinery and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MajorCustomersAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Customer [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation, Depletion and Amortization, Nonproduction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Depreciation, Depletion and Amortization, Nonproduction, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Depreciation, amortization and depletion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Comprehensive Income [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_USSaltParentHoldingsLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">US Salt Parent Holdings LLC [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_USSaltParentHoldingsLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">US Salt Parent Holdings LLC.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_USSaltParentHoldingsLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">US Salt Parent Holdings LLC</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EmeraldLakeCapitalLPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Emerald Lake Capital LP</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EmeraldLakeCapitalLPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Emerald Lake Capital LP [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EmeraldLakeCapitalLPMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Emerald Lake Capital LP.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationAmountOfContinuingCashFlowsAfterDisposal_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Repayment to Qoo10</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationAmountOfContinuingCashFlowsAfterDisposal_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operation, Amount of Continuing Cash Flows after Disposal</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Maximum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statistical Measurement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-Average Exercise Price, Exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Exercises in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Assets, Accumulated Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Accumulated Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EmeraldLakeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Emerald Lake</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EmeraldLakeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Emerald Lake [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EmeraldLakeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Emerald Lake.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Common Stock, Value, Issued, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Common Stock, Value, Issued, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Common Stock, Value, Issued, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Value, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, $0.0001 par value: 3,000,000 shares authorized as of March 31, 2026; 45,731 shares issued and outstanding as of March 31, 2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeasePrincipalPayments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Principal Payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeasePrincipalPayments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Financing cash flows from finance lease</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AresCapitalCreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Ares Capital Credit Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AresCapitalCreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Ares Capital Credit Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AresCapitalCreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Ares Capital Credit Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TemporaryEquityAnnualPercentageOfDistributionAccruedOnConsummationOfAcquisition_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity Annual Percentage of Distribution Accrued on Consummation of Acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TemporaryEquityAnnualPercentageOfDistributionAccruedOnConsummationOfAcquisition_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Temporary equity annual percentage of distribution accrued on consummation of acquisition.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TemporaryEquityAnnualPercentageOfDistributionAccruedOnConsummationOfAcquisition_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Annual percentage of distribution accrued on consummation of acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AccruedLegalSettlementsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Legal Settlements, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AccruedLegalSettlementsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accrued legal settlements, current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AccruedLegalSettlementsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Legal settlement accrual</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Equity, Including Portion Attributable to Noncontrolling Interest, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NonCashConversionOfRedeemableNoncontrollingInterestToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Non Cash Conversion of Redeemable Noncontrolling Interest to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NonCashConversionOfRedeemableNoncontrollingInterestToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Non cash conversion of redeemable noncontrolling interest to noncontrolling interest.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NonCashConversionOfRedeemableNoncontrollingInterestToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Conversion of redeemable noncontrolling interest to noncontrolling interest (Note 14)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AmortizationOfFinancingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortization of debt issuance cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AmortizationOfFinancingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amortization of Debt Issuance Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_InitialGrantMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Initial Grant [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_InitialGrantMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Initial grant member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_InitialGrantMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Initial Grant</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TransactionGrantMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Transaction Grant [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TransactionGrantMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Transaction grant member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_TransactionGrantMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Transaction Grant</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Volatility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Volatility Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Expected volatility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued term loan interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income (Loss), Net of Tax, Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Comprehensive Income (Loss), Net of Tax, Attributable to Noncontrolling Interest, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: comprehensive (income) attributable to redeemable non-controlling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Assets by Major Class [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDebtTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Schedule of Long-term Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDebtTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Debt [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity, Accretion to Redemption Value, Adjustment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Accreted redemption value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accretion to adjust redemption value of subsidiary's Preferred Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Less: adjustments attributable to redeemable non-controlling interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Adjustments attributable to redeemable non-controlling interest (Note 7)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SuretyBondsOutstandingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Surety bonds outstanding amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SuretyBondsOutstandingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Surety Bonds Outstanding Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SuretyBondsOutstandingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Surety bonds outstanding amount.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue from Contract with Customer [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentPeriodicPaymentPrincipal_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Periodic Payment, Principal</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentPeriodicPaymentPrincipal_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Quarterly principal payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CustomerConcentrationRiskMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Customer Concentration Risk [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CustomerConcentrationRiskMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Customer Concentration Risk</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DeferredTaxesArisingFromChangesInOwnership_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Taxes Arising from Changes in Ownership</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DeferredTaxesArisingFromChangesInOwnership_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Deferred taxes arising from changes in ownership.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_DeferredTaxesArisingFromChangesInOwnership_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred taxes arising from changes in ownership</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_GrossProceedsFormAdditionalPreferredUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gross Proceeds Form Additional Preferred Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_GrossProceedsFormAdditionalPreferredUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Gross proceeds form additional preferred units.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_GrossProceedsFormAdditionalPreferredUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Gross proceeds form preferred units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Asset, Expected Amortization, Year Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated net amortization expense, 2028</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedAmortizationOfDebtIssuanceCostsLineOfCreditArrangements_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Amortization of debt issuance cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedAmortizationOfDebtIssuanceCostsLineOfCreditArrangements_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Amortization of Debt Issuance Costs, Line of Credit Arrangements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Additional Paid in Capital, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Additional Paid in Capital, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Additional Paid in Capital, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional paid-in capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid in Capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">SOFR</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationsHeldforsaleMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Assets Held for Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DiscontinuedOperationsHeldforsaleMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Discontinued Operations, Held-for-Sale [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Asset, Expected Amortization, Year Three</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated net amortization expense, 2029</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income Tax Expense (Benefit), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Benefit from income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Benefit from income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Benefit from income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Benefit for income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EmployeeTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_EmployeeTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Employee type.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_StockIssuedDuringPeriodSharesStockOptionsRepurchased_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of Options , Repurchased</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_StockIssuedDuringPeriodSharesStockOptionsRepurchased_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period Shares Stock Options Repurchased</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_StockIssuedDuringPeriodSharesStockOptionsRepurchased_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Stock issued during period shares stock options repurchased.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByMeasurementFrequencyAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Measurement Frequency</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByMeasurementFrequencyAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Measurement Frequency [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance of Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from issuance of common stock from the backstopped rights offering</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Gross proceeds from common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share Based Compensation Arrangement By Share Based Payment Award [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsRepurchasedInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-Average Exercise Price, Repurchased</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsRepurchasedInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangements By Share Based Payment Award Options Repurchased In Period Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsRepurchasedInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangements by share based payment award options repurchased in period weighted average exercise price.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsidiary, Ownership Percentage, Noncontrolling Owner</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Percentage of noncontrolling parent interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Common Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Common Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskCreditRisk_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk, Credit Risk, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskCreditRisk_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Concentration of Credit and Customer Risk</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CompensationRelatedCostsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Compensation Related Costs, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CompensationRelatedCostsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unit-based Compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisposalGroupClassificationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group Classification [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RegistrationPaymentArrangementByArrangementAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Registration Payment Arrangement by Arrangement [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Receivable, Allowance for Credit Loss, Writeoff</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less: write-offs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Payments to Acquire Property, Plant, and Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Capital expenditures - purchases of property, plant and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Purchases of property, plant and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Capital expenditures - purchases of property, plant and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Capital expenditures - purchases of property, plant and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Number of Restricted Stock Units, Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of units, granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityByClassOfStockTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity, by Class of Stock [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableNetCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Receivable, after Allowance for Credit Loss, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InventoryPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Inventory, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InventoryPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Inventories and Other Inventories</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Statement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseInterestPaymentOnLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating cash flows from finance lease (interest payments)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseInterestPaymentOnLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Interest Payment on Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_OneMajorCustomerMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">One Major Customer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_OneMajorCustomerMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">One Major Customer [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_OneMajorCustomerMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">One Major Customer.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsAndNontradeReceivableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts and Nontrade Receivable [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsAndNontradeReceivableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred income tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Income Tax Expense (Benefit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Deferred Income Tax Expense (Benefit), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ContractWithCustomerSalesChannelDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Contract with Customer, Sales Channel [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionProFormaInformationNonrecurringAdjustmentsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Pro Forma Information [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares issued and sold</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock, Number of Shares Issued in Transaction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Sale of stock, number of shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, New Issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock - Rights Offering, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_OtherComprehensiveIncomeLossForeignExchangeRelatedAdjustmentIncludedInAssetSale_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Foreign-Exchange Related Adjustment Included in Asset Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_OtherComprehensiveIncomeLossForeignExchangeRelatedAdjustmentIncludedInAssetSale_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Other comprehensive income (loss),foreign-exchange related adjustment included in asset sale.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_OtherComprehensiveIncomeLossForeignExchangeRelatedAdjustmentIncludedInAssetSale_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Foreign exchange-related adjustment included in Asset Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Vested in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Number of units, vested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Number of Restricted Stock Units, Vested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_USSaltParentHoldingsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">USPH</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_USSaltParentHoldingsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">US Salt Parent Holdings [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_USSaltParentHoldingsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">US Salt Parent Holdings.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_USSaltParentHoldingsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">US Salt Parent Holdings</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Limited Liability Company (LLC) Members' Equity, Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Limited Liability Company (LLC) Members' Equity, Including Portion Attributable to Noncontrolling Interest, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Members' Equity, Ending Balances</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Members Equity, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LeasesRemainingLeaseTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Leases remaining lease term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LeasesRemainingLeaseTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Leases Remaining Lease Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LeasesRemainingLeaseTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Leases remaining lease term.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Recognized Liability Assumed, Long-Term Debt, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current maturities of long-term debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Earnings Per Share, Diluted, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss per share attributable to common stockholders, diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net income per share attributable to common stockholders, diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Operating Financial Results</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Segment Reporting Information, by Segment [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ExpenseRecognizedForTheTime-VestingIncentiveUnitsOverTheRequisiteServicePeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Expense recognized for the time-vesting incentive units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ExpenseRecognizedForTheTime-VestingIncentiveUnitsOverTheRequisiteServicePeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Expense Recognized for the Time-vesting Incentive Units Over the Requisite Service Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ExpenseRecognizedForTheTime-VestingIncentiveUnitsOverTheRequisiteServicePeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Expense recognized for the time-vesting incentive units over the requisite service period.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_TitleOfIndividualWithRelationshipToEntityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title and Position [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NumberOfPutativeClassActionLawsuits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of putative class action lawsuits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NumberOfPutativeClassActionLawsuits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number Of Putative Class Action Lawsuits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NumberOfPutativeClassActionLawsuits_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of putative class action lawsuits,</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total assets held-for-sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disposal Group, Including Discontinued Operation, Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CityAreaCode_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">City Area Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CityAreaCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">City Area Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionsProFormaRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pro forma net sales</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionsProFormaRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Pro Forma Information, Pro Forma Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfCapitalDistribution_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments of Capital Distribution</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfCapitalDistribution_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Member's distributions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfCapitalDistribution_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Member's distributions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long- term portion of finance lease liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Long-term portion of lease payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CumulativeFairValueOfGrant_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cumulative Fair Value Of Grant</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CumulativeFairValueOfGrant_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cumulative fair value of grant.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CumulativeFairValueOfGrant_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cumulative fair value of grant</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Face Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Term Loan Facility, principal</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument, aggregate principal amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntangibleAssetsFiniteLivedPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Assets, Finite-Lived, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntangibleAssetsFiniteLivedPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finite-lived Intangible Assets and Long-lived Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Senior secured revolving credit facility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Line of credit facility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NoncontrollingParentInterestPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncontrolling Parent Interest [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NoncontrollingParentInterestPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Noncontrolling parent interest.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_NoncontrollingParentInterestPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Noncontrolling Parent Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RepurchaseAgreementCounterpartyNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Counterparty Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LineOfCreditFacilityStandbyLetterOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Standby letter of credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LineOfCreditFacilityStandbyLetterOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line Of Credit Facility Standby Letter Of Credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LineOfCreditFacilityStandbyLetterOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Line of credit facility, standby letter of credit.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateFloorMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Floor Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateFloorMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Floor [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Variable Lease, Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Variable lease expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Weighted Average Remaining Lease Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingInformationLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting Information [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total lease expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease, Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of Restricted Stock Units, Exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Equity Instruments Other Than Options Exercisable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share based compensation arrangement by share based payment award equity instruments other than options exercisable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_WeightedAverageRemainingLeaseTermAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Remaining Lease Term [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_WeightedAverageRemainingLeaseTermAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Weighted Average Remaining Lease Term.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_WeightedAverageRemainingLeaseTermAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average remaining lease term (in years)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Consideration Transferred, Equity Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Business acquisition, equity rollover condiseration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Fair value of the equity consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property, plant and equipment, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Right-of-Use Asset Obtained in Exchange for Finance Lease Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill and Intangible Assets, Goodwill, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOfIntangibleAssetsFinitelived_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Impairment of Intangible Assets, Finite-Lived</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOfIntangibleAssetsFinitelived_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Impairment of finite-lived intangibles</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Income (Loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">(Loss) income from operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated Deficit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalents [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Share-based Payment Arrangement, Noncash Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Noncash Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Unit/Stock-based compensation</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_PropertyPlantAndEquipmentInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Property, plant and equipment in accounts payable.</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_BalanceSheetComponentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Balance sheet components.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ManagementFeePayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Miminum management fee payable in cash in quarterly installments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ManagementFeePayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Management Fee Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardAdditionalVestingRightsPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of additional vesting of award</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardAdditionalVestingRightsPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sharebased Compensation Arrangement By Sharebased Payment Award Award Additional Vesting Rights Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardAdditionalVestingRightsPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Sharebased Compensation Arrangement By Sharebased Payment Award Award Additional Vesting Rights Percentage</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ContractWithCustomerSalesChannelAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Contract with Customer, Sales Channel [Axis]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash flows from operating activities:</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConvertiblePreferredStockSharesIssuedUponConversion_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Convertable preferred unit</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_AnnualManagementFeeMinimumAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Annual management fee minimum amount.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LossContingencyAccrualCarryingValueCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loss Contingency, Accrual, Current</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_LesseeOperatingLeaseLiabilityPaymentsAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Thereafter</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_LocalPhoneNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Local Phone Number</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Agreement [Member]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="logc_CreditAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Credit Agreement</link:label>
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          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_LongTermDebtNoncurrent" xlink:to="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet" order="1" weight="-1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_LongTermDebtNoncurrent" xlink:to="us-gaap_LongTermDebtCurrent" order="2" weight="1" use="optional"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtNoncurrent" xlink:label="us-gaap_LongTermDebtNoncurrent"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentCarryingAmount" xlink:label="us-gaap_DebtInstrumentCarryingAmount"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtCurrent" xlink:label="us-gaap_LongTermDebtCurrent"/>
        </link:calculationLink>
        <link:calculationLink xlink:type="extended" xlink:role="http://ir.contextlogic.com/20260331/taxonomy/role/DisclosureSegmentInformationScheduleOfOperatingFinancialResultsDetails">
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" order="0" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_CostOfRevenue" order="1" weight="-1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_DepreciationAndAmortization" order="2" weight="-1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_SellingExpense" order="3" weight="-1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_AdministrativeFeesExpense" order="5" weight="-1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="logc_TransactionExpense" order="6" weight="-1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_InterestExpense" order="7" weight="-1" use="optional"/>
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          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_IncomeTaxExpenseBenefit" order="9" weight="-1" use="optional"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLoss" xlink:label="us-gaap_NetIncomeLoss"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CostOfRevenue" xlink:label="us-gaap_CostOfRevenue"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DepreciationAndAmortization" xlink:label="us-gaap_DepreciationAndAmortization"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SellingExpense" xlink:label="us-gaap_SellingExpense"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdministrativeFeesExpense" xlink:label="us-gaap_AdministrativeFeesExpense"/>
          <link:loc xlink:type="locator" xlink:href="logc-20260331.xsd#logc_TransactionExpense" xlink:label="logc_TransactionExpense"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpense" xlink:label="us-gaap_InterestExpense"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingOtherItemAmount" xlink:label="us-gaap_SegmentReportingOtherItemAmount"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxExpenseBenefit" xlink:label="us-gaap_IncomeTaxExpenseBenefit"/>
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      </link:linkbase>
    </xsd:appinfo>
  </xsd:annotation>
  <xsd:element id="logc_RetainedEarningsAccumulatedDeficitMemberEquity" name="RetainedEarningsAccumulatedDeficitMemberEquity" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_SummaryOfNoncontrollingInterestComponentOfTheCompanysCondensedConsolidatedStatementsOfOperationsTableTextBlock" name="SummaryOfNoncontrollingInterestComponentOfTheCompanysCondensedConsolidatedStatementsOfOperationsTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_BalanceSheetComponentsTextBlock" name="BalanceSheetComponentsTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_ClassAUnitsMember" name="ClassAUnitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_LeasesOperatingAndFinanceLeasesTextBlock" name="LeasesOperatingAndFinanceLeasesTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccruedLiabilities" name="BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccruedLiabilities" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_RightsOfferingMember" name="RightsOfferingMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_TemporaryEquityIssuanceOfSubsidiaryToNoncontrollingInterests" name="TemporaryEquityIssuanceOfSubsidiaryToNoncontrollingInterests" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_AbramsCapitalPartnersILPMember" name="AbramsCapitalPartnersILPMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_CreditAgreementMember" name="CreditAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_TermLoanMember" name="TermLoanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsVestedInPeriodWeightedAverageExercisePrice" name="ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsVestedInPeriodWeightedAverageExercisePrice" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_IssuanceOfNoncontrollingInterestUSSaltAcquisition" name="IssuanceOfNoncontrollingInterestUSSaltAcquisition" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_ExcessCashFlow" name="ExcessCashFlow" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_SeniorSecuredDebtMember" name="SeniorSecuredDebtMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_NumberOfPreferredUnits" name="NumberOfPreferredUnits" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="logc_PackagedMember" name="PackagedMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_NewYorkFederalReserveBankRateMember" name="NewYorkFederalReserveBankRateMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_RevenueStream1AMember" name="RevenueStream1AMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_WeightedAverageDiscountRateAbstract" name="WeightedAverageDiscountRateAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_LossContingencyNumberOfCasesDismissedByPlaintiff" name="LossContingencyNumberOfCasesDismissedByPlaintiff" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_USSaltHoldingsLLCMember" name="USSaltHoldingsLLCMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardAdditionalVestingRightsPercentage" name="SharebasedCompensationArrangementBySharebasedPaymentAwardAwardAdditionalVestingRightsPercentage" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_DisposalGroupIncludingDiscontinuedOperationMerchantsPayable" name="DisposalGroupIncludingDiscontinuedOperationMerchantsPayable" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_PercentageOfAcquiringBeneficialOwnership" name="PercentageOfAcquiringBeneficialOwnership" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="logc_PaymentOfTaxesRelatedToRSUSettlement" name="PaymentOfTaxesRelatedToRSUSettlement" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_AdditionalUnitsIssuableForFutureInvestment" name="AdditionalUnitsIssuableForFutureInvestment" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_BusinessCombinationPaymentOfUnitBasedCompensation" name="BusinessCombinationPaymentOfUnitBasedCompensation" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_BusinessAcquisitionsProFormaNetLossAttributableToNon-ControllingInterest" name="BusinessAcquisitionsProFormaNetLossAttributableToNon-ControllingInterest" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_LineOfCreditFacilityStandbyLetterOfCredit" name="LineOfCreditFacilityStandbyLetterOfCredit" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_NetLossesWouldBePercentageAttributedToClassOfMembersAtHighLevelHoldingsInNetLossPosition" name="NetLossesWouldBePercentageAttributedToClassOfMembersAtHighLevelHoldingsInNetLossPosition" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_TaxReturnOpenForExamination" name="TaxReturnOpenForExamination" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_PercentageOfQuarterlyManagementFee" name="PercentageOfQuarterlyManagementFee" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsRepurchasedInPeriodWeightedAverageExercisePrice" name="ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsRepurchasedInPeriodWeightedAverageExercisePrice" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_CreditAgreementExcessCashFlowPercentageDescription" name="CreditAgreementExcessCashFlowPercentageDescription" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_DisposalGroupIncludingDiscontinuedOperationRightOfUseAssets" name="DisposalGroupIncludingDiscontinuedOperationRightOfUseAssets" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_EmployeeTypeDomain" name="EmployeeTypeDomain" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_TimeVestingIncentiveUnitsMember" name="TimeVestingIncentiveUnitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_LiborMember" name="LiborMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_IncreaseDecreaseInOtherInventories" name="IncreaseDecreaseInOtherInventories" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_ProceedsFromIssuanceOfSubsidiaryMembershipUnitsFromBackstoppedRightsOffering" name="ProceedsFromIssuanceOfSubsidiaryMembershipUnitsFromBackstoppedRightsOffering" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_ClassAMemberUnitsMember" name="ClassAMemberUnitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_SellersRepresentativeExpenseFund" name="SellersRepresentativeExpenseFund" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_SaltReservesMember" name="SaltReservesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_ClassPUnitsMember" name="ClassPUnitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_EmeraldLakeCapitalLPMember" name="EmeraldLakeCapitalLPMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisable" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsExercisable" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="logc_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentPortionOfLeaseLiability" name="BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentPortionOfLeaseLiability" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_ScheduleOfLeaseTermAndDiscountRateInformationRelatedToLeaseTableTextBlock" name="ScheduleOfLeaseTermAndDiscountRateInformationRelatedToLeaseTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_ClassBMemberUnitsMember" name="ClassBMemberUnitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_DisposalGroupIncludingDiscontinuedOperationNetAssetsSoldPursuantToTheAssetSale" name="DisposalGroupIncludingDiscontinuedOperationNetAssetsSoldPursuantToTheAssetSale" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_ExpenseRecognizedForTheTime-VestingIncentiveUnitsOverTheRequisiteServicePeriod" name="ExpenseRecognizedForTheTime-VestingIncentiveUnitsOverTheRequisiteServicePeriod" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_GrossProceedsFormAdditionalPreferredUnits" name="GrossProceedsFormAdditionalPreferredUnits" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_LesseeOperatingLeaseLiabilityPaymentsAfterYearFour" name="LesseeOperatingLeaseLiabilityPaymentsAfterYearFour" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_EstimatedUsefulLivesOfPropertyPlantAndEquipmentTableTextBlock" name="EstimatedUsefulLivesOfPropertyPlantAndEquipmentTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_TransactionGrantMember" name="TransactionGrantMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_NonUnionEmployeesMember" name="NonUnionEmployeesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_ScheduleOfLongTermAndDiscountRateInformationRelatedToLeasesTableTextBlock" name="ScheduleOfLongTermAndDiscountRateInformationRelatedToLeasesTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_SubscriptionPrice" name="SubscriptionPrice" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_NonPackagedMember" name="NonPackagedMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_TermLoanFacilityMember" name="TermLoanFacilityMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_RevenueStream1AOneMember" name="RevenueStream1AOneMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_Sharebasedcompensationarrangementbysharebasedpaymentawardoptionsgrantdatefairvalue" name="Sharebasedcompensationarrangementbysharebasedpaymentawardoptionsgrantdatefairvalue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsEquityValue" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsEquityValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_TemporaryEquityAnnualPercentageOfDistributionAccruedOnConsummationOfAcquisition" name="TemporaryEquityAnnualPercentageOfDistributionAccruedOnConsummationOfAcquisition" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_DisposalGroupIncludingDiscontinuedOperationCashAdjustmentPursuantToTheAssetSale" name="DisposalGroupIncludingDiscontinuedOperationCashAdjustmentPursuantToTheAssetSale" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_IssuanceOfSubsidiaryMembershipUnitsRightsOfferingBackstop" name="IssuanceOfSubsidiaryMembershipUnitsRightsOfferingBackstop" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_DemandRegistrationMember" name="DemandRegistrationMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_ScheduleOfPrepaidExpensesAndOtherAssetsCurrentTableTextBlock" name="ScheduleOfPrepaidExpensesAndOtherAssetsCurrentTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_NumberOfMajorCustomer" name="NumberOfMajorCustomer" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_NoncontrollingParentInterestPolicyTextBlock" name="NoncontrollingParentInterestPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_AttributedToClassAMembersMember" name="AttributedToClassAMembersMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_NonCashConversionOfRedeemableNoncontrollingInterestToNoncontrollingInterest" name="NonCashConversionOfRedeemableNoncontrollingInterestToNoncontrollingInterest" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_OperatingLeaseExpiringYear" name="OperatingLeaseExpiringYear" type="xbrli:gYearItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="logc_StockIssuedDuringPeriodSharesStockOptionsRepurchased" name="StockIssuedDuringPeriodSharesStockOptionsRepurchased" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_BusinessAcquisitionsProFormaNetIncomeAttributableToNon-ControllingInterest" name="BusinessAcquisitionsProFormaNetIncomeAttributableToNon-ControllingInterest" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_RightOfUseAssetsObtainedInExchangeForLeaseLiabilitiesAbstract" name="RightOfUseAssetsObtainedInExchangeForLeaseLiabilitiesAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_CollectionOfSubscriptionNoteReceivable" name="CollectionOfSubscriptionNoteReceivable" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_PercentageOfAnnualManagementFee" name="PercentageOfAnnualManagementFee" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_ScheduleOfConsiderationTransferredTableTextBlock" name="ScheduleOfConsiderationTransferredTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_SupplementalCashFlowInformationRelatedToLeasesTableTextBlock" name="SupplementalCashFlowInformationRelatedToLeasesTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsDiscountForLackOfMarketability" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsDiscountForLackOfMarketability" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_TemporaryEquityAnnualPercentageOfDistributionAccruedUntilConsummationOfAcquisition" name="TemporaryEquityAnnualPercentageOfDistributionAccruedUntilConsummationOfAcquisition" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_EmploymentAgreementMember" name="EmploymentAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_NoncontrollingInterestPolicyTextBlock" name="NoncontrollingInterestPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_InvestmentAgreementMember" name="InvestmentAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_AbramsBackstopAgreementsMember" name="AbramsBackstopAgreementsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_CostOfRevenueMember" name="CostOfRevenueMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_AccretionOfStockIssuanceCosts" name="AccretionOfStockIssuanceCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_AnnualManagementFeeMinimumAmount" name="AnnualManagementFeeMinimumAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_ConversionOfRedeemableNoncontrollingInterestToNoncontrollingInterest" name="ConversionOfRedeemableNoncontrollingInterestToNoncontrollingInterest" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_EquityAndNon-ControllingInterestTextBlock" name="EquityAndNon-ControllingInterestTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_BaseSalary" name="BaseSalary" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_PercentageOfNoncontrollingParentInterestRepresentedAggregator" name="PercentageOfNoncontrollingParentInterestRepresentedAggregator" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="logc_RedeemableNoncontrollingInterestPolicyTextBlock" name="RedeemableNoncontrollingInterestPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_TotalMembersEquityAndStockholdersEquity" name="TotalMembersEquityAndStockholdersEquity" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_DisposalGroupIncludingDiscontinuedOperationRefundsLiability" name="DisposalGroupIncludingDiscontinuedOperationRefundsLiability" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_EquityExchangedForOwnershipInUSSalt" name="EquityExchangedForOwnershipInUSSalt" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_ReferenceRateMember" name="ReferenceRateMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_EmeraldLakeMember" name="EmeraldLakeMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_PaymentsForBusinessCombinationCashConsideration" name="PaymentsForBusinessCombinationCashConsideration" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_IncreaseInOperatingLossCarryforwards" name="IncreaseInOperatingLossCarryforwards" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_ServiceAndPerformanceBasedVestingMember" name="ServiceAndPerformanceBasedVestingMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_LesseeOperatingAndFinanceLeaseLiabilityMaturityTableTextBlock" name="LesseeOperatingAndFinanceLeaseLiabilityMaturityTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_AccountingStandardsUpdate2025-05ProspectiveMember" name="AccountingStandardsUpdate2025-05ProspectiveMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_BasisOfPresentationAndConsolidationPolicyTextBlock" name="BasisOfPresentationAndConsolidationPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_NetAssetsOfDisposalGroupIncludingDiscontinuedOperation" name="NetAssetsOfDisposalGroupIncludingDiscontinuedOperation" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_OtherComprehensiveIncomeLossForeignExchangeRelatedAdjustmentIncludedInAssetSale" name="OtherComprehensiveIncomeLossForeignExchangeRelatedAdjustmentIncludedInAssetSale" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_ProceedsFromIssuanceOfSubsidiaryMembershipUnitsPriorToConversion" name="ProceedsFromIssuanceOfSubsidiaryMembershipUnitsPriorToConversion" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_DisposalGroupIncludingDiscontinuedOperationExcludedCashAtClosing" name="DisposalGroupIncludingDiscontinuedOperationExcludedCashAtClosing" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_UnionEmployeesMember" name="UnionEmployeesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_PropertyPlantAndEquipmentInAccountsPayable" name="PropertyPlantAndEquipmentInAccountsPayable" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_RailCarRepairAccrualCurrent" name="RailCarRepairAccrualCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_CollectivelyOwnedPercentage" name="CollectivelyOwnedPercentage" type="xbrli:pureItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_ContributionsAxis" name="ContributionsAxis" type="xbrli:stringItemType" substitutionGroup="xbrldt:dimensionItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_ScheduleOfIntangibleAssetsAndRelatedAccumulatedAmortizationTableTextBlock" name="ScheduleOfIntangibleAssetsAndRelatedAccumulatedAmortizationTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_USSaltParentHoldingsLLCMember" name="USSaltParentHoldingsLLCMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_WellCappingAccrualCurrent" name="WellCappingAccrualCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_EstimatedNetAmortizationExpense" name="EstimatedNetAmortizationExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_AbramsCapitalPartnersIILPMember" name="AbramsCapitalPartnersIILPMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_NumberOfPutativeClassActionLawsuits" name="NumberOfPutativeClassActionLawsuits" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_PercentageOfAnnualDiscretionaryBonus" name="PercentageOfAnnualDiscretionaryBonus" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_PercentageOfCashCollateralizedRemainByBuyer" name="PercentageOfCashCollateralizedRemainByBuyer" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_SuretyBondsOutstandingAmount" name="SuretyBondsOutstandingAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_IncomeLossAttributableToRedeemableNoncontrollingInterest" name="IncomeLossAttributableToRedeemableNoncontrollingInterest" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_Performance-BasedClassPUnitsMember" name="Performance-BasedClassPUnitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_USSaltIntermediateHoldingsLLCMember" name="USSaltIntermediateHoldingsLLCMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_WilmingtonTrustCreditAgreementMember" name="WilmingtonTrustCreditAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_ContributionTwoMember" name="ContributionTwoMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_ScheduleOfDepreciationAndDepletionExpenseIncludedInStatementsOfOperationsTableTextBlock" name="ScheduleOfDepreciationAndDepletionExpenseIncludedInStatementsOfOperationsTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_ScheduleOfPurchaseConsiderationTransferredTableTextBlock" name="ScheduleOfPurchaseConsiderationTransferredTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_ExpectedProceedsFromRightsOfferingAndBackstopAgreements" name="ExpectedProceedsFromRightsOfferingAndBackstopAgreements" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_BusinessCombinationRepaymentOfAcqurieeDebt" name="BusinessCombinationRepaymentOfAcqurieeDebt" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_EstimatedTransactionCostsIncurredInExpenses" name="EstimatedTransactionCostsIncurredInExpenses" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_EmployeeTypeAxis" name="EmployeeTypeAxis" type="xbrli:stringItemType" substitutionGroup="xbrldt:dimensionItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_OperatingLeaseExpenseAbstract" name="OperatingLeaseExpenseAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_EligibleLong-TermIncentiveProgramVestingPerformancePeriod" name="EligibleLong-TermIncentiveProgramVestingPerformancePeriod" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_TemporaryEquityAccruedDistributionsAmount" name="TemporaryEquityAccruedDistributionsAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_RevenueStream1BMember" name="RevenueStream1BMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_ClassBUnitsMember" name="ClassBUnitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_ProfessionalServicesAgreementMember" name="ProfessionalServicesAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_TransactionExpensesMember" name="TransactionExpensesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_PercentageOfCashCollateralizedRemainByCompany" name="PercentageOfCashCollateralizedRemainByCompany" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour" name="FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnDerivativesAndMarketableSecuritiesArisingDuringPeriodNetOfTax" name="OtherComprehensiveIncomeUnrealizedHoldingGainLossOnDerivativesAndMarketableSecuritiesArisingDuringPeriodNetOfTax" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_PurchaseObligationPayableTerm" name="PurchaseObligationPayableTerm" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_UnpaidManagementFees" name="UnpaidManagementFees" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_Time-BasedClassPUnitsMember" name="Time-BasedClassPUnitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_NoncashLeaseExpense" name="NoncashLeaseExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_TransactionExpense" name="TransactionExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_ColocationAndCloudServicesArrangementMember" name="ColocationAndCloudServicesArrangementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_DavidSugarmanEmploymentAgreementMember" name="DavidSugarmanEmploymentAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRightOfUseAssets" name="BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRightOfUseAssets" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_AttributedToClassBMembersUntilAllClassBCapitalContributionErodedMember" name="AttributedToClassBMembersUntilAllClassBCapitalContributionErodedMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFour" name="LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFour" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_UnreturnedCapitalOfClassAUnitholdersBeforeDistributions" name="UnreturnedCapitalOfClassAUnitholdersBeforeDistributions" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_USPHClassBUnitsMember" name="USPHClassBUnitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_FundsToTheSellersRepresentativeAdjustedFromEscrowAmount" name="FundsToTheSellersRepresentativeAdjustedFromEscrowAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_RevenueStream1BOneMember" name="RevenueStream1BOneMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_CumulativeFairValueOfGrant" name="CumulativeFairValueOfGrant" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_MaintenanceMaterials" name="MaintenanceMaterials" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_LeasesRemainingLeaseTerm" name="LeasesRemainingLeaseTerm" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="logc_BCPBackstopAgreementMember" name="BCPBackstopAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_CommitmentsAndContingenciesDisclosureTable" name="CommitmentsAndContingenciesDisclosureTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_SaleOfStockConsiderationReceivableOnTransaction" name="SaleOfStockConsiderationReceivableOnTransaction" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_AresCapitalCreditAgreementMember" name="AresCapitalCreditAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_AccruedLegalSettlementsCurrent" name="AccruedLegalSettlementsCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_DeferredTaxesArisingFromChangesInOwnership" name="DeferredTaxesArisingFromChangesInOwnership" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_CashPaidForAmountsIncludedInMeasurementOfLeaseLiabilitiesAbstract" name="CashPaidForAmountsIncludedInMeasurementOfLeaseLiabilitiesAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_DebtIssuanceCostsPolicyTextBlock" name="DebtIssuanceCostsPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_TaxDistributions" name="TaxDistributions" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_PreferredStockPurchaseRightsMember" name="PreferredStockPurchaseRightsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_AccruedDividendsAndAccretionToAdjustRedemptionValueOfSubsidiarysPreferredUnits" name="AccruedDividendsAndAccretionToAdjustRedemptionValueOfSubsidiarysPreferredUnits" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_DisposalGroupIncludingDiscontinuedOperationFundsReceivable" name="DisposalGroupIncludingDiscontinuedOperationFundsReceivable" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_ClassAConvertiblePreferredUnitsMember" name="ClassAConvertiblePreferredUnitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_Service-BasedVestingMember" name="Service-BasedVestingMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_PaymentsForRepaymentOfPrincipalOnTermLoan" name="PaymentsForRepaymentOfPrincipalOnTermLoan" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_WeightedAverageRemainingLeaseTermAbstract" name="WeightedAverageRemainingLeaseTermAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_AccruedAndUnpaidDistributionsPerShare" name="AccruedAndUnpaidDistributionsPerShare" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_RedeemableNoncontrollingInterestDisclosureTextBlock" name="RedeemableNoncontrollingInterestDisclosureTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_Customer1Member" name="Customer1Member" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_USPHClassAUnitsMember" name="USPHClassAUnitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_LineOfCreditFacilityAdditionalBorrowingCapacity" name="LineOfCreditFacilityAdditionalBorrowingCapacity" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_MembersEquitySubscriptionNoteReceivable" name="MembersEquitySubscriptionNoteReceivable" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_EscrowAgreementMember" name="EscrowAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_BusinessCombinationPaymentOfOutstandingDebtAndRelatedFeesAndBalances" name="BusinessCombinationPaymentOfOutstandingDebtAndRelatedFeesAndBalances" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_LossContingencyNumberOfCasesCoordinatedAndConsolidated" name="LossContingencyNumberOfCasesCoordinatedAndConsolidated" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="logc_ContributionsDomain" name="ContributionsDomain" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_InitialGrantMember" name="InitialGrantMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_AggregateEnterpriseValueOfAcquisitionOfBusinessesOrAssets" name="AggregateEnterpriseValueOfAcquisitionOfBusinessesOrAssets" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_PermitsMember" name="PermitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_ValueOfAdditionalUnitsIssuableForFutureInvestment" name="ValueOfAdditionalUnitsIssuableForFutureInvestment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_PackagingAndSupplies" name="PackagingAndSupplies" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_OneMajorCustomerMember" name="OneMajorCustomerMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_KClassPUnitAwardMember" name="KClassPUnitAwardMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_USSaltParentHoldingsMember" name="USSaltParentHoldingsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_FinanceLeaseExpiringYear" name="FinanceLeaseExpiringYear" type="xbrli:gYearItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="logc_ContributionOneMember" name="ContributionOneMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_GrossProceedsFromRegistrationRightsAgreement" name="GrossProceedsFromRegistrationRightsAgreement" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="logc_FinanceLeaseLiabilityPaymentsDueAfterYearFour" name="FinanceLeaseLiabilityPaymentsDueAfterYearFour" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_LineOfCreditFacilityReducedPrincipalAmount" name="LineOfCreditFacilityReducedPrincipalAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="logc_SubscriptionReceivableMember" name="SubscriptionReceivableMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_BCPSpecialOpportunitiesFundIIIOriginationsLPMember" name="BCPSpecialOpportunitiesFundIIIOriginationsLPMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_CommitmentsAndContingenciesDisclosureLineItems" name="CommitmentsAndContingenciesDisclosureLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="logc_SubscriptionNoteReceivableMember" name="SubscriptionNoteReceivableMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
</xsd:schema>
