<?xml version="1.0" encoding="US-ASCII"?>
<!-- Generated by Broadridge Transform (tm) - http://www.broadridge.com -->
<!-- Created: Tue Jul 21 20:55:22 UTC 2026 -->
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_AssetsCurrent_lbl" xml:lang="en-US">Total Current Assets</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_AssetsNoncurrent_lbl" xml:lang="en-US">Total Non-current Assets</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_Assets_lbl" xml:lang="en-US">Total Assets</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xml:lang="en-US">Total Current liabilities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesCurrent" xlink:to="us-gaap_LiabilitiesCurrent_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Liabilities"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_Liabilities_lbl" xml:lang="en-US">Total Liabilities</label>
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    <loc xlink:type="locator" xlink:label="us-gaap_StatementClassOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementClassOfStockAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementClassOfStockAxis_lbl" xml:lang="en-US">Class of Stock [Axis]</label>
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    <loc xlink:type="locator" xlink:label="us-gaap_MembersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MembersEquity"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_MembersEquity_lbl" xml:lang="en-US">Total Members&#8217; Equity</label>
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    <loc xlink:type="locator" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xml:lang="en-US">Total Liabilities and Members&#8217; Equity</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_LiabilitiesAndStockholdersEquity_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xml:lang="en-US">Balances</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:to="us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl0" xml:lang="en-US">Balances</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:to="us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CommonUnitOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonUnitOutstanding"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_CommonUnitOutstanding_lbl" xml:lang="en-US">Balances (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonUnitOutstanding" xlink:to="us-gaap_CommonUnitOutstanding_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_CommonUnitOutstanding_lbl0" xml:lang="en-US">Balances (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonUnitOutstanding" xlink:to="us-gaap_CommonUnitOutstanding_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xml:lang="en-US">Equity Components [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementEquityComponentsAxis" xlink:to="us-gaap_StatementEquityComponentsAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xml:lang="en-US">Net Cash Provided by Operating Activities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xml:lang="en-US">Net cash Used in Investing activities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xml:lang="en-US">Net Cash Used in Financing Activities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xml:lang="en-US">Net Change in Cash and Cash Equivalents</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xml:lang="en-US">Cash and Cash Equivalents, Beginning of Year</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl0" xml:lang="en-US">Cash and Cash Equivalents, End of Year</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentByTypeAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis_lbl" xml:lang="en-US">Long-Lived Asset, Class [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:to="us-gaap_PropertyPlantAndEquipmentByTypeAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RangeAxis_lbl" xml:lang="en-US">Statistical Measurement [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_RangeAxis" xlink:to="srt_RangeAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AccountsReceivableNetCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableNetCurrent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xml:lang="en-US">Total</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableNetCurrent" xlink:to="us-gaap_AccountsReceivableNetCurrent_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl0" xml:lang="en-US">Accounts receivable, net</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableNetCurrent" xlink:to="us-gaap_AccountsReceivableNetCurrent_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InventoryNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InventoryNet"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_InventoryNet_lbl" xml:lang="en-US">Total</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryNet" xlink:to="us-gaap_InventoryNet_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InventoryNet_lbl0" xml:lang="en-US">Inventories</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryNet" xlink:to="us-gaap_InventoryNet_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PrepaidExpenseCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrepaidExpenseCurrent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_PrepaidExpenseCurrent_lbl" xml:lang="en-US">Total</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PrepaidExpenseCurrent" xlink:to="us-gaap_PrepaidExpenseCurrent_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PrepaidExpenseCurrent_lbl0" xml:lang="en-US">Prepaid expenses</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PrepaidExpenseCurrent" xlink:to="us-gaap_PrepaidExpenseCurrent_lbl0"/>
    <loc xlink:type="locator" xlink:label="logc_StatementOfIncomeLocationAxis" xlink:href="logc-20260226.xsd#logc_StatementOfIncomeLocationAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_StatementOfIncomeLocationAxis_lbl" xml:lang="en-US">Statement of Income Location Axis</label>
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    <loc xlink:type="locator" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis_lbl" xml:lang="en-US">Intangible Asset, Indefinite-Lived, Class [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis" xlink:to="us-gaap_IndefiniteLivedIntangibleAssetsByMajorClassAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AccruedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedLiabilitiesCurrent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xml:lang="en-US">Total</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccruedLiabilitiesCurrent" xlink:to="us-gaap_AccruedLiabilitiesCurrent_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl0" xml:lang="en-US">Accrued liabilities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccruedLiabilitiesCurrent" xlink:to="us-gaap_AccruedLiabilitiesCurrent_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AssetRetirementObligation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetRetirementObligation"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_AssetRetirementObligation_lbl" xml:lang="en-US">Asset retirement obligation, beginning of year</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligation" xlink:to="us-gaap_AssetRetirementObligation_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_AssetRetirementObligation_lbl0" xml:lang="en-US">Asset retirement obligation, end of year</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligation" xlink:to="us-gaap_AssetRetirementObligation_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CashAndCashEquivalentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashAndCashEquivalentsAxis_lbl" xml:lang="en-US">Cash and Cash Equivalents [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashAndCashEquivalentsAxis" xlink:to="us-gaap_CashAndCashEquivalentsAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xml:lang="en-US">Number of Units beginning</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl0" xml:lang="en-US">Number of Units ending</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xml:lang="en-US">Weighted Average Exercise Price Outstanding</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl0" xml:lang="en-US">Weighted Average Exercise Price Outstanding</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl0"/>
    <loc xlink:type="locator" xlink:label="logc_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm1" xlink:href="logc-20260226.xsd#logc_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="logc_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm1_lbl" xml:lang="en-US">Weighted Average Remaining Term Outstanding(In Years)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm1" xlink:to="logc_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm1_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="logc_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm1_lbl0" xml:lang="en-US">Weighted Average Remaining Term Outstanding(In Years)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm1" xlink:to="logc_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm1_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber_lbl" xml:lang="en-US">Number of Units Exercisable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice_lbl" xml:lang="en-US">Weighted Average Exercise Price Exercisable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_Unrecognizedcompensationexpensetotal" xlink:href="logc-20260226.xsd#logc_Unrecognizedcompensationexpensetotal"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="logc_Unrecognizedcompensationexpensetotal_lbl" xml:lang="en-US">Total</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_Unrecognizedcompensationexpensetotal" xlink:to="logc_Unrecognizedcompensationexpensetotal_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_BusinessAcquisitionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionAxis_lbl" xml:lang="en-US">Business Combination [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionAxis" xlink:to="us-gaap_BusinessAcquisitionAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharesOutstanding"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_SharesOutstanding_lbl" xml:lang="en-US">Beginning balance, Units (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharesOutstanding" xlink:to="us-gaap_SharesOutstanding_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_SharesOutstanding_lbl0" xml:lang="en-US">Ending balance, Units (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharesOutstanding" xlink:to="us-gaap_SharesOutstanding_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquity"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:label="us-gaap_StockholdersEquity_lbl" xml:lang="en-US">Beginning balance</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_StockholdersEquity_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:label="us-gaap_StockholdersEquity_lbl0" xml:lang="en-US">Ending balance</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_StockholdersEquity_lbl0"/>
    <loc xlink:type="locator" xlink:label="logc_FinanceLeaseCost" xlink:href="logc-20260226.xsd#logc_FinanceLeaseCost"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="logc_FinanceLeaseCost_lbl" xml:lang="en-US">Total finance lease cost</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_FinanceLeaseCost" xlink:to="logc_FinanceLeaseCost_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LeaseCost"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LeaseCost_lbl" xml:lang="en-US">Total lease expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LeaseCost" xlink:to="us-gaap_LeaseCost_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xml:lang="en-US">Total future undiscounted lease payments</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDue"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDue_lbl" xml:lang="en-US">Total future undiscounted lease payments</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:to="us-gaap_FinanceLeaseLiabilityPaymentsDue_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_DocumentType" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentType"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_DocumentType_lbl" xml:lang="en-US">Document Type</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentType" xlink:to="dei_DocumentType_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_DocumentPeriodEndDate" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentPeriodEndDate"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_DocumentPeriodEndDate_lbl" xml:lang="en-US">Document Period End Date</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentPeriodEndDate" xlink:to="dei_DocumentPeriodEndDate_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityRegistrantName"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityRegistrantName_lbl" xml:lang="en-US">Entity Registrant Name</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityRegistrantName" xlink:to="dei_EntityRegistrantName_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityIncorporationStateCountryCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityIncorporationStateCountryCode"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityIncorporationStateCountryCode_lbl" xml:lang="en-US">Entity Incorporation, State or Country Code</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityIncorporationStateCountryCode" xlink:to="dei_EntityIncorporationStateCountryCode_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityFileNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFileNumber"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityFileNumber_lbl" xml:lang="en-US">Entity File Number</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityFileNumber" xlink:to="dei_EntityFileNumber_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityTaxIdentificationNumber"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityTaxIdentificationNumber_lbl" xml:lang="en-US">Entity Tax Identification Number</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityTaxIdentificationNumber" xlink:to="dei_EntityTaxIdentificationNumber_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityAddressAddressLine1_lbl" xml:lang="en-US">Entity Address, Address Line One</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressAddressLine1" xlink:to="dei_EntityAddressAddressLine1_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityAddressAddressLine2" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine2"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityAddressAddressLine2_lbl" xml:lang="en-US">Entity Address, Address Line Two</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressAddressLine2" xlink:to="dei_EntityAddressAddressLine2_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressCityOrTown"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityAddressCityOrTown_lbl" xml:lang="en-US">Entity Address, City or Town</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressCityOrTown" xlink:to="dei_EntityAddressCityOrTown_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressStateOrProvince"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityAddressStateOrProvince_lbl" xml:lang="en-US">Entity Address, State or Province</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressStateOrProvince" xlink:to="dei_EntityAddressStateOrProvince_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressPostalZipCode"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityAddressPostalZipCode_lbl" xml:lang="en-US">Entity Address, Postal Zip Code</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressPostalZipCode" xlink:to="dei_EntityAddressPostalZipCode_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CityAreaCode"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_CityAreaCode_lbl" xml:lang="en-US">City Area Code</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_CityAreaCode" xlink:to="dei_CityAreaCode_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LocalPhoneNumber"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_LocalPhoneNumber_lbl" xml:lang="en-US">Local Phone Number</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_LocalPhoneNumber" xlink:to="dei_LocalPhoneNumber_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_WrittenCommunications" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_WrittenCommunications"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_WrittenCommunications_lbl" xml:lang="en-US">Written Communications</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_WrittenCommunications" xlink:to="dei_WrittenCommunications_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_SolicitingMaterial" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_SolicitingMaterial"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_SolicitingMaterial_lbl" xml:lang="en-US">Soliciting Material</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_SolicitingMaterial" xlink:to="dei_SolicitingMaterial_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_PreCommencementTenderOffer" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_PreCommencementTenderOffer"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_PreCommencementTenderOffer_lbl" xml:lang="en-US">Pre-commencement Tender Offer</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_PreCommencementTenderOffer" xlink:to="dei_PreCommencementTenderOffer_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_PreCommencementIssuerTenderOffer" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_PreCommencementIssuerTenderOffer"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_PreCommencementIssuerTenderOffer_lbl" xml:lang="en-US">Pre-commencement Issuer Tender Offer</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_PreCommencementIssuerTenderOffer" xlink:to="dei_PreCommencementIssuerTenderOffer_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_Security12bTitle"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_Security12bTitle_lbl" xml:lang="en-US">Title of 12(b) Security</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_Security12bTitle" xlink:to="dei_Security12bTitle_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_TradingSymbol"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_TradingSymbol_lbl" xml:lang="en-US">Trading Symbol</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_TradingSymbol" xlink:to="dei_TradingSymbol_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityEmergingGrowthCompany"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityEmergingGrowthCompany_lbl" xml:lang="en-US">Entity Emerging Growth Company</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityEmergingGrowthCompany" xlink:to="dei_EntityEmergingGrowthCompany_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_AmendmentDescription" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_AmendmentDescription"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_AmendmentDescription_lbl" xml:lang="en-US">Amendment Description</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_AmendmentDescription" xlink:to="dei_AmendmentDescription_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCentralIndexKey"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_EntityCentralIndexKey_lbl" xml:lang="en-US">Entity Central Index Key</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityCentralIndexKey" xlink:to="dei_EntityCentralIndexKey_lbl"/>
    <loc xlink:type="locator" xlink:label="dei_AmendmentFlag" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_AmendmentFlag"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="dei_AmendmentFlag_lbl" xml:lang="en-US">Amendment Flag</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_AmendmentFlag" xlink:to="dei_AmendmentFlag_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetsAbstract_lbl" xml:lang="en-US">ASSETS</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsAbstract" xlink:to="us-gaap_AssetsAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AssetsCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsCurrentAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xml:lang="en-US">Current Assets</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsCurrentAbstract" xlink:to="us-gaap_AssetsCurrentAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xml:lang="en-US">Cash and cash equivalents</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AssetsNoncurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsNoncurrentAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetsNoncurrentAbstract_lbl" xml:lang="en-US">Non-current Assets</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsNoncurrentAbstract" xlink:to="us-gaap_AssetsNoncurrentAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PropertyPlantAndEquipmentNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentNet"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xml:lang="en-US">Plant, property and equipment, net</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentNet" xlink:to="us-gaap_PropertyPlantAndEquipmentNet_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl0" xml:lang="en-US">Total</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentNet" xlink:to="us-gaap_PropertyPlantAndEquipmentNet_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_Goodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Goodwill"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_Goodwill_lbl" xml:lang="en-US">Goodwill</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Goodwill" xlink:to="us-gaap_Goodwill_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IntangibleAssetsNetExcludingGoodwill"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xml:lang="en-US">Intangibles, net</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:to="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xml:lang="en-US">Operating lease right-of-use assets</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseRightOfUseAsset" xlink:to="us-gaap_OperatingLeaseRightOfUseAsset_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinanceLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseRightOfUseAsset"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseRightOfUseAsset_lbl" xml:lang="en-US">Finance lease right-of-use assets</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseRightOfUseAsset" xlink:to="us-gaap_FinanceLeaseRightOfUseAsset_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherInventoryNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherInventoryNoncurrent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherInventoryNoncurrent_lbl" xml:lang="en-US">Other inventories</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherInventoryNoncurrent" xlink:to="us-gaap_OtherInventoryNoncurrent_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_LiabilitiesAndMembersEquityAbstract" xlink:href="logc-20260226.xsd#logc_LiabilitiesAndMembersEquityAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_LiabilitiesAndMembersEquityAbstract_lbl" xml:lang="en-US">LIABILITIES AND MEMBERS&#8217; EQUITY</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_LiabilitiesAndMembersEquityAbstract" xlink:to="logc_LiabilitiesAndMembersEquityAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LiabilitiesCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesCurrentAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xml:lang="en-US">Current Liabilities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesCurrentAbstract" xlink:to="us-gaap_LiabilitiesCurrentAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AccountsPayableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsPayableCurrent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xml:lang="en-US">Accounts payable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsPayableCurrent" xlink:to="us-gaap_AccountsPayableCurrent_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LongTermDebtCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtCurrent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xml:lang="en-US">Current maturities of long- term debt</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtCurrent" xlink:to="us-gaap_LongTermDebtCurrent_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_LongTermDebtCurrent_lbl0" xml:lang="en-US">Current portion</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtCurrent" xlink:to="us-gaap_LongTermDebtCurrent_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilityCurrent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xml:lang="en-US">Current portion of operating lease liability</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseLiabilityCurrent" xlink:to="us-gaap_OperatingLeaseLiabilityCurrent_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl0" xml:lang="en-US">Current portion</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseLiabilityCurrent" xlink:to="us-gaap_OperatingLeaseLiabilityCurrent_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityCurrent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent_lbl" xml:lang="en-US">Current portion of finance lease liability</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityCurrent" xlink:to="us-gaap_FinanceLeaseLiabilityCurrent_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent_lbl0" xml:lang="en-US">Current portion</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityCurrent" xlink:to="us-gaap_FinanceLeaseLiabilityCurrent_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LiabilitiesNoncurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesNoncurrentAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LiabilitiesNoncurrentAbstract_lbl" xml:lang="en-US">Non-current Liabilities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesNoncurrentAbstract" xlink:to="us-gaap_LiabilitiesNoncurrentAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LongTermDebtNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtNoncurrent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xml:lang="en-US">Long- term debt, net of current maturities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtNoncurrent" xlink:to="us-gaap_LongTermDebtNoncurrent_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl0" xml:lang="en-US">Long-term portion</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtNoncurrent" xlink:to="us-gaap_LongTermDebtNoncurrent_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilityNoncurrent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xml:lang="en-US">Long- term portion of operating lease liability</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:to="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl0" xml:lang="en-US">Long-term portion of lease payments</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:to="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityNoncurrent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl" xml:lang="en-US">Long- term portion of finance lease liability</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:to="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl0" xml:lang="en-US">Long-term portion of lease payments</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:to="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AssetRetirementObligationsNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetRetirementObligationsNoncurrent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetRetirementObligationsNoncurrent_lbl" xml:lang="en-US">Asset retirement obligations</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligationsNoncurrent" xlink:to="us-gaap_AssetRetirementObligationsNoncurrent_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_MembersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MembersEquityAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MembersEquityAbstract_lbl" xml:lang="en-US">Members&#8217; Equity</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MembersEquityAbstract" xlink:to="us-gaap_MembersEquityAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_MembersCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MembersCapital"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MembersCapital_lbl" xml:lang="en-US">Members capital</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MembersCapital" xlink:to="us-gaap_MembersCapital_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LimitedPartnersCapitalAccountUnitsIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LimitedPartnersCapitalAccountUnitsIssued"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LimitedPartnersCapitalAccountUnitsIssued_lbl" xml:lang="en-US">Members&apos; units issued (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LimitedPartnersCapitalAccountUnitsIssued" xlink:to="us-gaap_LimitedPartnersCapitalAccountUnitsIssued_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding_lbl" xml:lang="en-US">Members&apos; units outstanding (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding" xlink:to="us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_RetainedEarningsAccumulatedDeficitMemberEquity" xlink:href="logc-20260226.xsd#logc_RetainedEarningsAccumulatedDeficitMemberEquity"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_RetainedEarningsAccumulatedDeficitMemberEquity_lbl" xml:lang="en-US">Retained earnings (accumulated deficit)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RetainedEarningsAccumulatedDeficitMemberEquity" xlink:to="logc_RetainedEarningsAccumulatedDeficitMemberEquity_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_MembersEquityAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MembersEquityAttributableToNoncontrollingInterest"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MembersEquityAttributableToNoncontrollingInterest_lbl" xml:lang="en-US">Noncontrolling parent interest</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MembersEquityAttributableToNoncontrollingInterest" xlink:to="us-gaap_MembersEquityAttributableToNoncontrollingInterest_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_Revenues" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Revenues"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_Revenues_lbl" xml:lang="en-US">Revenue</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Revenues" xlink:to="us-gaap_Revenues_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CostOfRevenue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CostOfRevenue"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CostOfRevenue_lbl" xml:lang="en-US">Cost of Revenue</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CostOfRevenue" xlink:to="us-gaap_CostOfRevenue_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_CostOfRevenue_lbl0" xml:lang="en-US">Cost of revenues</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CostOfRevenue" xlink:to="us-gaap_CostOfRevenue_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_GrossProfit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GrossProfit"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_GrossProfit_lbl" xml:lang="en-US">Gross Profit</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GrossProfit" xlink:to="us-gaap_GrossProfit_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SellingGeneralAndAdministrativeExpense"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xml:lang="en-US">Selling, general and administrative expenses</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SellingGeneralAndAdministrativeExpense" xlink:to="us-gaap_SellingGeneralAndAdministrativeExpense_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OperatingIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingIncomeLoss"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xml:lang="en-US">Operating Income</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingIncomeLoss" xlink:to="us-gaap_OperatingIncomeLoss_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NonoperatingIncomeExpenseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonoperatingIncomeExpenseAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NonoperatingIncomeExpenseAbstract_lbl" xml:lang="en-US">Other Income (Expenses)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NonoperatingIncomeExpenseAbstract" xlink:to="us-gaap_NonoperatingIncomeExpenseAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ForeignCurrencyTransactionGainLossBeforeTax"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ForeignCurrencyTransactionGainLossBeforeTax_lbl" xml:lang="en-US">Foreign currency income (loss)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:to="us-gaap_ForeignCurrencyTransactionGainLossBeforeTax_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLoss"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetIncomeLoss_lbl" xml:lang="en-US">Net Income</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_NetIncomeLoss_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetIncomeLoss_lbl0" xml:lang="en-US">Net income</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_NetIncomeLoss_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_NetIncomeLoss_lbl1" xml:lang="en-US">Net income (loss)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_NetIncomeLoss_lbl1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl" xml:lang="en-US">Net income attributable to Parent Holdings Class A unitholders</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl0" xml:lang="en-US">Net income attributable to Parent Holdings Class A unitholders, basic</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xml:lang="en-US">Basic weighted average Class A units outstanding (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl0" xml:lang="en-US">Weighted average Class A units outstanding, basic</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xml:lang="en-US">diluted weighted average Class A units outstanding (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl0" xml:lang="en-US">Weighted average Class A units outstanding, diluted</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_EarningsPerShareBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareBasic"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xml:lang="en-US">Earnings per unit attributable to Class A unit, basic (in Dollars per share)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerShareBasic" xlink:to="us-gaap_EarningsPerShareBasic_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_EarningsPerShareBasic_lbl0" xml:lang="en-US">Earnings per unit attributable to Class A unitholders, basic</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerShareBasic" xlink:to="us-gaap_EarningsPerShareBasic_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_EarningsPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareDiluted"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xml:lang="en-US">Earnings per unit attributable to Class A unit, diluted (in Dollars per share)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerShareDiluted" xlink:to="us-gaap_EarningsPerShareDiluted_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_EarningsPerShareDiluted_lbl0" xml:lang="en-US">Earnings per unit attributable to Class A unitholders, diluted</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerShareDiluted" xlink:to="us-gaap_EarningsPerShareDiluted_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PartnersCapitalAccountContributions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PartnersCapitalAccountContributions"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PartnersCapitalAccountContributions_lbl" xml:lang="en-US">Members&#8217; contributions</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PartnersCapitalAccountContributions" xlink:to="us-gaap_PartnersCapitalAccountContributions_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PartnersCapitalAccountUnitsContributed" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PartnersCapitalAccountUnitsContributed"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PartnersCapitalAccountUnitsContributed_lbl" xml:lang="en-US">Members&#8217; contributions (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PartnersCapitalAccountUnitsContributed" xlink:to="us-gaap_PartnersCapitalAccountUnitsContributed_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_CollectionOfSubscriptionNoteReceivable" xlink:href="logc-20260226.xsd#logc_CollectionOfSubscriptionNoteReceivable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_CollectionOfSubscriptionNoteReceivable_lbl" xml:lang="en-US">Collection of subscription note receivable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_CollectionOfSubscriptionNoteReceivable" xlink:to="logc_CollectionOfSubscriptionNoteReceivable_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PartnersCapitalAccountUnitBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PartnersCapitalAccountUnitBasedCompensation"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PartnersCapitalAccountUnitBasedCompensation_lbl" xml:lang="en-US">Unit-based compensation expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PartnersCapitalAccountUnitBasedCompensation" xlink:to="us-gaap_PartnersCapitalAccountUnitBasedCompensation_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PartnersCapitalAccountUnitsUnitbasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PartnersCapitalAccountUnitsUnitbasedCompensation"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PartnersCapitalAccountUnitsUnitbasedCompensation_lbl" xml:lang="en-US">Unit-based compensation expense (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PartnersCapitalAccountUnitsUnitbasedCompensation" xlink:to="us-gaap_PartnersCapitalAccountUnitsUnitbasedCompensation_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_CancellationOfAmountUnitsPurchasedAndCorrespondingSubscriptionNoteReceivable" xlink:href="logc-20260226.xsd#logc_CancellationOfAmountUnitsPurchasedAndCorrespondingSubscriptionNoteReceivable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_CancellationOfAmountUnitsPurchasedAndCorrespondingSubscriptionNoteReceivable_lbl" xml:lang="en-US">Cancellation of units purchased and corresponding subscription note receivable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_CancellationOfAmountUnitsPurchasedAndCorrespondingSubscriptionNoteReceivable" xlink:to="logc_CancellationOfAmountUnitsPurchasedAndCorrespondingSubscriptionNoteReceivable_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_CancellationOfUnitsPurchasedAndCorrespondingSubscriptionNoteReceivable" xlink:href="logc-20260226.xsd#logc_CancellationOfUnitsPurchasedAndCorrespondingSubscriptionNoteReceivable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_CancellationOfUnitsPurchasedAndCorrespondingSubscriptionNoteReceivable_lbl" xml:lang="en-US">Cancellation of units purchased and corresponding subscription note receivable (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_CancellationOfUnitsPurchasedAndCorrespondingSubscriptionNoteReceivable" xlink:to="logc_CancellationOfUnitsPurchasedAndCorrespondingSubscriptionNoteReceivable_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xml:lang="en-US">Cash Flow from Operating Activities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xml:lang="en-US">Adjustments to reconcile net income to net cash from operating activities:</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DepreciationDepletionAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DepreciationDepletionAndAmortization"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xml:lang="en-US">Depreciation, depletion, and amortization</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DepreciationDepletionAndAmortization" xlink:to="us-gaap_DepreciationDepletionAndAmortization_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_LossDueToCasualty" xlink:href="logc-20260226.xsd#logc_LossDueToCasualty"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_LossDueToCasualty_lbl" xml:lang="en-US">Loss due to casualty</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_LossDueToCasualty" xlink:to="logc_LossDueToCasualty_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AmortizationOfFinancingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfFinancingCosts"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AmortizationOfFinancingCosts_lbl" xml:lang="en-US">Amortization of debt issuance cost</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AmortizationOfFinancingCosts" xlink:to="us-gaap_AmortizationOfFinancingCosts_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ProvisionForDoubtfulAccounts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProvisionForDoubtfulAccounts"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProvisionForDoubtfulAccounts_lbl" xml:lang="en-US">Bad debt expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProvisionForDoubtfulAccounts" xlink:to="us-gaap_ProvisionForDoubtfulAccounts_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensation"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensation_lbl" xml:lang="en-US">Unit-based compensation expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensation" xlink:to="us-gaap_ShareBasedCompensation_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_NoncashLeaseExpense" xlink:href="logc-20260226.xsd#logc_NoncashLeaseExpense"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_NoncashLeaseExpense_lbl" xml:lang="en-US">Non-cash lease expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_NoncashLeaseExpense" xlink:to="logc_NoncashLeaseExpense_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_lbl" xml:lang="en-US">Amortization of finance right-of-use assets</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:to="us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinanceLeaseInterestExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseInterestExpense"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseInterestExpense_lbl" xml:lang="en-US">Interest on finance leases</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseInterestExpense" xlink:to="us-gaap_FinanceLeaseInterestExpense_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_FinanceLeaseInterestExpense_lbl0" xml:lang="en-US">Interest on lease liabilities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseInterestExpense" xlink:to="us-gaap_FinanceLeaseInterestExpense_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AssetRetirementObligationAccretionExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetRetirementObligationAccretionExpense"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetRetirementObligationAccretionExpense_lbl" xml:lang="en-US">Accretion of asset retirement obligation</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligationAccretionExpense" xlink:to="us-gaap_AssetRetirementObligationAccretionExpense_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_AssetRetirementObligationAccretionExpense_lbl0" xml:lang="en-US">Accretion of expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligationAccretionExpense" xlink:to="us-gaap_AssetRetirementObligationAccretionExpense_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOperatingCapitalAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xml:lang="en-US">Changes in operating assets and liabilities:</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:to="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_IncreaseDecreaseInOtherInventoriesAmount" xlink:href="logc-20260226.xsd#logc_IncreaseDecreaseInOtherInventoriesAmount"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_IncreaseDecreaseInOtherInventoriesAmount_lbl" xml:lang="en-US">Other inventories</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_IncreaseDecreaseInOtherInventoriesAmount" xlink:to="logc_IncreaseDecreaseInOtherInventoriesAmount_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccountsPayable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable_lbl" xml:lang="en-US">Accounts payable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInAccountsPayable" xlink:to="us-gaap_IncreaseDecreaseInAccountsPayable_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOperatingLeaseLiability"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInOperatingLeaseLiability_lbl" xml:lang="en-US">Operating lease liabilities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:to="us-gaap_IncreaseDecreaseInOperatingLeaseLiability_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccruedLiabilities"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilities_lbl" xml:lang="en-US">Accrued liabilities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:to="us-gaap_IncreaseDecreaseInAccruedLiabilities_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xml:lang="en-US">Cash Flow from Investing Activities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xml:lang="en-US">Cash Flow from Financing Activities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_ProceedsFromCollectionOfSubscriptionNoteReceivable" xlink:href="logc-20260226.xsd#logc_ProceedsFromCollectionOfSubscriptionNoteReceivable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_ProceedsFromCollectionOfSubscriptionNoteReceivable_lbl" xml:lang="en-US">Proceeds from collection of subscription note receivable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ProceedsFromCollectionOfSubscriptionNoteReceivable" xlink:to="logc_ProceedsFromCollectionOfSubscriptionNoteReceivable_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SupplementalCashFlowInformationAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xml:lang="en-US">Supplemental cash flow information</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SupplementalCashFlowInformationAbstract" xlink:to="us-gaap_SupplementalCashFlowInformationAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestPaidNet"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InterestPaidNet_lbl" xml:lang="en-US">Cash paid for interest</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestPaidNet" xlink:to="us-gaap_InterestPaidNet_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoncashInvestingAndFinancingItemsAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NoncashInvestingAndFinancingItemsAbstract_lbl" xml:lang="en-US">Supplemental non-cash investing and financing information:</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:to="us-gaap_NoncashInvestingAndFinancingItemsAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_RepaymentOfSubscriptionReceivableFromProceedsOfUnitsRepurchase" xlink:href="logc-20260226.xsd#logc_RepaymentOfSubscriptionReceivableFromProceedsOfUnitsRepurchase"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_RepaymentOfSubscriptionReceivableFromProceedsOfUnitsRepurchase_lbl" xml:lang="en-US">Repayment of subscription receivable from proceeds of units repurchase</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RepaymentOfSubscriptionReceivableFromProceedsOfUnitsRepurchase" xlink:to="logc_RepaymentOfSubscriptionReceivableFromProceedsOfUnitsRepurchase_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_PropertyPlantAndEquipmentInAccountsPayable" xlink:href="logc-20260226.xsd#logc_PropertyPlantAndEquipmentInAccountsPayable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_PropertyPlantAndEquipmentInAccountsPayable_lbl" xml:lang="en-US">Property, plant and equipment in accounts payable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PropertyPlantAndEquipmentInAccountsPayable" xlink:to="logc_PropertyPlantAndEquipmentInAccountsPayable_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_AdditionsAndChangesInAssetRetirementObligations" xlink:href="logc-20260226.xsd#logc_AdditionsAndChangesInAssetRetirementObligations"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_AdditionsAndChangesInAssetRetirementObligations_lbl" xml:lang="en-US">Additions and changes in asset retirement obligations</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_AdditionsAndChangesInAssetRetirementObligations" xlink:to="logc_AdditionsAndChangesInAssetRetirementObligations_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_MembersEquitySubscriptionNoteReceivable" xlink:href="logc-20260226.xsd#logc_MembersEquitySubscriptionNoteReceivable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="logc_MembersEquitySubscriptionNoteReceivable_lbl" xml:lang="en-US">Subscription note receivable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_MembersEquitySubscriptionNoteReceivable" xlink:to="logc_MembersEquitySubscriptionNoteReceivable_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainLossOnSaleOfPropertyPlantEquipment"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_GainLossOnSaleOfPropertyPlantEquipment_lbl" xml:lang="en-US">Loss on disposal of property, plant and equipment</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:to="us-gaap_GainLossOnSaleOfPropertyPlantEquipment_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestExpenseNonoperating" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseNonoperating"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xml:lang="en-US">Interest expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestExpenseNonoperating" xlink:to="us-gaap_InterestExpenseNonoperating_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_IncomeLossAttributableToRedeemableNoncontrollingInterest" xlink:href="logc-20260226.xsd#logc_IncomeLossAttributableToRedeemableNoncontrollingInterest"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="logc_IncomeLossAttributableToRedeemableNoncontrollingInterest_lbl" xml:lang="en-US">Net income attributable to noncontrolling parent interest</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_IncomeLossAttributableToRedeemableNoncontrollingInterest" xlink:to="logc_IncomeLossAttributableToRedeemableNoncontrollingInterest_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PartnersCapitalAccountDistributions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PartnersCapitalAccountDistributions"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PartnersCapitalAccountDistributions_lbl" xml:lang="en-US">Members&#8217; distributions</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PartnersCapitalAccountDistributions" xlink:to="us-gaap_PartnersCapitalAccountDistributions_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PartnersCapitalAccountTreasuryUnitsPurchases" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PartnersCapitalAccountTreasuryUnitsPurchases"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PartnersCapitalAccountTreasuryUnitsPurchases_lbl" xml:lang="en-US">Repurchase of units</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PartnersCapitalAccountTreasuryUnitsPurchases" xlink:to="us-gaap_PartnersCapitalAccountTreasuryUnitsPurchases_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PartnersCapitalAccountUnitsTreasury" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PartnersCapitalAccountUnitsTreasury"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PartnersCapitalAccountUnitsTreasury_lbl" xml:lang="en-US">Repurchase of units (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PartnersCapitalAccountUnitsTreasury" xlink:to="us-gaap_PartnersCapitalAccountUnitsTreasury_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InsuranceRecoveries" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InsuranceRecoveries"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_InsuranceRecoveries_lbl" xml:lang="en-US">Gain from insurance recovery</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InsuranceRecoveries" xlink:to="us-gaap_InsuranceRecoveries_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_GainLossOnSaleOfBusiness" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainLossOnSaleOfBusiness"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_GainLossOnSaleOfBusiness_lbl" xml:lang="en-US">Loss on disposals</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GainLossOnSaleOfBusiness" xlink:to="us-gaap_GainLossOnSaleOfBusiness_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccountsReceivable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xml:lang="en-US">Accounts receivable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:to="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInInventories" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInInventories"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_IncreaseDecreaseInInventories_lbl" xml:lang="en-US">Inventory</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInInventories" xlink:to="us-gaap_IncreaseDecreaseInInventories_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInPrepaidExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInPrepaidExpense"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_IncreaseDecreaseInPrepaidExpense_lbl" xml:lang="en-US">Prepaid expenses</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInPrepaidExpense" xlink:to="us-gaap_IncreaseDecreaseInPrepaidExpense_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xml:lang="en-US">Purchases of plant, property, and equipment</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:to="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl0" xml:lang="en-US">Capital expenditures - purchases of plant, property and equipment</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:to="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl0"/>
    <loc xlink:type="locator" xlink:label="logc_PaymentsForRepaymentOfPrincipalOnTermLoan" xlink:href="logc-20260226.xsd#logc_PaymentsForRepaymentOfPrincipalOnTermLoan"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="logc_PaymentsForRepaymentOfPrincipalOnTermLoan_lbl" xml:lang="en-US">Repayment of principal on term loan</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PaymentsForRepaymentOfPrincipalOnTermLoan" xlink:to="logc_PaymentsForRepaymentOfPrincipalOnTermLoan_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_RepaymentOfPrincipalOfFinanceLeasesObligations" xlink:href="logc-20260226.xsd#logc_RepaymentOfPrincipalOfFinanceLeasesObligations"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="logc_RepaymentOfPrincipalOfFinanceLeasesObligations_lbl" xml:lang="en-US">Repayment of principal of finance leases obligations</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RepaymentOfPrincipalOfFinanceLeasesObligations" xlink:to="logc_RepaymentOfPrincipalOfFinanceLeasesObligations_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_PaymentsOfCapitalContributions" xlink:href="logc-20260226.xsd#logc_PaymentsOfCapitalContributions"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="logc_PaymentsOfCapitalContributions_lbl" xml:lang="en-US">Members&#8217; contributions</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PaymentsOfCapitalContributions" xlink:to="logc_PaymentsOfCapitalContributions_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PaymentsOfCapitalDistribution" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfCapitalDistribution"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsOfCapitalDistribution_lbl" xml:lang="en-US">Members&#8217; distributions</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsOfCapitalDistribution" xlink:to="us-gaap_PaymentsOfCapitalDistribution_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_DistributionToNoncontrollingParentInterest" xlink:href="logc-20260226.xsd#logc_DistributionToNoncontrollingParentInterest"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="logc_DistributionToNoncontrollingParentInterest_lbl" xml:lang="en-US">Distribution to noncontrolling parent interest</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_DistributionToNoncontrollingParentInterest" xlink:to="logc_DistributionToNoncontrollingParentInterest_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PaymentsForRepurchaseOfEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsForRepurchaseOfEquity"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_PaymentsForRepurchaseOfEquity_lbl" xml:lang="en-US">Repurchase of units</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsForRepurchaseOfEquity" xlink:to="us-gaap_PaymentsForRepurchaseOfEquity_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CommonClassAMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassAMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonClassAMember_lbl" xml:lang="en-US">Class A</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonClassAMember" xlink:to="us-gaap_CommonClassAMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CommonClassBMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassBMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommonClassBMember_lbl" xml:lang="en-US">Class B</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonClassBMember" xlink:to="us-gaap_CommonClassBMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_ClassAMemberUnitsMember" xlink:href="logc-20260226.xsd#logc_ClassAMemberUnitsMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_ClassAMemberUnitsMember_lbl" xml:lang="en-US">Class A</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ClassAMemberUnitsMember" xlink:to="logc_ClassAMemberUnitsMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_MemberUnitsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MemberUnitsMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MemberUnitsMember_lbl" xml:lang="en-US">Member Units</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MemberUnitsMember" xlink:to="us-gaap_MemberUnitsMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_ClassBMemberUnitsMember" xlink:href="logc-20260226.xsd#logc_ClassBMemberUnitsMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_ClassBMemberUnitsMember_lbl" xml:lang="en-US">Class B</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ClassBMemberUnitsMember" xlink:to="logc_ClassBMemberUnitsMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_SubscriptionNoteReceivableMember" xlink:href="logc-20260226.xsd#logc_SubscriptionNoteReceivableMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_SubscriptionNoteReceivableMember_lbl" xml:lang="en-US">Subscription Note Receivable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_SubscriptionNoteReceivableMember" xlink:to="logc_SubscriptionNoteReceivableMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RetainedEarningsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RetainedEarningsMember_lbl" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RetainedEarningsMember" xlink:to="us-gaap_RetainedEarningsMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NoncontrollingInterestMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoncontrollingInterestMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NoncontrollingInterestMember_lbl" xml:lang="en-US">Noncontrolling Parent Interest</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NoncontrollingInterestMember" xlink:to="us-gaap_NoncontrollingInterestMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NatureOfOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NatureOfOperations"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NatureOfOperations_lbl" xml:lang="en-US">Nature of operations and basis of presentation</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NatureOfOperations" xlink:to="us-gaap_NatureOfOperations_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SignificantAccountingPoliciesTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xml:lang="en-US">Significant accounting policies</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="us-gaap_SignificantAccountingPoliciesTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_EstimatedUsefulLivesOfPropertyPlantAndEquipmentTableTextBlock" xlink:href="logc-20260226.xsd#logc_EstimatedUsefulLivesOfPropertyPlantAndEquipmentTableTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_EstimatedUsefulLivesOfPropertyPlantAndEquipmentTableTextBlock_lbl" xml:lang="en-US">Schedule of Estimated Useful Lives of Property, Plant and Equipment</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_EstimatedUsefulLivesOfPropertyPlantAndEquipmentTableTextBlock" xlink:to="logc_EstimatedUsefulLivesOfPropertyPlantAndEquipmentTableTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentUsefulLife"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLife_lbl" xml:lang="en-US">Useful lives of assets</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:to="us-gaap_PropertyPlantAndEquipmentUsefulLife_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AccountsAndNontradeReceivableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsAndNontradeReceivableTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsAndNontradeReceivableTextBlock_lbl" xml:lang="en-US">Accounts receivable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsAndNontradeReceivableTextBlock" xlink:to="us-gaap_AccountsAndNontradeReceivableTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_lbl" xml:lang="en-US">Schedule of Accounts Receivable, Net of Allowance for Expected Credit Losses</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:to="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AccountsReceivableGrossCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableGrossCurrent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsReceivableGrossCurrent_lbl" xml:lang="en-US">Accounts receivables</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableGrossCurrent" xlink:to="us-gaap_AccountsReceivableGrossCurrent_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock_lbl" xml:lang="en-US">Schedule of Roll forward of Allowance for Expected Credit Losses</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock" xlink:to="us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivable_lbl" xml:lang="en-US">Beginning balance</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:to="us-gaap_AllowanceForDoubtfulAccountsReceivable_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivablePeriodIncreaseDecrease" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivablePeriodIncreaseDecrease"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivablePeriodIncreaseDecrease_lbl" xml:lang="en-US">Total</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllowanceForDoubtfulAccountsReceivablePeriodIncreaseDecrease" xlink:to="us-gaap_AllowanceForDoubtfulAccountsReceivablePeriodIncreaseDecrease_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InventoryDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InventoryDisclosureTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InventoryDisclosureTextBlock_lbl" xml:lang="en-US">Inventories</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryDisclosureTextBlock" xlink:to="us-gaap_InventoryDisclosureTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfInventoryCurrentTableTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfInventoryCurrentTableTextBlock_lbl" xml:lang="en-US">Schedule of Inventory</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:to="us-gaap_ScheduleOfInventoryCurrentTableTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InventoryFinishedGoods" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InventoryFinishedGoods"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InventoryFinishedGoods_lbl" xml:lang="en-US">Finished goods</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryFinishedGoods" xlink:to="us-gaap_InventoryFinishedGoods_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_PackagingAndSupplies" xlink:href="logc-20260226.xsd#logc_PackagingAndSupplies"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_PackagingAndSupplies_lbl" xml:lang="en-US">Packaging and supplies</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PackagingAndSupplies" xlink:to="logc_PackagingAndSupplies_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_MaintenanceMaterials" xlink:href="logc-20260226.xsd#logc_MaintenanceMaterials"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_MaintenanceMaterials_lbl" xml:lang="en-US">Maintenance materials</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_MaintenanceMaterials" xlink:to="logc_MaintenanceMaterials_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_PrepaidExpensesDisclosureTextBlock" xlink:href="logc-20260226.xsd#logc_PrepaidExpensesDisclosureTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_PrepaidExpensesDisclosureTextBlock_lbl" xml:lang="en-US">Prepaid expenses</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PrepaidExpensesDisclosureTextBlock" xlink:to="logc_PrepaidExpensesDisclosureTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfPrepaidExpensesAndOtherAssetsCurrentTableTextBlock" xlink:href="logc-20260226.xsd#logc_ScheduleOfPrepaidExpensesAndOtherAssetsCurrentTableTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_ScheduleOfPrepaidExpensesAndOtherAssetsCurrentTableTextBlock_lbl" xml:lang="en-US">Schedule of Prepaid Expenses</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfPrepaidExpensesAndOtherAssetsCurrentTableTextBlock" xlink:to="logc_ScheduleOfPrepaidExpensesAndOtherAssetsCurrentTableTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PrepaidInsurance" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrepaidInsurance"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PrepaidInsurance_lbl" xml:lang="en-US">Prepaid insurance</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PrepaidInsurance" xlink:to="us-gaap_PrepaidInsurance_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PrepaidTaxes" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrepaidTaxes"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PrepaidTaxes_lbl" xml:lang="en-US">Prepaid real estate taxes</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PrepaidTaxes" xlink:to="us-gaap_PrepaidTaxes_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_PrepaidHealthBenefits" xlink:href="logc-20260226.xsd#logc_PrepaidHealthBenefits"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_PrepaidHealthBenefits_lbl" xml:lang="en-US">Prepaid health benefits</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PrepaidHealthBenefits" xlink:to="logc_PrepaidHealthBenefits_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherPrepaidExpenseCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherPrepaidExpenseCurrent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherPrepaidExpenseCurrent_lbl" xml:lang="en-US">Other prepaid expenses</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherPrepaidExpenseCurrent" xlink:to="us-gaap_OtherPrepaidExpenseCurrent_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock_lbl" xml:lang="en-US">Plant, property and equipment, net</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:to="us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentTextBlock_lbl" xml:lang="en-US">Schedule of Plant Property and Equipment, Net</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:to="us-gaap_PropertyPlantAndEquipmentTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PropertyPlantAndEquipmentGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentGross"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xml:lang="en-US">Property, plant and equipment, gross</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentGross" xlink:to="us-gaap_PropertyPlantAndEquipmentGross_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfDepreciationAndDepletionExpenseIncludedInStatementsOfOperationsTableTextBlock" xlink:href="logc-20260226.xsd#logc_ScheduleOfDepreciationAndDepletionExpenseIncludedInStatementsOfOperationsTableTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_ScheduleOfDepreciationAndDepletionExpenseIncludedInStatementsOfOperationsTableTextBlock_lbl" xml:lang="en-US">Schedule of Depreciation and Depletion Expense Included in Statements of Operations</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfDepreciationAndDepletionExpenseIncludedInStatementsOfOperationsTableTextBlock" xlink:to="logc_ScheduleOfDepreciationAndDepletionExpenseIncludedInStatementsOfOperationsTableTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_Depreciation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Depreciation"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_Depreciation_lbl" xml:lang="en-US">Total</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Depreciation" xlink:to="us-gaap_Depreciation_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_lbl" xml:lang="en-US">Goodwill and Intangible assets</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:to="us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfIntangibleAssetsAndRelatedAccumulatedAmortizationTableTextBlock" xlink:href="logc-20260226.xsd#logc_ScheduleOfIntangibleAssetsAndRelatedAccumulatedAmortizationTableTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_ScheduleOfIntangibleAssetsAndRelatedAccumulatedAmortizationTableTextBlock_lbl" xml:lang="en-US">Schedule of Intangible Assets and Related Accumulated Amortization which are included in Intangible Assets, Net</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfIntangibleAssetsAndRelatedAccumulatedAmortizationTableTextBlock" xlink:to="logc_ScheduleOfIntangibleAssetsAndRelatedAccumulatedAmortizationTableTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsGross"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross_lbl" xml:lang="en-US">Gross Carrying Amount</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsGross" xlink:to="us-gaap_FiniteLivedIntangibleAssetsGross_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl" xml:lang="en-US">Accumulated Amortization</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsNet"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl" xml:lang="en-US">Amount</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsNet" xlink:to="us-gaap_FiniteLivedIntangibleAssetsNet_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock_lbl" xml:lang="en-US">Accrued liabilities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock" xlink:to="us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_lbl" xml:lang="en-US">Schedule of Accrued Liabilities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock" xlink:to="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeRelatedLiabilitiesCurrent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xml:lang="en-US">Accrued payroll, bonus and employee benefits</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:to="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AccruedInsuranceCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedInsuranceCurrent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccruedInsuranceCurrent_lbl" xml:lang="en-US">Insurance accruals</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccruedInsuranceCurrent" xlink:to="us-gaap_AccruedInsuranceCurrent_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAccruedLiabilitiesCurrent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent_lbl" xml:lang="en-US">Other accruals</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherAccruedLiabilitiesCurrent" xlink:to="us-gaap_OtherAccruedLiabilitiesCurrent_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AssetRetirementObligationDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetRetirementObligationDisclosureTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetRetirementObligationDisclosureTextBlock_lbl" xml:lang="en-US">Asset retirement obligations</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligationDisclosureTextBlock" xlink:to="us-gaap_AssetRetirementObligationDisclosureTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ScheduleOfChangeInAssetRetirementObligationTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfChangeInAssetRetirementObligationTableTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfChangeInAssetRetirementObligationTableTextBlock_lbl" xml:lang="en-US">Summary of Changes in Asset Retirement Obligation</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfChangeInAssetRetirementObligationTableTextBlock" xlink:to="us-gaap_ScheduleOfChangeInAssetRetirementObligationTableTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AssetRetirementObligationLiabilitiesIncurred" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetRetirementObligationLiabilitiesIncurred"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetRetirementObligationLiabilitiesIncurred_lbl" xml:lang="en-US">Liabilities incurred</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligationLiabilitiesIncurred" xlink:to="us-gaap_AssetRetirementObligationLiabilitiesIncurred_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LongTermDebtTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermDebtTextBlock_lbl" xml:lang="en-US">Long-term debt</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtTextBlock" xlink:to="us-gaap_LongTermDebtTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ScheduleOfDebtTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDebtTableTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfDebtTableTextBlock_lbl" xml:lang="en-US">Schedule of Long-Term Debt</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfDebtTableTextBlock" xlink:to="us-gaap_ScheduleOfDebtTableTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtInstrumentCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentCarryingAmount"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xml:lang="en-US">Term loan</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentCarryingAmount" xlink:to="us-gaap_DebtInstrumentCarryingAmount_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_lbl" xml:lang="en-US">Schedule of Annual Maturities of the Principal Amount of Total Debt Due</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:to="us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_lbl" xml:lang="en-US">2026</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:to="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_lbl" xml:lang="en-US">2027</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:to="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_lbl" xml:lang="en-US">2028</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:to="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebt"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:label="us-gaap_LongTermDebt_lbl" xml:lang="en-US">Total maturities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebt" xlink:to="us-gaap_LongTermDebt_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FairValueDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosuresTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xml:lang="en-US">Fair value measurement</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueDisclosuresTextBlock" xlink:to="us-gaap_FairValueDisclosuresTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock_lbl" xml:lang="en-US">Schedule of Cash and Cash Equivalents</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:to="us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsFairValueDisclosure"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashAndCashEquivalentsFairValueDisclosure_lbl" xml:lang="en-US">Total cash and cash equivalents</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:to="us-gaap_CashAndCashEquivalentsFairValueDisclosure_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl" xml:lang="en-US">Members&apos; equity</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_EarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xml:lang="en-US">Earnings per unit</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerShareTextBlock" xlink:to="us-gaap_EarningsPerShareTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xml:lang="en-US">Schedule of calculation of Earnings Per Share, Basic and Diluted Earnings Per Unit</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:to="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_lbl" xml:lang="en-US">Net income attributable to Parent Holdings Class A unitholders, diluted</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:to="us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_lbl" xml:lang="en-US">Unit-based compensation</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:to="us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock_lbl" xml:lang="en-US">Schedule of Weighted-Average Assumptions</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock" xlink:to="us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_FairValueOfClassSharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedBUnitFairvalueofClassBunit" xlink:href="logc-20260226.xsd#logc_FairValueOfClassSharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedBUnitFairvalueofClassBunit"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_FairValueOfClassSharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedBUnitFairvalueofClassBunit_lbl" xml:lang="en-US">Fair value of Class B unit</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_FairValueOfClassSharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedBUnitFairvalueofClassBunit" xlink:to="logc_FairValueOfClassSharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedBUnitFairvalueofClassBunit_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_lbl" xml:lang="en-US">Risk-free interest rate</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate_lbl" xml:lang="en-US">Volatility</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate_lbl" xml:lang="en-US">Dividend yield</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_lbl" xml:lang="en-US">Expected term</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1" xlink:to="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ScheduleOfShareBasedCompensationActivityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfShareBasedCompensationActivityTableTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfShareBasedCompensationActivityTableTextBlock_lbl" xml:lang="en-US">Schedule of Class B Units Activity</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfShareBasedCompensationActivityTableTextBlock" xlink:to="us-gaap_ScheduleOfShareBasedCompensationActivityTableTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xml:lang="en-US">Number of Units Granted</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xml:lang="en-US">Weighted Average Exercise Price Granted</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" xlink:to="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsRepurchasedWeightedAveragesExercisePrice" xlink:href="logc-20260226.xsd#logc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsRepurchasedWeightedAveragesExercisePrice"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsRepurchasedWeightedAveragesExercisePrice_lbl" xml:lang="en-US">Weighted Average Exercise Price Repurchased</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsRepurchasedWeightedAveragesExercisePrice" xlink:to="logc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsRepurchasedWeightedAveragesExercisePrice_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice_lbl" xml:lang="en-US">Weighted Average Exercise Price Forfeited</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice" xlink:to="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1_lbl" xml:lang="en-US">Weighted Average Remaining Term Outstanding(In Years) Exercisable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1" xlink:to="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfUnrecognizedCompensationExpenseTableTextBlock" xlink:href="logc-20260226.xsd#logc_ScheduleOfUnrecognizedCompensationExpenseTableTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_ScheduleOfUnrecognizedCompensationExpenseTableTextBlock_lbl" xml:lang="en-US">Schedule of Unrecognized Compensation Expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfUnrecognizedCompensationExpenseTableTextBlock" xlink:to="logc_ScheduleOfUnrecognizedCompensationExpenseTableTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_unrecognizedcompensationexpenseyearone" xlink:href="logc-20260226.xsd#logc_unrecognizedcompensationexpenseyearone"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_unrecognizedcompensationexpenseyearone_lbl" xml:lang="en-US">2026</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_unrecognizedcompensationexpenseyearone" xlink:to="logc_unrecognizedcompensationexpenseyearone_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_unrecognizedcompensationexpenseyeartwo" xlink:href="logc-20260226.xsd#logc_unrecognizedcompensationexpenseyeartwo"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_unrecognizedcompensationexpenseyeartwo_lbl" xml:lang="en-US">2027</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_unrecognizedcompensationexpenseyeartwo" xlink:to="logc_unrecognizedcompensationexpenseyeartwo_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_unrecognizedcompensationexpenseyearthree" xlink:href="logc-20260226.xsd#logc_unrecognizedcompensationexpenseyearthree"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_unrecognizedcompensationexpenseyearthree_lbl" xml:lang="en-US">2028</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_unrecognizedcompensationexpenseyearthree" xlink:to="logc_unrecognizedcompensationexpenseyearthree_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_Unrecognizedcompensationexpenseyearfour" xlink:href="logc-20260226.xsd#logc_Unrecognizedcompensationexpenseyearfour"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_Unrecognizedcompensationexpenseyearfour_lbl" xml:lang="en-US">2029</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_Unrecognizedcompensationexpenseyearfour" xlink:to="logc_Unrecognizedcompensationexpenseyearfour_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock_lbl" xml:lang="en-US">Retirement plan</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock" xlink:to="us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsDisclosureTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_lbl" xml:lang="en-US">Related party transaction</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:to="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock_lbl" xml:lang="en-US">Schedule of Activities of Class A Units and Subscription Notes Receivable from Employees and Board of Direct</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:to="us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_IssuanceOfNotesReceivableFromRelatedPartiesUnits" xlink:href="logc-20260226.xsd#logc_IssuanceOfNotesReceivableFromRelatedPartiesUnits"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_IssuanceOfNotesReceivableFromRelatedPartiesUnits_lbl" xml:lang="en-US">Issuance, Units (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_IssuanceOfNotesReceivableFromRelatedPartiesUnits" xlink:to="logc_IssuanceOfNotesReceivableFromRelatedPartiesUnits_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_IssuanceOfNotesReceivableFromRelatedParties" xlink:href="logc-20260226.xsd#logc_IssuanceOfNotesReceivableFromRelatedParties"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_IssuanceOfNotesReceivableFromRelatedParties_lbl" xml:lang="en-US">Issuance</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_IssuanceOfNotesReceivableFromRelatedParties" xlink:to="logc_IssuanceOfNotesReceivableFromRelatedParties_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_RepurchaseUnitsFromRelatedParties" xlink:href="logc-20260226.xsd#logc_RepurchaseUnitsFromRelatedParties"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_RepurchaseUnitsFromRelatedParties_lbl" xml:lang="en-US">Repurchase, Units (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RepurchaseUnitsFromRelatedParties" xlink:to="logc_RepurchaseUnitsFromRelatedParties_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_RepurchaseOfNotesReceivableFromRelatedParties" xlink:href="logc-20260226.xsd#logc_RepurchaseOfNotesReceivableFromRelatedParties"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_RepurchaseOfNotesReceivableFromRelatedParties_lbl" xml:lang="en-US">Repurchase</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RepurchaseOfNotesReceivableFromRelatedParties" xlink:to="logc_RepurchaseOfNotesReceivableFromRelatedParties_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_CancellationOfUnitsPurchasedAndTheCorrespondingSubscriptionNotesReceivableUnits" xlink:href="logc-20260226.xsd#logc_CancellationOfUnitsPurchasedAndTheCorrespondingSubscriptionNotesReceivableUnits"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_CancellationOfUnitsPurchasedAndTheCorrespondingSubscriptionNotesReceivableUnits_lbl" xml:lang="en-US">Cancellation of units purchased and the corresponding subscription notes receivable, Units (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_CancellationOfUnitsPurchasedAndTheCorrespondingSubscriptionNotesReceivableUnits" xlink:to="logc_CancellationOfUnitsPurchasedAndTheCorrespondingSubscriptionNotesReceivableUnits_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_CancellationOfUnitsPurchasedAndTheCorrespondingSubscriptionNotesReceivable" xlink:href="logc-20260226.xsd#logc_CancellationOfUnitsPurchasedAndTheCorrespondingSubscriptionNotesReceivable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_CancellationOfUnitsPurchasedAndTheCorrespondingSubscriptionNotesReceivable_lbl" xml:lang="en-US">Cancellation of units purchased and the corresponding subscription notes receivable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_CancellationOfUnitsPurchasedAndTheCorrespondingSubscriptionNotesReceivable" xlink:to="logc_CancellationOfUnitsPurchasedAndTheCorrespondingSubscriptionNotesReceivable_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_RepaymentUnitsFromRelatedParties" xlink:href="logc-20260226.xsd#logc_RepaymentUnitsFromRelatedParties"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_RepaymentUnitsFromRelatedParties_lbl" xml:lang="en-US">Repayment, Units (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RepaymentUnitsFromRelatedParties" xlink:to="logc_RepaymentUnitsFromRelatedParties_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RepaymentOfNotesReceivableFromRelatedParties" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentOfNotesReceivableFromRelatedParties"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RepaymentOfNotesReceivableFromRelatedParties_lbl" xml:lang="en-US">Repayment</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RepaymentOfNotesReceivableFromRelatedParties" xlink:to="us-gaap_RepaymentOfNotesReceivableFromRelatedParties_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl" xml:lang="en-US">Commitments and Contingencies</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:to="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LeaseCostTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LeaseCostTableTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LeaseCostTableTextBlock_lbl" xml:lang="en-US">Schedule of Elements of Lease Costs</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LeaseCostTableTextBlock" xlink:to="us-gaap_LeaseCostTableTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_OperatingLeaseExpenseAbstract" xlink:href="logc-20260226.xsd#logc_OperatingLeaseExpenseAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_OperatingLeaseExpenseAbstract_lbl" xml:lang="en-US">Operating lease expense:</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_OperatingLeaseExpenseAbstract" xlink:to="logc_OperatingLeaseExpenseAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OperatingLeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseCost"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseCost_lbl" xml:lang="en-US">Operating lease expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseCost" xlink:to="us-gaap_OperatingLeaseCost_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_FinanceLeaseExpenseAbstract" xlink:href="logc-20260226.xsd#logc_FinanceLeaseExpenseAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_FinanceLeaseExpenseAbstract_lbl" xml:lang="en-US">Finance lease expense:</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_FinanceLeaseExpenseAbstract" xlink:to="logc_FinanceLeaseExpenseAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinanceLeaseRightOfUseAssetAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseRightOfUseAssetAmortization"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseRightOfUseAssetAmortization_lbl" xml:lang="en-US">Amortization of lease assets</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseRightOfUseAssetAmortization" xlink:to="us-gaap_FinanceLeaseRightOfUseAssetAmortization_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ShortTermLeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShortTermLeaseCost"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShortTermLeaseCost_lbl" xml:lang="en-US">Short term lease expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShortTermLeaseCost" xlink:to="us-gaap_ShortTermLeaseCost_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_VariableLeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableLeaseCost"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_VariableLeaseCost_lbl" xml:lang="en-US">Variable lease expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_VariableLeaseCost" xlink:to="us-gaap_VariableLeaseCost_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfLeaseTermAndDiscountRateInformationRelatedToLeaseTableTextBlock" xlink:href="logc-20260226.xsd#logc_ScheduleOfLeaseTermAndDiscountRateInformationRelatedToLeaseTableTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_ScheduleOfLeaseTermAndDiscountRateInformationRelatedToLeaseTableTextBlock_lbl" xml:lang="en-US">Schedule of Lease Term and Discount Rate Information</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfLeaseTermAndDiscountRateInformationRelatedToLeaseTableTextBlock" xlink:to="logc_ScheduleOfLeaseTermAndDiscountRateInformationRelatedToLeaseTableTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_lbl" xml:lang="en-US">Operating leases</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:to="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_lbl" xml:lang="en-US">Finance leases</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:to="us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_WeightedAverageDiscountRateAbstract" xlink:href="logc-20260226.xsd#logc_WeightedAverageDiscountRateAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_WeightedAverageDiscountRateAbstract_lbl" xml:lang="en-US">Weighted-average discount rate:</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_WeightedAverageDiscountRateAbstract" xlink:to="logc_WeightedAverageDiscountRateAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_lbl" xml:lang="en-US">Operating leases</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:to="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_lbl" xml:lang="en-US">Finance leases</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:to="us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_SupplementalCashFlowInformationRelatedToLeasesTableTextBlock" xlink:href="logc-20260226.xsd#logc_SupplementalCashFlowInformationRelatedToLeasesTableTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_SupplementalCashFlowInformationRelatedToLeasesTableTextBlock_lbl" xml:lang="en-US">Schedule of Supplemental Cash Flow Information</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_SupplementalCashFlowInformationRelatedToLeasesTableTextBlock" xlink:to="logc_SupplementalCashFlowInformationRelatedToLeasesTableTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_CashPaidForAmountsIncludedInTheMeasurementOfLeaseLiabilitiesAbstract" xlink:href="logc-20260226.xsd#logc_CashPaidForAmountsIncludedInTheMeasurementOfLeaseLiabilitiesAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_CashPaidForAmountsIncludedInTheMeasurementOfLeaseLiabilitiesAbstract_lbl" xml:lang="en-US">Cash paid for amounts included in the measurement of lease liabilities:</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_CashPaidForAmountsIncludedInTheMeasurementOfLeaseLiabilitiesAbstract" xlink:to="logc_CashPaidForAmountsIncludedInTheMeasurementOfLeaseLiabilitiesAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinanceLeaseInterestPaymentOnLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseInterestPaymentOnLiability"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseInterestPaymentOnLiability_lbl" xml:lang="en-US">Operating cash flows from finance lease (interest payments)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseInterestPaymentOnLiability" xlink:to="us-gaap_FinanceLeaseInterestPaymentOnLiability_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OperatingLeasePayments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeasePayments"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeasePayments_lbl" xml:lang="en-US">Operating cash flows from operating leases</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeasePayments" xlink:to="us-gaap_OperatingLeasePayments_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinanceLeasePrincipalPayments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeasePrincipalPayments"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeasePrincipalPayments_lbl" xml:lang="en-US">Financing cash flows from finance lease</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeasePrincipalPayments" xlink:to="us-gaap_FinanceLeasePrincipalPayments_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_RightOfUseAssetsObtainedInExchangeForLeaseLiabilitiesAbstract" xlink:href="logc-20260226.xsd#logc_RightOfUseAssetsObtainedInExchangeForLeaseLiabilitiesAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_RightOfUseAssetsObtainedInExchangeForLeaseLiabilitiesAbstract_lbl" xml:lang="en-US">Right-of-use assets obtained in exchange for lease liabilities:</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RightOfUseAssetsObtainedInExchangeForLeaseLiabilitiesAbstract" xlink:to="logc_RightOfUseAssetsObtainedInExchangeForLeaseLiabilitiesAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_lbl" xml:lang="en-US">Operating leases</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:to="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_lbl" xml:lang="en-US">Finance leases</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:to="us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_LesseeOperatingAndFinanceLeaseLiabilityMaturityTableTextBlock" xlink:href="logc-20260226.xsd#logc_LesseeOperatingAndFinanceLeaseLiabilityMaturityTableTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_LesseeOperatingAndFinanceLeaseLiabilityMaturityTableTextBlock_lbl" xml:lang="en-US">Schedule of Future Maturities of Lease Liabilities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_LesseeOperatingAndFinanceLeaseLiabilityMaturityTableTextBlock" xlink:to="logc_LesseeOperatingAndFinanceLeaseLiabilityMaturityTableTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xml:lang="en-US">2026</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xml:lang="en-US">2026</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xml:lang="en-US">2027</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo_lbl" xml:lang="en-US">2027</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:to="us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xml:lang="en-US">2028</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree_lbl" xml:lang="en-US">2028</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree" xlink:to="us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_lbl" xml:lang="en-US">2029</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour_lbl" xml:lang="en-US">2029</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour" xlink:to="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_lbl" xml:lang="en-US">2030</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive_lbl" xml:lang="en-US">2030</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive" xlink:to="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_lbl" xml:lang="en-US">Thereafter</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive_lbl" xml:lang="en-US">Thereafter</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive" xlink:to="us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiability"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xml:lang="en-US">Present value of lease payments</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseLiability" xlink:to="us-gaap_OperatingLeaseLiability_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinanceLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiability"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FinanceLeaseLiability_lbl" xml:lang="en-US">Present value of lease payments</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiability" xlink:to="us-gaap_FinanceLeaseLiability_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingDisclosureTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xml:lang="en-US">Segment Information</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingDisclosureTextBlock" xlink:to="us-gaap_SegmentReportingDisclosureTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xml:lang="en-US">Schedule of Operating Financial Results</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:to="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_lbl" xml:lang="en-US">Revenue</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:to="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CostOfGoodsAndServiceExcludingDepreciationDepletionAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CostOfGoodsAndServiceExcludingDepreciationDepletionAndAmortization"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CostOfGoodsAndServiceExcludingDepreciationDepletionAndAmortization_lbl" xml:lang="en-US">Cost of revenue</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CostOfGoodsAndServiceExcludingDepreciationDepletionAndAmortization" xlink:to="us-gaap_CostOfGoodsAndServiceExcludingDepreciationDepletionAndAmortization_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DepreciationAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DepreciationAndAmortization"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DepreciationAndAmortization_lbl" xml:lang="en-US">Depreciation, amortization and depletion</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DepreciationAndAmortization" xlink:to="us-gaap_DepreciationAndAmortization_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SellingExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SellingExpense"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SellingExpense_lbl" xml:lang="en-US">Selling expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SellingExpense" xlink:to="us-gaap_SellingExpense_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AdministrativeFeesExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdministrativeFeesExpense"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdministrativeFeesExpense_lbl" xml:lang="en-US">Administrative expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdministrativeFeesExpense" xlink:to="us-gaap_AdministrativeFeesExpense_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpense"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InterestExpense_lbl" xml:lang="en-US">Interest expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestExpense" xlink:to="us-gaap_InterestExpense_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SegmentReportingOtherItemAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingOtherItemAmount"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SegmentReportingOtherItemAmount_lbl" xml:lang="en-US">Other segment items</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingOtherItemAmount" xlink:to="us-gaap_SegmentReportingOtherItemAmount_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SubsequentEventsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventsTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xml:lang="en-US">Subsequent events</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventsTextBlock" xlink:to="us-gaap_SubsequentEventsTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_lbl" xml:lang="en-US">Less: allowance for expected credit losses</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:to="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs_lbl" xml:lang="en-US">Write-offs</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs" xlink:to="us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xml:lang="en-US">Accumulated depreciation and depletion</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:to="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AssetRetirementObligationRevisionOfEstimate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetRetirementObligationRevisionOfEstimate"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_AssetRetirementObligationRevisionOfEstimate_lbl" xml:lang="en-US">Changes in estimated obligations</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligationRevisionOfEstimate" xlink:to="us-gaap_AssetRetirementObligationRevisionOfEstimate_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet_lbl" xml:lang="en-US">Unamortized debt issuance</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet" xlink:to="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesToBeRepurchasedNextYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesToBeRepurchasedNextYear"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesToBeRepurchasedNextYear_lbl" xml:lang="en-US">Number of Units Repurchased</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesToBeRepurchasedNextYear" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesToBeRepurchasedNextYear_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod_lbl" xml:lang="en-US">Number of Units Forfeited</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xml:lang="en-US">Imputed interest</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:label="us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount_lbl" xml:lang="en-US">Imputed interest</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xlink:to="us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_BuildingImprovementsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BuildingImprovementsMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BuildingImprovementsMember_lbl" xml:lang="en-US">Buildings and Improvements [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BuildingImprovementsMember" xlink:to="us-gaap_BuildingImprovementsMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_MachineryAndEquipmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MachineryAndEquipmentMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MachineryAndEquipmentMember_lbl" xml:lang="en-US">Machinery and Equipment [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MachineryAndEquipmentMember" xlink:to="us-gaap_MachineryAndEquipmentMember_lbl"/>
    <loc xlink:type="locator" xlink:label="srt_MinimumMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MinimumMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_MinimumMember_lbl" xml:lang="en-US">Minimum [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MinimumMember" xlink:to="srt_MinimumMember_lbl"/>
    <loc xlink:type="locator" xlink:label="srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MaximumMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_MaximumMember_lbl" xml:lang="en-US">Maximum [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MaximumMember" xlink:to="srt_MaximumMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LandMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LandMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LandMember_lbl" xml:lang="en-US">Land [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LandMember" xlink:to="us-gaap_LandMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_BuildingAndBuildingImprovementsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BuildingAndBuildingImprovementsMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BuildingAndBuildingImprovementsMember_lbl" xml:lang="en-US">Building and Building Improvements [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BuildingAndBuildingImprovementsMember" xlink:to="us-gaap_BuildingAndBuildingImprovementsMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_SaltReservesMember" xlink:href="logc-20260226.xsd#logc_SaltReservesMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_SaltReservesMember_lbl" xml:lang="en-US">Salt Reserves [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_SaltReservesMember" xlink:to="logc_SaltReservesMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ConstructionInProgressMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConstructionInProgressMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConstructionInProgressMember_lbl" xml:lang="en-US">Construction in Progress [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConstructionInProgressMember" xlink:to="us-gaap_ConstructionInProgressMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_CostOfRevenueMember" xlink:href="logc-20260226.xsd#logc_CostOfRevenueMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_CostOfRevenueMember_lbl" xml:lang="en-US">Cost of Revenue [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_CostOfRevenueMember" xlink:to="logc_CostOfRevenueMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_SellingGeneralAndAdministrativeExpenseMember" xlink:href="logc-20260226.xsd#logc_SellingGeneralAndAdministrativeExpenseMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_SellingGeneralAndAdministrativeExpenseMember_lbl" xml:lang="en-US">Selling General and Administrative Expense [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_SellingGeneralAndAdministrativeExpenseMember" xlink:to="logc_SellingGeneralAndAdministrativeExpenseMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_TradeNamesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TradeNamesMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TradeNamesMember_lbl" xml:lang="en-US">Tradename [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TradeNamesMember" xlink:to="us-gaap_TradeNamesMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CustomerRelationshipsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CustomerRelationshipsMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CustomerRelationshipsMember_lbl" xml:lang="en-US">Customer Relationships [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CustomerRelationshipsMember" xlink:to="us-gaap_CustomerRelationshipsMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CashMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashMember_lbl" xml:lang="en-US">Cash [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashMember" xlink:to="us-gaap_CashMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_MoneyMarketFundsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MoneyMarketFundsMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MoneyMarketFundsMember_lbl" xml:lang="en-US">Money Market Funds [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MoneyMarketFundsMember" xlink:to="us-gaap_MoneyMarketFundsMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_USSaltParentHoldingsLLCMember" xlink:href="logc-20260226.xsd#logc_USSaltParentHoldingsLLCMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_USSaltParentHoldingsLLCMember_lbl" xml:lang="en-US">US Salt Parent Holdings, LLC [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_USSaltParentHoldingsLLCMember" xlink:to="logc_USSaltParentHoldingsLLCMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_ClassAUnitsMember" xlink:href="logc-20260226.xsd#logc_ClassAUnitsMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_ClassAUnitsMember_lbl" xml:lang="en-US">Class A units [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ClassAUnitsMember" xlink:to="logc_ClassAUnitsMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_ClassAUnitsAmountMember" xlink:href="logc-20260226.xsd#logc_ClassAUnitsAmountMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_ClassAUnitsAmountMember_lbl" xml:lang="en-US">Class A Units Amount [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ClassAUnitsAmountMember" xlink:to="logc_ClassAUnitsAmountMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_SubscriptionReceivableMember" xlink:href="logc-20260226.xsd#logc_SubscriptionReceivableMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_SubscriptionReceivableMember_lbl" xml:lang="en-US">Subscription Receivable [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_SubscriptionReceivableMember" xlink:to="logc_SubscriptionReceivableMember_lbl"/>
    <loc xlink:type="locator" xlink:label="srt_OwnershipAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_OwnershipAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_OwnershipAxis_lbl" xml:lang="en-US">Ownership [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_OwnershipAxis" xlink:to="srt_OwnershipAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="srt_ProductOrServiceAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductOrServiceAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProductOrServiceAxis_lbl" xml:lang="en-US">Product and Service [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProductOrServiceAxis" xlink:to="srt_ProductOrServiceAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="srt_StatementGeographicalAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_StatementGeographicalAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_StatementGeographicalAxis_lbl" xml:lang="en-US">Geographical [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_StatementGeographicalAxis" xlink:to="srt_StatementGeographicalAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskByBenchmarkAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskByBenchmarkAxis_lbl" xml:lang="en-US">Concentration Risk Benchmark [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:to="us-gaap_ConcentrationRiskByBenchmarkAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ConcentrationRiskByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskByTypeAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskByTypeAxis_lbl" xml:lang="en-US">Concentration Risk Type [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskByTypeAxis" xlink:to="us-gaap_ConcentrationRiskByTypeAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="srt_MajorCustomersAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MajorCustomersAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_MajorCustomersAxis_lbl" xml:lang="en-US">Customer [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MajorCustomersAxis" xlink:to="srt_MajorCustomersAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CreditFacilityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CreditFacilityAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CreditFacilityAxis_lbl" xml:lang="en-US">Credit Facility [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CreditFacilityAxis" xlink:to="us-gaap_CreditFacilityAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentAxis_lbl" xml:lang="en-US">Debt Instrument [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentAxis" xlink:to="us-gaap_DebtInstrumentAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_VariableRateAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableRateAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_VariableRateAxis_lbl" xml:lang="en-US">Variable Rate [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_VariableRateAxis" xlink:to="us-gaap_VariableRateAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_VestingAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VestingAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_VestingAxis_lbl" xml:lang="en-US">Vesting [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_VestingAxis" xlink:to="us-gaap_VestingAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PlanNameAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PlanNameAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PlanNameAxis_lbl" xml:lang="en-US">Plan Name [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PlanNameAxis" xlink:to="us-gaap_PlanNameAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RelatedPartyTransactionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionAxis_lbl" xml:lang="en-US">Related Party Transaction [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionAxis" xlink:to="us-gaap_RelatedPartyTransactionAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl" xml:lang="en-US">Related and Nonrelated Parties [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LongTermPurchaseCommitmentByCategoryOfItemPurchasedAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermPurchaseCommitmentByCategoryOfItemPurchasedAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermPurchaseCommitmentByCategoryOfItemPurchasedAxis_lbl" xml:lang="en-US">Category of Item Purchased [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermPurchaseCommitmentByCategoryOfItemPurchasedAxis" xlink:to="us-gaap_LongTermPurchaseCommitmentByCategoryOfItemPurchasedAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SubsidiarySaleOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsidiarySaleOfStockAxis"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xml:lang="en-US">Sale of Stock [Axis]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsidiarySaleOfStockAxis" xlink:to="us-gaap_SubsidiarySaleOfStockAxis_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AccountingPoliciesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountingPoliciesAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountingPoliciesAbstract_lbl" xml:lang="en-US">Accounting Policies [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountingPoliciesAbstract" xlink:to="us-gaap_AccountingPoliciesAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl" xml:lang="en-US">Percentage of owns members interest</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:to="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl0" xml:lang="en-US">Percentage of noncontrolling parent interest</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:to="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterestOwnershipPercentageByParent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByParent_lbl" xml:lang="en-US">Percentage of ownership interest</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:to="us-gaap_MinorityInterestOwnershipPercentageByParent_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ConcentrationRiskPercentage1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskPercentage1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConcentrationRiskPercentage1_lbl" xml:lang="en-US">Percentage of net sales</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskPercentage1" xlink:to="us-gaap_ConcentrationRiskPercentage1_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_NumberOfMajorCustomer" xlink:href="logc-20260226.xsd#logc_NumberOfMajorCustomer"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_NumberOfMajorCustomer_lbl" xml:lang="en-US">Number of major customer</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_NumberOfMajorCustomer" xlink:to="logc_NumberOfMajorCustomer_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestCostsCapitalized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestCostsCapitalized"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InterestCostsCapitalized_lbl" xml:lang="en-US">Capitalized interest cost</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestCostsCapitalized" xlink:to="us-gaap_InterestCostsCapitalized_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_LeasesRemainingLeaseTerm" xlink:href="logc-20260226.xsd#logc_LeasesRemainingLeaseTerm"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_LeasesRemainingLeaseTerm_lbl" xml:lang="en-US">Leases remaining lease term</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_LeasesRemainingLeaseTerm" xlink:to="logc_LeasesRemainingLeaseTerm_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetUsefulLife"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetUsefulLife_lbl" xml:lang="en-US">Finite lived intangible asset useful lives</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:to="us-gaap_FiniteLivedIntangibleAssetUsefulLife_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ImpairmentOfIntangibleAssetsFinitelived" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ImpairmentOfIntangibleAssetsFinitelived"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ImpairmentOfIntangibleAssetsFinitelived_lbl" xml:lang="en-US">Impairment of finite-lived intangibles</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ImpairmentOfIntangibleAssetsFinitelived" xlink:to="us-gaap_ImpairmentOfIntangibleAssetsFinitelived_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AdvertisingExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdvertisingExpense"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdvertisingExpense_lbl" xml:lang="en-US">Advertising costs</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdvertisingExpense" xlink:to="us-gaap_AdvertisingExpense_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense_lbl" xml:lang="en-US">Unrecognized tax benefits, interest and penalties</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense" xlink:to="us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_UnrecognizedTaxBenefitDuration" xlink:href="logc-20260226.xsd#logc_UnrecognizedTaxBenefitDuration"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_UnrecognizedTaxBenefitDuration_lbl" xml:lang="en-US">Unrecognized tax benefit duration</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_UnrecognizedTaxBenefitDuration" xlink:to="logc_UnrecognizedTaxBenefitDuration_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NumberOfOperatingSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NumberOfOperatingSegments"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xml:lang="en-US">Number of operating segment</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NumberOfOperatingSegments" xlink:to="us-gaap_NumberOfOperatingSegments_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:label="us-gaap_NumberOfOperatingSegments_lbl0" xml:lang="en-US">Number of operating segments (in segment)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NumberOfOperatingSegments" xlink:to="us-gaap_NumberOfOperatingSegments_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InventoryWriteDown" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InventoryWriteDown"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InventoryWriteDown_lbl" xml:lang="en-US">Inventory obsolescence</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryWriteDown" xlink:to="us-gaap_InventoryWriteDown_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_InventoryWrittenOff" xlink:href="logc-20260226.xsd#logc_InventoryWrittenOff"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_InventoryWrittenOff_lbl" xml:lang="en-US">Inventory written off</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_InventoryWrittenOff" xlink:to="logc_InventoryWrittenOff_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax_lbl" xml:lang="en-US">Gain (loss) from disposal operation</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax" xlink:to="us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AmortizationOfIntangibleAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfIntangibleAssets"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AmortizationOfIntangibleAssets_lbl" xml:lang="en-US">Amortization expense of the finite-lived intangible assets</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AmortizationOfIntangibleAssets" xlink:to="us-gaap_AmortizationOfIntangibleAssets_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_lbl" xml:lang="en-US">Estimated net amortization expense, 2026</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_lbl" xml:lang="en-US">Estimated net amortization expense, 2027</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_lbl" xml:lang="en-US">Estimated net amortization expense, 2028</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_lbl" xml:lang="en-US">Estimated net amortization expense, 2029</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive_lbl" xml:lang="en-US">Estimated net amortization expense, 2030</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFive"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFive_lbl" xml:lang="en-US">Estimated net amortization expense, thereafter</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFive" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFive_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1_lbl" xml:lang="en-US">Remaining useful lives for the intangible assets</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xlink:to="us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_SuretyBondsOutstandingAmount" xlink:href="logc-20260226.xsd#logc_SuretyBondsOutstandingAmount"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_SuretyBondsOutstandingAmount_lbl" xml:lang="en-US">Surety bonds outstanding amount</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_SuretyBondsOutstandingAmount" xlink:to="logc_SuretyBondsOutstandingAmount_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xml:lang="en-US">Line of credit facility</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:to="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentInterestRateEffectivePercentage"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentInterestRateEffectivePercentage_lbl" xml:lang="en-US">Interest rate</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:to="us-gaap_DebtInstrumentInterestRateEffectivePercentage_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentBasisSpreadOnVariableRate1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xml:lang="en-US">Basis spread on variable rate</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:to="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtInstrumentPeriodicPaymentPrincipal" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentPeriodicPaymentPrincipal"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentPeriodicPaymentPrincipal_lbl" xml:lang="en-US">Quarterly principal payments</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentPeriodicPaymentPrincipal" xlink:to="us-gaap_DebtInstrumentPeriodicPaymentPrincipal_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtInstrumentMaturityDate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentMaturityDate"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DebtInstrumentMaturityDate_lbl" xml:lang="en-US">Debt instrument, maturity date</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentMaturityDate" xlink:to="us-gaap_DebtInstrumentMaturityDate_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_lbl" xml:lang="en-US">Commitment fee percentage</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:to="us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LineOfCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCredit"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LineOfCredit_lbl" xml:lang="en-US">Outstanding borrowings</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCredit" xlink:to="us-gaap_LineOfCredit_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LineOfCreditFacilityCommitmentFeeAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityCommitmentFeeAmount"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LineOfCreditFacilityCommitmentFeeAmount_lbl" xml:lang="en-US">Unused amount of credit available</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCreditFacilityCommitmentFeeAmount" xlink:to="us-gaap_LineOfCreditFacilityCommitmentFeeAmount_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DeferredFinanceCostsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredFinanceCostsNet"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xml:lang="en-US">Debt issuance costs</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredFinanceCostsNet" xlink:to="us-gaap_DeferredFinanceCostsNet_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AccumulatedAmortizationOfDebtIssuanceCostsLineOfCreditArrangements" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedAmortizationOfDebtIssuanceCostsLineOfCreditArrangements"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccumulatedAmortizationOfDebtIssuanceCostsLineOfCreditArrangements_lbl" xml:lang="en-US">Amortization of debt issuance cost</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccumulatedAmortizationOfDebtIssuanceCostsLineOfCreditArrangements" xlink:to="us-gaap_AccumulatedAmortizationOfDebtIssuanceCostsLineOfCreditArrangements_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_UnreturnedCapitalOfClassAUnitholdersBeforeDistributions" xlink:href="logc-20260226.xsd#logc_UnreturnedCapitalOfClassAUnitholdersBeforeDistributions"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_UnreturnedCapitalOfClassAUnitholdersBeforeDistributions_lbl" xml:lang="en-US">Total unreturned capital (in Dollars)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_UnreturnedCapitalOfClassAUnitholdersBeforeDistributions" xlink:to="logc_UnreturnedCapitalOfClassAUnitholdersBeforeDistributions_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_TaxDistributions" xlink:href="logc-20260226.xsd#logc_TaxDistributions"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_TaxDistributions_lbl" xml:lang="en-US">Tax distributions (in Dollars)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_TaxDistributions" xlink:to="logc_TaxDistributions_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage_lbl" xml:lang="en-US">Percentage of vesting of award</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage" xlink:to="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1_lbl" xml:lang="en-US">Incentive units vested requisite service period</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingRights" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingRights"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingRights_lbl" xml:lang="en-US">Incentive units vesting rights, description</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingRights" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingRights_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_PercentageOfNoncontrollingParentInterestRepresentedAggregator" xlink:href="logc-20260226.xsd#logc_PercentageOfNoncontrollingParentInterestRepresentedAggregator"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_PercentageOfNoncontrollingParentInterestRepresentedAggregator_lbl" xml:lang="en-US">Noncontrolling parent ownership interest</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PercentageOfNoncontrollingParentInterestRepresentedAggregator" xlink:to="logc_PercentageOfNoncontrollingParentInterestRepresentedAggregator_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xml:lang="en-US">Weighted average grant date fair value, granted</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeePercent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeePercent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeePercent_lbl" xml:lang="en-US">Salary deferred contribution percent</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeePercent" xlink:to="us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeePercent_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent_lbl" xml:lang="en-US">Employees&#8217; contribution period percent</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent" xlink:to="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DefinedContributionPlanEmployersMatchingContributionAnnualVestingPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DefinedContributionPlanEmployersMatchingContributionAnnualVestingPercentage"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DefinedContributionPlanEmployersMatchingContributionAnnualVestingPercentage_lbl" xml:lang="en-US">Semi monthly safe harbor contribution vest percent</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DefinedContributionPlanEmployersMatchingContributionAnnualVestingPercentage" xlink:to="us-gaap_DefinedContributionPlanEmployersMatchingContributionAnnualVestingPercentage_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch_lbl" xml:lang="en-US">Semi monthly safe harbor contribution percent</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch" xlink:to="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DefinedContributionPlanCostRecognized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DefinedContributionPlanCostRecognized"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DefinedContributionPlanCostRecognized_lbl" xml:lang="en-US">Employer portion of contributions (in Dollars)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DefinedContributionPlanCostRecognized" xlink:to="us-gaap_DefinedContributionPlanCostRecognized_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DescriptionOfDefinedContributionPensionAndOtherPostretirementPlans" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DescriptionOfDefinedContributionPensionAndOtherPostretirementPlans"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_DescriptionOfDefinedContributionPensionAndOtherPostretirementPlans_lbl" xml:lang="en-US">Defined contribution plan, description</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DescriptionOfDefinedContributionPensionAndOtherPostretirementPlans" xlink:to="us-gaap_DescriptionOfDefinedContributionPensionAndOtherPostretirementPlans_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_AnnualManagementFeeMinimumAmount" xlink:href="logc-20260226.xsd#logc_AnnualManagementFeeMinimumAmount"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_AnnualManagementFeeMinimumAmount_lbl" xml:lang="en-US">Annual management fee minimum amount</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_AnnualManagementFeeMinimumAmount" xlink:to="logc_AnnualManagementFeeMinimumAmount_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_PercentageOfAnnualManagementFee" xlink:href="logc-20260226.xsd#logc_PercentageOfAnnualManagementFee"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_PercentageOfAnnualManagementFee_lbl" xml:lang="en-US">Percentage of annual management fee</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PercentageOfAnnualManagementFee" xlink:to="logc_PercentageOfAnnualManagementFee_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ManagementFeePayable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ManagementFeePayable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ManagementFeePayable_lbl" xml:lang="en-US">Management fee payable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ManagementFeePayable" xlink:to="us-gaap_ManagementFeePayable_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_PercentageOfQuarterlyManagementFee" xlink:href="logc-20260226.xsd#logc_PercentageOfQuarterlyManagementFee"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_PercentageOfQuarterlyManagementFee_lbl" xml:lang="en-US">Percentage of quarterly management fee</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PercentageOfQuarterlyManagementFee" xlink:to="logc_PercentageOfQuarterlyManagementFee_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ManagementFeeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ManagementFeeExpense"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ManagementFeeExpense_lbl" xml:lang="en-US">Management fees</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ManagementFeeExpense" xlink:to="us-gaap_ManagementFeeExpense_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_OperationAndFinanceLeasesExpiringYear" xlink:href="logc-20260226.xsd#logc_OperationAndFinanceLeasesExpiringYear"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_OperationAndFinanceLeasesExpiringYear_lbl" xml:lang="en-US">Operation and finance leases, expiring year</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_OperationAndFinanceLeasesExpiringYear" xlink:to="logc_OperationAndFinanceLeasesExpiringYear_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LongTermPurchaseCommitmentAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermPurchaseCommitmentAmount"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LongTermPurchaseCommitmentAmount_lbl" xml:lang="en-US">Equipment and construction contracts</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermPurchaseCommitmentAmount" xlink:to="us-gaap_LongTermPurchaseCommitmentAmount_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl" xml:lang="en-US">Number of shares issued upon right offering (in Shares)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:to="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SaleOfStockPricePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockPricePerShare"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl" xml:lang="en-US">Exercise price per share (in Dollars per share)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SaleOfStockPricePerShare" xlink:to="us-gaap_SaleOfStockPricePerShare_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_ProceedsFromRightsOffering" xlink:href="logc-20260226.xsd#logc_ProceedsFromRightsOffering"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_ProceedsFromRightsOffering_lbl" xml:lang="en-US">Proceeds from rights offering</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ProceedsFromRightsOffering" xlink:to="logc_ProceedsFromRightsOffering_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationConsiderationTransferred1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xml:lang="en-US">Business acquisition, purchase price</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationConsiderationTransferred1" xlink:to="us-gaap_BusinessCombinationConsiderationTransferred1_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PaymentsToAcquireBusinessesGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireBusinessesGross"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PaymentsToAcquireBusinessesGross_lbl" xml:lang="en-US">Business acquisition, cash payment</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquireBusinessesGross" xlink:to="us-gaap_PaymentsToAcquireBusinessesGross_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ProceedsFromIssuanceOfLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromIssuanceOfLongTermDebt"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ProceedsFromIssuanceOfLongTermDebt_lbl" xml:lang="en-US">Net borrowing proceeds from term loans</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromIssuanceOfLongTermDebt" xlink:to="us-gaap_ProceedsFromIssuanceOfLongTermDebt_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_lbl" xml:lang="en-US">Equity rollover consideration</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:to="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_UseOfEstimates" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_UseOfEstimates"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_UseOfEstimates_lbl" xml:lang="en-US">Use of Estimates</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_UseOfEstimates" xlink:to="us-gaap_UseOfEstimates_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RevenueRecognitionPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueRecognitionPolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RevenueRecognitionPolicyTextBlock_lbl" xml:lang="en-US">Revenue Recognition</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenueRecognitionPolicyTextBlock" xlink:to="us-gaap_RevenueRecognitionPolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CostOfSalesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CostOfSalesPolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CostOfSalesPolicyTextBlock_lbl" xml:lang="en-US">Cost of Revenue</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CostOfSalesPolicyTextBlock" xlink:to="us-gaap_CostOfSalesPolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TradeAndOtherAccountsReceivablePolicy"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_TradeAndOtherAccountsReceivablePolicy_lbl" xml:lang="en-US">Accounts Receivable, net and Allowance for Expected Credit Losses</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:to="us-gaap_TradeAndOtherAccountsReceivablePolicy_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsPolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CashAndCashEquivalentsPolicyTextBlock_lbl" xml:lang="en-US">Cash and Cash Equivalents</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:to="us-gaap_CashAndCashEquivalentsPolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ConcentrationRiskCreditRisk" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskCreditRisk"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ConcentrationRiskCreditRisk_lbl" xml:lang="en-US">Concentration of Credit and Customer Risk</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskCreditRisk" xlink:to="us-gaap_ConcentrationRiskCreditRisk_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InventoryPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InventoryPolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InventoryPolicyTextBlock_lbl" xml:lang="en-US">Inventories and Other Inventories</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryPolicyTextBlock" xlink:to="us-gaap_InventoryPolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentPolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_lbl" xml:lang="en-US">Plant, Property and Equipment, Net</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:to="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LesseeLeasesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeLeasesPolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_LesseeLeasesPolicyTextBlock_lbl" xml:lang="en-US">Leases</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeLeasesPolicyTextBlock" xlink:to="us-gaap_LesseeLeasesPolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_DebtIssuanceCostsPolicyTextBlock" xlink:href="logc-20260226.xsd#logc_DebtIssuanceCostsPolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_DebtIssuanceCostsPolicyTextBlock_lbl" xml:lang="en-US">Debt Issuance Costs</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_DebtIssuanceCostsPolicyTextBlock" xlink:to="logc_DebtIssuanceCostsPolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_EnvironmentalCostsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EnvironmentalCostsPolicy"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EnvironmentalCostsPolicy_lbl" xml:lang="en-US">Environmental Cost</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EnvironmentalCostsPolicy" xlink:to="us-gaap_EnvironmentalCostsPolicy_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AssetRetirementObligationsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetRetirementObligationsPolicy"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AssetRetirementObligationsPolicy_lbl" xml:lang="en-US">Asset Retirement Obligations</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligationsPolicy" xlink:to="us-gaap_AssetRetirementObligationsPolicy_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IntangibleAssetsFiniteLivedPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IntangibleAssetsFiniteLivedPolicy"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IntangibleAssetsFiniteLivedPolicy_lbl" xml:lang="en-US">Finite-lived Intangible Assets and Long-lived Assets</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IntangibleAssetsFiniteLivedPolicy" xlink:to="us-gaap_IntangibleAssetsFiniteLivedPolicy_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_lbl" xml:lang="en-US">Goodwill</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:to="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AdvertisingCostsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdvertisingCostsPolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AdvertisingCostsPolicyTextBlock_lbl" xml:lang="en-US">Advertising Costs</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdvertisingCostsPolicyTextBlock" xlink:to="us-gaap_AdvertisingCostsPolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CompensationRelatedCostsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CompensationRelatedCostsPolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CompensationRelatedCostsPolicyTextBlock_lbl" xml:lang="en-US">Unit-based Compensation</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CompensationRelatedCostsPolicyTextBlock" xlink:to="us-gaap_CompensationRelatedCostsPolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ReceivablesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReceivablesPolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ReceivablesPolicyTextBlock_lbl" xml:lang="en-US">Subscription Note Receivable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ReceivablesPolicyTextBlock" xlink:to="us-gaap_ReceivablesPolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_NoncontrollingParentInterestPolicyTextBlock" xlink:href="logc-20260226.xsd#logc_NoncontrollingParentInterestPolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_NoncontrollingParentInterestPolicyTextBlock_lbl" xml:lang="en-US">Noncontrolling Parent Interest</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_NoncontrollingParentInterestPolicyTextBlock" xlink:to="logc_NoncontrollingParentInterestPolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_EarningsPerSharePolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerSharePolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_EarningsPerSharePolicyTextBlock_lbl" xml:lang="en-US">Earnings per Unit (EPU)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerSharePolicyTextBlock" xlink:to="us-gaap_EarningsPerSharePolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncomeTaxPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxPolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_IncomeTaxPolicyTextBlock_lbl" xml:lang="en-US">Income Taxes</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxPolicyTextBlock" xlink:to="us-gaap_IncomeTaxPolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_lbl" xml:lang="en-US">Foreign Currency Transactions</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:to="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingPolicyPolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SegmentReportingPolicyPolicyTextBlock_lbl" xml:lang="en-US">Segment</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:to="us-gaap_SegmentReportingPolicyPolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xml:lang="en-US">Recent Accounting Pronouncements</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_USSaltHoldingsLLCMember" xlink:href="logc-20260226.xsd#logc_USSaltHoldingsLLCMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_USSaltHoldingsLLCMember_lbl" xml:lang="en-US">US Salt Holdings LLC [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_USSaltHoldingsLLCMember" xlink:to="logc_USSaltHoldingsLLCMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_USSaltLLCMember" xlink:href="logc-20260226.xsd#logc_USSaltLLCMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_USSaltLLCMember_lbl" xml:lang="en-US">US Salt, LLC [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_USSaltLLCMember" xlink:to="logc_USSaltLLCMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_EmeraldLakeCapitalLPMember" xlink:href="logc-20260226.xsd#logc_EmeraldLakeCapitalLPMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_EmeraldLakeCapitalLPMember_lbl" xml:lang="en-US">Emerald Lake Capital LP [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_EmeraldLakeCapitalLPMember" xlink:to="logc_EmeraldLakeCapitalLPMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_USSaltParentHoldingsMember" xlink:href="logc-20260226.xsd#logc_USSaltParentHoldingsMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_USSaltParentHoldingsMember_lbl" xml:lang="en-US">US Salt Parent Holdings [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_USSaltParentHoldingsMember" xlink:to="logc_USSaltParentHoldingsMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_ParentHoldingsAndAggregatorMember" xlink:href="logc-20260226.xsd#logc_ParentHoldingsAndAggregatorMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_ParentHoldingsAndAggregatorMember_lbl" xml:lang="en-US">Parent Holdings and Aggregator [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ParentHoldingsAndAggregatorMember" xlink:to="logc_ParentHoldingsAndAggregatorMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_IntermediateHoldingsMember" xlink:href="logc-20260226.xsd#logc_IntermediateHoldingsMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_IntermediateHoldingsMember_lbl" xml:lang="en-US">Intermediate Holdings [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_IntermediateHoldingsMember" xlink:to="logc_IntermediateHoldingsMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ShippingAndHandlingMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShippingAndHandlingMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShippingAndHandlingMember_lbl" xml:lang="en-US">Shipping and Handling [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShippingAndHandlingMember" xlink:to="us-gaap_ShippingAndHandlingMember_lbl"/>
    <loc xlink:type="locator" xlink:label="srt_NorthAmericaMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_NorthAmericaMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="srt_NorthAmericaMember_lbl" xml:lang="en-US">North America [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_NorthAmericaMember" xlink:to="srt_NorthAmericaMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SalesRevenueNetMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SalesRevenueNetMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SalesRevenueNetMember_lbl" xml:lang="en-US">Revenue Benchmark [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SalesRevenueNetMember" xlink:to="us-gaap_SalesRevenueNetMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RevenueFromRightsConcentrationRiskMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromRightsConcentrationRiskMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RevenueFromRightsConcentrationRiskMember_lbl" xml:lang="en-US">Revenue from Rights Concentration Risk [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenueFromRightsConcentrationRiskMember" xlink:to="us-gaap_RevenueFromRightsConcentrationRiskMember_lbl"/>
    <loc xlink:type="locator" xlink:label="country_US" xlink:href="https://xbrl.sec.gov/country/2026/country-2026.xsd#country_US"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="country_US_lbl" xml:lang="en-US">UNITED STATES</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="country_US" xlink:to="country_US_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AccountsReceivableMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_AccountsReceivableMember_lbl" xml:lang="en-US">Accounts Receivable [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableMember" xlink:to="us-gaap_AccountsReceivableMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CustomerConcentrationRiskMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CustomerConcentrationRiskMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CustomerConcentrationRiskMember_lbl" xml:lang="en-US">Customer Concentration Risk [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CustomerConcentrationRiskMember" xlink:to="us-gaap_CustomerConcentrationRiskMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_Customer1Member" xlink:href="logc-20260226.xsd#logc_Customer1Member"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_Customer1Member_lbl" xml:lang="en-US">Customer 1 [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_Customer1Member" xlink:to="logc_Customer1Member_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_USSaltIntermediateHoldingsLLCMember" xlink:href="logc-20260226.xsd#logc_USSaltIntermediateHoldingsLLCMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_USSaltIntermediateHoldingsLLCMember_lbl" xml:lang="en-US">US Salt Intermediate Holdings, LLC [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_USSaltIntermediateHoldingsLLCMember" xlink:to="logc_USSaltIntermediateHoldingsLLCMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_TermLoanMember" xlink:href="logc-20260226.xsd#logc_TermLoanMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_TermLoanMember_lbl" xml:lang="en-US">Term Loan [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_TermLoanMember" xlink:to="logc_TermLoanMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_AresCapitalCreditAgreementMember" xlink:href="logc-20260226.xsd#logc_AresCapitalCreditAgreementMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_AresCapitalCreditAgreementMember_lbl" xml:lang="en-US">Ares Capital Credit Agreement [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_AresCapitalCreditAgreementMember" xlink:to="logc_AresCapitalCreditAgreementMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RevolvingCreditFacilityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevolvingCreditFacilityMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_RevolvingCreditFacilityMember_lbl" xml:lang="en-US">Revolving Credit Facility [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevolvingCreditFacilityMember" xlink:to="us-gaap_RevolvingCreditFacilityMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember_lbl" xml:lang="en-US">Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember" xlink:to="us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PrimeRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrimeRateMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_PrimeRateMember_lbl" xml:lang="en-US">Prime Rate [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PrimeRateMember" xlink:to="us-gaap_PrimeRateMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_NewYorkFederalReserveBankRateMember" xlink:href="logc-20260226.xsd#logc_NewYorkFederalReserveBankRateMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_NewYorkFederalReserveBankRateMember_lbl" xml:lang="en-US">New York Federal Reserve Bank Rate [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_NewYorkFederalReserveBankRateMember" xlink:to="logc_NewYorkFederalReserveBankRateMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestRateFloorMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestRateFloorMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_InterestRateFloorMember_lbl" xml:lang="en-US">Interest Rate Floor [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestRateFloorMember" xlink:to="us-gaap_InterestRateFloorMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_USPHClassBUnitsMember" xlink:href="logc-20260226.xsd#logc_USPHClassBUnitsMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_USPHClassBUnitsMember_lbl" xml:lang="en-US">USPH Class B Units [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_USPHClassBUnitsMember" xlink:to="logc_USPHClassBUnitsMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_ServiceBasedVestingMember" xlink:href="logc-20260226.xsd#logc_ServiceBasedVestingMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_ServiceBasedVestingMember_lbl" xml:lang="en-US">Service Based Vesting [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ServiceBasedVestingMember" xlink:to="logc_ServiceBasedVestingMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_ServiceAndPerformanceBasedVestingMember" xlink:href="logc-20260226.xsd#logc_ServiceAndPerformanceBasedVestingMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_ServiceAndPerformanceBasedVestingMember_lbl" xml:lang="en-US">Service and Performance Based Vesting [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ServiceAndPerformanceBasedVestingMember" xlink:to="logc_ServiceAndPerformanceBasedVestingMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_TimeVestingIncentiveUnitsMember" xlink:href="logc-20260226.xsd#logc_TimeVestingIncentiveUnitsMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_TimeVestingIncentiveUnitsMember_lbl" xml:lang="en-US">Time Vesting Incentive Units [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_TimeVestingIncentiveUnitsMember" xlink:to="logc_TimeVestingIncentiveUnitsMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheTwoMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationAwardTrancheTwoMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheTwoMember_lbl" xml:lang="en-US">Share-Based Payment Arrangement, Tranche Two [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationAwardTrancheTwoMember" xlink:to="us-gaap_ShareBasedCompensationAwardTrancheTwoMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheThreeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationAwardTrancheThreeMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheThreeMember_lbl" xml:lang="en-US">Share-Based Payment Arrangement, Tranche Three [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationAwardTrancheThreeMember" xlink:to="us-gaap_ShareBasedCompensationAwardTrancheThreeMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_EmeraldLakeMember" xlink:href="logc-20260226.xsd#logc_EmeraldLakeMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_EmeraldLakeMember_lbl" xml:lang="en-US">Emerald Lake [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_EmeraldLakeMember" xlink:to="logc_EmeraldLakeMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_ProfitSharingPlanMember" xlink:href="logc-20260226.xsd#logc_ProfitSharingPlanMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_ProfitSharingPlanMember_lbl" xml:lang="en-US">Profit Sharing Plan [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ProfitSharingPlanMember" xlink:to="logc_ProfitSharingPlanMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_ProfessionalServicesAgreementMember" xlink:href="logc-20260226.xsd#logc_ProfessionalServicesAgreementMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_ProfessionalServicesAgreementMember_lbl" xml:lang="en-US">Professional Services Agreement [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ProfessionalServicesAgreementMember" xlink:to="logc_ProfessionalServicesAgreementMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CapitalAdditionsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CapitalAdditionsMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="us-gaap_CapitalAdditionsMember_lbl" xml:lang="en-US">Capital Addition Purchase Commitments [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CapitalAdditionsMember" xlink:to="us-gaap_CapitalAdditionsMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_CustomerOneMember" xlink:href="logc-20260226.xsd#logc_CustomerOneMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_CustomerOneMember_lbl" xml:lang="en-US">Customer One [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_CustomerOneMember" xlink:to="logc_CustomerOneMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_RightsOfferingMember" xlink:href="logc-20260226.xsd#logc_RightsOfferingMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_RightsOfferingMember_lbl" xml:lang="en-US">Rights Offering [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RightsOfferingMember" xlink:to="logc_RightsOfferingMember_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_ContextLogicMember" xlink:href="logc-20260226.xsd#logc_ContextLogicMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:label="logc_ContextLogicMember_lbl" xml:lang="en-US">ContextLogic [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ContextLogicMember" xlink:to="logc_ContextLogicMember_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ClassOfStockDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ClassOfStockDomain_lbl" xml:lang="en-US">Class of Stock [Domain]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="us-gaap_ClassOfStockDomain_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementTable"/>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementLineItems_lbl" xml:lang="en-US">Statement [Line Items]</label>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EquityComponentDomain" xlink:to="us-gaap_EquityComponentDomain_lbl"/>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_RangeMember_lbl" xml:lang="en-US">Statistical Measurement [Domain]</label>
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    <loc xlink:type="locator" xlink:label="logc_SignificantaccountingpoliciesScheduleofEstimatedUsefulLivesofPropertyPlantandEquipmentDetailsLineItems" xlink:href="logc-20260226.xsd#logc_SignificantaccountingpoliciesScheduleofEstimatedUsefulLivesofPropertyPlantandEquipmentDetailsLineItems"/>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_SignificantaccountingpoliciesScheduleofEstimatedUsefulLivesofPropertyPlantandEquipmentDetailsLineItems" xlink:to="logc_SignificantaccountingpoliciesScheduleofEstimatedUsefulLivesofPropertyPlantandEquipmentDetailsLineItems_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfPropertyPlantAndEquipmentTable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" xml:lang="en-US">Property, Plant, and Equipment [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:to="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl"/>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xml:lang="en-US">Property, Plant, and Equipment [Line Items]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentLineItems" xlink:to="us-gaap_PropertyPlantAndEquipmentLineItems_lbl"/>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_StatementOfIncomeLocationDomainDomain" xlink:to="logc_StatementOfIncomeLocationDomainDomain_lbl"/>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_PlantpropertyandequipmentnetScheduleofDepreciationandDepletionExpenseIncludedinStatementsofOperationsDetailsTable_lbl" xml:lang="en-US">Plant, property and equipment, net - Schedule of Depreciation and Depletion Expense Included in Statements of Operations (Details) [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PlantpropertyandequipmentnetScheduleofDepreciationandDepletionExpenseIncludedinStatementsofOperationsDetailsTable" xlink:to="logc_PlantpropertyandequipmentnetScheduleofDepreciationandDepletionExpenseIncludedinStatementsofOperationsDetailsTable_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_PlantpropertyandequipmentnetScheduleofDepreciationandDepletionExpenseIncludedinStatementsofOperationsDetailsLineItems" xlink:href="logc-20260226.xsd#logc_PlantpropertyandequipmentnetScheduleofDepreciationandDepletionExpenseIncludedinStatementsofOperationsDetailsLineItems"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_PlantpropertyandequipmentnetScheduleofDepreciationandDepletionExpenseIncludedinStatementsofOperationsDetailsLineItems_lbl" xml:lang="en-US">Plant, property and equipment, net - Schedule of Depreciation and Depletion Expense Included in Statements of Operations (Details) [Line Items]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PlantpropertyandequipmentnetScheduleofDepreciationandDepletionExpenseIncludedinStatementsofOperationsDetailsLineItems" xlink:to="logc_PlantpropertyandequipmentnetScheduleofDepreciationandDepletionExpenseIncludedinStatementsofOperationsDetailsLineItems_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain_lbl" xml:lang="en-US">Intangible Asset, Indefinite-Lived, Class [Domain]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:to="us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_GoodwillandIntangibleassetsScheduleofIntangibleAssetsandRelatedAccumulatedAmortizationwhichareincludedinIntangibleAssetsNetDetailsTable" xlink:href="logc-20260226.xsd#logc_GoodwillandIntangibleassetsScheduleofIntangibleAssetsandRelatedAccumulatedAmortizationwhichareincludedinIntangibleAssetsNetDetailsTable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_GoodwillandIntangibleassetsScheduleofIntangibleAssetsandRelatedAccumulatedAmortizationwhichareincludedinIntangibleAssetsNetDetailsTable_lbl" xml:lang="en-US">Goodwill and Intangible assets - Schedule of Intangible Assets and Related Accumulated Amortization which are included in Intangible Assets, Net (Details) [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_GoodwillandIntangibleassetsScheduleofIntangibleAssetsandRelatedAccumulatedAmortizationwhichareincludedinIntangibleAssetsNetDetailsTable" xlink:to="logc_GoodwillandIntangibleassetsScheduleofIntangibleAssetsandRelatedAccumulatedAmortizationwhichareincludedinIntangibleAssetsNetDetailsTable_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_GoodwillandIntangibleassetsScheduleofIntangibleAssetsandRelatedAccumulatedAmortizationwhichareincludedinIntangibleAssetsNetDetailsLineItems" xlink:href="logc-20260226.xsd#logc_GoodwillandIntangibleassetsScheduleofIntangibleAssetsandRelatedAccumulatedAmortizationwhichareincludedinIntangibleAssetsNetDetailsLineItems"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_GoodwillandIntangibleassetsScheduleofIntangibleAssetsandRelatedAccumulatedAmortizationwhichareincludedinIntangibleAssetsNetDetailsLineItems_lbl" xml:lang="en-US">Goodwill and Intangible assets - Schedule of Intangible Assets and Related Accumulated Amortization which are included in Intangible Assets, Net (Details) [Line Items]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_GoodwillandIntangibleassetsScheduleofIntangibleAssetsandRelatedAccumulatedAmortizationwhichareincludedinIntangibleAssetsNetDetailsLineItems" xlink:to="logc_GoodwillandIntangibleassetsScheduleofIntangibleAssetsandRelatedAccumulatedAmortizationwhichareincludedinIntangibleAssetsNetDetailsLineItems_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember_lbl" xml:lang="en-US">Cash and Cash Equivalents [Domain]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember" xlink:to="us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember_lbl"/>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfCashAndCashEquivalentsTable_lbl" xml:lang="en-US">Cash and Cash Equivalent [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfCashAndCashEquivalentsTable" xlink:to="us-gaap_ScheduleOfCashAndCashEquivalentsTable_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CashAndCashEquivalentsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsLineItems"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashAndCashEquivalentsLineItems_lbl" xml:lang="en-US">Cash and Cash Equivalents [Line Items]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashAndCashEquivalentsLineItems" xlink:to="us-gaap_CashAndCashEquivalentsLineItems_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_BusinessAcquisitionAcquireeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessAcquisitionAcquireeDomain_lbl" xml:lang="en-US">Business Combination [Domain]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessAcquisitionAcquireeDomain" xlink:to="us-gaap_BusinessAcquisitionAcquireeDomain_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_lbl" xml:lang="en-US">Related Party Transaction [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_lbl"/>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionLineItems_lbl" xml:lang="en-US">Related Party Transaction [Line Items]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_RelatedPartyTransactionLineItems_lbl"/>
    <loc xlink:type="locator" xlink:label="srt_OwnershipDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_OwnershipDomain"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_OwnershipDomain_lbl" xml:lang="en-US">Ownership [Domain]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_OwnershipDomain" xlink:to="srt_OwnershipDomain_lbl"/>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_NatureofoperationsandbasisofpresentationDetailsTable_lbl" xml:lang="en-US">Nature of operations and basis of presentation (Details) [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_NatureofoperationsandbasisofpresentationDetailsTable" xlink:to="logc_NatureofoperationsandbasisofpresentationDetailsTable_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_NatureofoperationsandbasisofpresentationDetailsLineItems" xlink:href="logc-20260226.xsd#logc_NatureofoperationsandbasisofpresentationDetailsLineItems"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_NatureofoperationsandbasisofpresentationDetailsLineItems_lbl" xml:lang="en-US">Nature of operations and basis of presentation (Details) [Line Items]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_NatureofoperationsandbasisofpresentationDetailsLineItems" xlink:to="logc_NatureofoperationsandbasisofpresentationDetailsLineItems_lbl"/>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_SegmentGeographicalDomain_lbl" xml:lang="en-US">Geographical [Domain]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_SegmentGeographicalDomain" xlink:to="srt_SegmentGeographicalDomain_lbl"/>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_ProductsAndServicesDomain_lbl" xml:lang="en-US">Product and Service [Domain]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_ProductsAndServicesDomain" xlink:to="srt_ProductsAndServicesDomain_lbl"/>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskTypeDomain" xlink:to="us-gaap_ConcentrationRiskTypeDomain_lbl"/>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_NameOfMajorCustomerDomain" xlink:to="srt_NameOfMajorCustomerDomain_lbl"/>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskBenchmarkDomain" xlink:to="us-gaap_ConcentrationRiskBenchmarkDomain_lbl"/>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_SignificantaccountingpoliciesDetailsTable_lbl" xml:lang="en-US">Significant accounting policies (Details) [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_SignificantaccountingpoliciesDetailsTable" xlink:to="logc_SignificantaccountingpoliciesDetailsTable_lbl"/>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_SignificantaccountingpoliciesDetailsLineItems_lbl" xml:lang="en-US">Significant accounting policies (Details) [Line Items]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_SignificantaccountingpoliciesDetailsLineItems" xlink:to="logc_SignificantaccountingpoliciesDetailsLineItems_lbl"/>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CreditFacilityDomain" xlink:to="us-gaap_CreditFacilityDomain_lbl"/>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_VariableRateDomain" xlink:to="us-gaap_VariableRateDomain_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentNameDomain_lbl" xml:lang="en-US">Debt Instrument, Name [Domain]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentNameDomain" xlink:to="us-gaap_DebtInstrumentNameDomain_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_LongtermdebtDetailsTable" xlink:href="logc-20260226.xsd#logc_LongtermdebtDetailsTable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_LongtermdebtDetailsTable_lbl" xml:lang="en-US">Long-term debt (Details) [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_LongtermdebtDetailsTable" xlink:to="logc_LongtermdebtDetailsTable_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_LongtermdebtDetailsLineItems" xlink:href="logc-20260226.xsd#logc_LongtermdebtDetailsLineItems"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_LongtermdebtDetailsLineItems_lbl" xml:lang="en-US">Long-term debt (Details) [Line Items]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_LongtermdebtDetailsLineItems" xlink:to="logc_LongtermdebtDetailsLineItems_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_VestingDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VestingDomain"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_VestingDomain_lbl" xml:lang="en-US">Vesting [Domain]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_VestingDomain" xlink:to="us-gaap_VestingDomain_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_MembersequityDetailsTable" xlink:href="logc-20260226.xsd#logc_MembersequityDetailsTable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_MembersequityDetailsTable_lbl" xml:lang="en-US">Members&apos; equity (Details) [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_MembersequityDetailsTable" xlink:to="logc_MembersequityDetailsTable_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_MembersequityDetailsLineItems" xlink:href="logc-20260226.xsd#logc_MembersequityDetailsLineItems"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_MembersequityDetailsLineItems_lbl" xml:lang="en-US">Members&apos; equity (Details) [Line Items]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_MembersequityDetailsLineItems" xlink:to="logc_MembersequityDetailsLineItems_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PlanNameDomain"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PlanNameDomain_lbl" xml:lang="en-US">Plan Name [Domain]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PlanNameDomain" xlink:to="us-gaap_PlanNameDomain_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_RetirementplanDetailsTable" xlink:href="logc-20260226.xsd#logc_RetirementplanDetailsTable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_RetirementplanDetailsTable_lbl" xml:lang="en-US">Retirement plan (Details) [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RetirementplanDetailsTable" xlink:to="logc_RetirementplanDetailsTable_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_RetirementplanDetailsLineItems" xlink:href="logc-20260226.xsd#logc_RetirementplanDetailsLineItems"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_RetirementplanDetailsLineItems_lbl" xml:lang="en-US">Retirement plan (Details) [Line Items]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RetirementplanDetailsLineItems" xlink:to="logc_RetirementplanDetailsLineItems_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RelatedPartyTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionDomain"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionDomain_lbl" xml:lang="en-US">Related Party Transaction [Domain]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionDomain" xlink:to="us-gaap_RelatedPartyTransactionDomain_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RelatedPartyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyDomain"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyDomain_lbl" xml:lang="en-US">Related and Nonrelated Parties [Domain]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="us-gaap_RelatedPartyDomain_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_RelatedpartytransactionDetailsTable" xlink:href="logc-20260226.xsd#logc_RelatedpartytransactionDetailsTable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_RelatedpartytransactionDetailsTable_lbl" xml:lang="en-US">Related party transaction (Details) [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RelatedpartytransactionDetailsTable" xlink:to="logc_RelatedpartytransactionDetailsTable_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_RelatedpartytransactionDetailsLineItems" xlink:href="logc-20260226.xsd#logc_RelatedpartytransactionDetailsLineItems"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_RelatedpartytransactionDetailsLineItems_lbl" xml:lang="en-US">Related party transaction (Details) [Line Items]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RelatedpartytransactionDetailsLineItems" xlink:to="logc_RelatedpartytransactionDetailsLineItems_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LongTermPurchaseCommitmentCategoryOfItemPurchasedDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermPurchaseCommitmentCategoryOfItemPurchasedDomain"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermPurchaseCommitmentCategoryOfItemPurchasedDomain_lbl" xml:lang="en-US">Long-Term Purchase Commitment, Category of Item Purchased [Domain]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermPurchaseCommitmentCategoryOfItemPurchasedDomain" xlink:to="us-gaap_LongTermPurchaseCommitmentCategoryOfItemPurchasedDomain_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_CommitmentsandContingenciesDetailsTable" xlink:href="logc-20260226.xsd#logc_CommitmentsandContingenciesDetailsTable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_CommitmentsandContingenciesDetailsTable_lbl" xml:lang="en-US">Commitments and Contingencies (Details) [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_CommitmentsandContingenciesDetailsTable" xlink:to="logc_CommitmentsandContingenciesDetailsTable_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_CommitmentsandContingenciesDetailsLineItems" xlink:href="logc-20260226.xsd#logc_CommitmentsandContingenciesDetailsLineItems"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_CommitmentsandContingenciesDetailsLineItems_lbl" xml:lang="en-US">Commitments and Contingencies (Details) [Line Items]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_CommitmentsandContingenciesDetailsLineItems" xlink:to="logc_CommitmentsandContingenciesDetailsLineItems_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_SegmentInformationDetailsTable" xlink:href="logc-20260226.xsd#logc_SegmentInformationDetailsTable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_SegmentInformationDetailsTable_lbl" xml:lang="en-US">Segment Information (Details) [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_SegmentInformationDetailsTable" xlink:to="logc_SegmentInformationDetailsTable_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_SegmentInformationDetailsLineItems" xlink:href="logc-20260226.xsd#logc_SegmentInformationDetailsLineItems"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_SegmentInformationDetailsLineItems_lbl" xml:lang="en-US">Segment Information (Details) [Line Items]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_SegmentInformationDetailsLineItems" xlink:to="logc_SegmentInformationDetailsLineItems_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockNameOfTransactionDomain"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xml:lang="en-US">Sale of Stock [Domain]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="us-gaap_SaleOfStockNameOfTransactionDomain_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_SubsequenteventsDetailsTable" xlink:href="logc-20260226.xsd#logc_SubsequenteventsDetailsTable"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_SubsequenteventsDetailsTable_lbl" xml:lang="en-US">Subsequent events (Details) [Table]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_SubsequenteventsDetailsTable" xlink:to="logc_SubsequenteventsDetailsTable_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_SubsequenteventsDetailsLineItems" xlink:href="logc-20260226.xsd#logc_SubsequenteventsDetailsLineItems"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_SubsequenteventsDetailsLineItems_lbl" xml:lang="en-US">Subsequent events (Details) [Line Items]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_SubsequenteventsDetailsLineItems" xlink:to="logc_SubsequenteventsDetailsLineItems_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_AdditionsAndChangesInAssetRetirementObligations_lbl0" xml:lang="en-US">The amount of additions and changes in asset retirement obligations.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_AdditionsAndChangesInAssetRetirementObligations" xlink:to="logc_AdditionsAndChangesInAssetRetirementObligations_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_AnnualManagementFeeMinimumAmount_lbl0" xml:lang="en-US">Annual management fee minimum amount</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_AnnualManagementFeeMinimumAmount" xlink:to="logc_AnnualManagementFeeMinimumAmount_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_CancellationOfAmountUnitsPurchasedAndCorrespondingSubscriptionNoteReceivable_lbl0" xml:lang="en-US">Cancellation of amount units purchased and corresponding subscription note receivable.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_CancellationOfAmountUnitsPurchasedAndCorrespondingSubscriptionNoteReceivable" xlink:to="logc_CancellationOfAmountUnitsPurchasedAndCorrespondingSubscriptionNoteReceivable_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_CancellationOfUnitsPurchasedAndCorrespondingSubscriptionNoteReceivable_lbl0" xml:lang="en-US">Cancellation of units purchased and corresponding subscription note receivable.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_CancellationOfUnitsPurchasedAndCorrespondingSubscriptionNoteReceivable" xlink:to="logc_CancellationOfUnitsPurchasedAndCorrespondingSubscriptionNoteReceivable_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_CancellationOfUnitsPurchasedAndTheCorrespondingSubscriptionNotesReceivable_lbl0" xml:lang="en-US">The amount of cancellation of units purchased and the corresponding subscription notes receivable.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_CancellationOfUnitsPurchasedAndTheCorrespondingSubscriptionNotesReceivable" xlink:to="logc_CancellationOfUnitsPurchasedAndTheCorrespondingSubscriptionNotesReceivable_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_CancellationOfUnitsPurchasedAndTheCorrespondingSubscriptionNotesReceivableUnits_lbl0" xml:lang="en-US">Number of cancellation of units purchased and the corresponding subscription notes receivable, units.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_CancellationOfUnitsPurchasedAndTheCorrespondingSubscriptionNotesReceivableUnits" xlink:to="logc_CancellationOfUnitsPurchasedAndTheCorrespondingSubscriptionNotesReceivableUnits_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_CollectionOfSubscriptionNoteReceivable_lbl0" xml:lang="en-US">Collection of subscription note receivable.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_CollectionOfSubscriptionNoteReceivable" xlink:to="logc_CollectionOfSubscriptionNoteReceivable_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_DebtIssuanceCostsPolicyTextBlock_lbl0" xml:lang="en-US">Disclosure of accounting policy for debt issuance costs.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_DebtIssuanceCostsPolicyTextBlock" xlink:to="logc_DebtIssuanceCostsPolicyTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_DistributionToNoncontrollingParentInterest_lbl0" xml:lang="en-US">The amount of distribution to noncontrolling parent interest.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_DistributionToNoncontrollingParentInterest" xlink:to="logc_DistributionToNoncontrollingParentInterest_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_EstimatedUsefulLivesOfPropertyPlantAndEquipmentTableTextBlock_lbl0" xml:lang="en-US">Estimated useful lives of property, plant and equipment.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_EstimatedUsefulLivesOfPropertyPlantAndEquipmentTableTextBlock" xlink:to="logc_EstimatedUsefulLivesOfPropertyPlantAndEquipmentTableTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_FairValueOfClassSharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedBUnitFairvalueofClassBunit_lbl0" xml:lang="en-US">The fair value of class b unit assumption that is used in valuing an option on its own shares.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_FairValueOfClassSharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedBUnitFairvalueofClassBunit" xlink:to="logc_FairValueOfClassSharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedBUnitFairvalueofClassBunit_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_FinanceLeaseCost_lbl0" xml:lang="en-US">Amount of finance lease cost.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_FinanceLeaseCost" xlink:to="logc_FinanceLeaseCost_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_IncomeLossAttributableToRedeemableNoncontrollingInterest_lbl0" xml:lang="en-US">Income (loss) attributable to redeemable noncontrolling interest.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_IncomeLossAttributableToRedeemableNoncontrollingInterest" xlink:to="logc_IncomeLossAttributableToRedeemableNoncontrollingInterest_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_IncreaseDecreaseInOtherInventoriesAmount_lbl0" xml:lang="en-US">The amount of increase decrease in other inventories.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_IncreaseDecreaseInOtherInventoriesAmount" xlink:to="logc_IncreaseDecreaseInOtherInventoriesAmount_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_InventoryWrittenOff_lbl0" xml:lang="en-US">Inventory written off.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_InventoryWrittenOff" xlink:to="logc_InventoryWrittenOff_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_IssuanceOfNotesReceivableFromRelatedParties_lbl0" xml:lang="en-US">The amount of issuance.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_IssuanceOfNotesReceivableFromRelatedParties" xlink:to="logc_IssuanceOfNotesReceivableFromRelatedParties_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_IssuanceOfNotesReceivableFromRelatedPartiesUnits_lbl0" xml:lang="en-US">Number of shares issuance, units.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_IssuanceOfNotesReceivableFromRelatedPartiesUnits" xlink:to="logc_IssuanceOfNotesReceivableFromRelatedPartiesUnits_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_LeasesRemainingLeaseTerm_lbl0" xml:lang="en-US">Leases remaining lease term.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_LeasesRemainingLeaseTerm" xlink:to="logc_LeasesRemainingLeaseTerm_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_LossDueToCasualty_lbl0" xml:lang="en-US">The amount of loss due to casualty.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_LossDueToCasualty" xlink:to="logc_LossDueToCasualty_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_MaintenanceMaterials_lbl0" xml:lang="en-US">Represents the amount of maintenance materials.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_MaintenanceMaterials" xlink:to="logc_MaintenanceMaterials_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_MembersEquitySubscriptionNoteReceivable_lbl0" xml:lang="en-US">Amount of member capital in equity subscription note receivable.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_MembersEquitySubscriptionNoteReceivable" xlink:to="logc_MembersEquitySubscriptionNoteReceivable_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_NoncashLeaseExpense_lbl0" xml:lang="en-US">The amount of non-cash lease expense.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_NoncashLeaseExpense" xlink:to="logc_NoncashLeaseExpense_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_NoncontrollingParentInterestPolicyTextBlock_lbl0" xml:lang="en-US">Disclosure of accounting policy for noncontrolling parent interest.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_NoncontrollingParentInterestPolicyTextBlock" xlink:to="logc_NoncontrollingParentInterestPolicyTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_NumberOfMajorCustomer_lbl0" xml:lang="en-US">Number of major customer.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_NumberOfMajorCustomer" xlink:to="logc_NumberOfMajorCustomer_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_OperationAndFinanceLeasesExpiringYear_lbl0" xml:lang="en-US">Operation and finance leases, expiring year.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_OperationAndFinanceLeasesExpiringYear" xlink:to="logc_OperationAndFinanceLeasesExpiringYear_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_PackagingAndSupplies_lbl0" xml:lang="en-US">Represents the amount of packaging and supplies.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PackagingAndSupplies" xlink:to="logc_PackagingAndSupplies_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_PaymentsForRepaymentOfPrincipalOnTermLoan_lbl0" xml:lang="en-US">The amount of repayment of principal on term loan.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PaymentsForRepaymentOfPrincipalOnTermLoan" xlink:to="logc_PaymentsForRepaymentOfPrincipalOnTermLoan_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_PaymentsOfCapitalContributions_lbl0" xml:lang="en-US">The amount of members contributions</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PaymentsOfCapitalContributions" xlink:to="logc_PaymentsOfCapitalContributions_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_PercentageOfAnnualManagementFee_lbl0" xml:lang="en-US">Percentage of annual management fee.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PercentageOfAnnualManagementFee" xlink:to="logc_PercentageOfAnnualManagementFee_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_PercentageOfNoncontrollingParentInterestRepresentedAggregator_lbl0" xml:lang="en-US">Percentage of noncontrolling parent interest represented aggregator.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PercentageOfNoncontrollingParentInterestRepresentedAggregator" xlink:to="logc_PercentageOfNoncontrollingParentInterestRepresentedAggregator_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_PercentageOfQuarterlyManagementFee_lbl0" xml:lang="en-US">Percentage of quarterly management fee.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PercentageOfQuarterlyManagementFee" xlink:to="logc_PercentageOfQuarterlyManagementFee_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_PrepaidExpensesDisclosureTextBlock_lbl0" xml:lang="en-US">The entire disclosure for prepaid expenses.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PrepaidExpensesDisclosureTextBlock" xlink:to="logc_PrepaidExpensesDisclosureTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_PrepaidHealthBenefits_lbl0" xml:lang="en-US">Prepaid health benefits.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PrepaidHealthBenefits" xlink:to="logc_PrepaidHealthBenefits_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_ProceedsFromCollectionOfSubscriptionNoteReceivable_lbl0" xml:lang="en-US">The amount of proceeds from collection of subscription note receivable.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ProceedsFromCollectionOfSubscriptionNoteReceivable" xlink:to="logc_ProceedsFromCollectionOfSubscriptionNoteReceivable_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_ProceedsFromRightsOffering_lbl0" xml:lang="en-US">Proceeds from rights offering.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ProceedsFromRightsOffering" xlink:to="logc_ProceedsFromRightsOffering_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_PropertyPlantAndEquipmentInAccountsPayable_lbl0" xml:lang="en-US">The amount of property, plant and equipment in accounts payable.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PropertyPlantAndEquipmentInAccountsPayable" xlink:to="logc_PropertyPlantAndEquipmentInAccountsPayable_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_RepaymentOfPrincipalOfFinanceLeasesObligations_lbl0" xml:lang="en-US">The amount of repayment of principal of finance leases obligations.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RepaymentOfPrincipalOfFinanceLeasesObligations" xlink:to="logc_RepaymentOfPrincipalOfFinanceLeasesObligations_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_RepaymentOfSubscriptionReceivableFromProceedsOfUnitsRepurchase_lbl0" xml:lang="en-US">The amount of repayment of subscription receivable from proceeds of units repurchase.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RepaymentOfSubscriptionReceivableFromProceedsOfUnitsRepurchase" xlink:to="logc_RepaymentOfSubscriptionReceivableFromProceedsOfUnitsRepurchase_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_RepaymentUnitsFromRelatedParties_lbl0" xml:lang="en-US">Number of repayment, units.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RepaymentUnitsFromRelatedParties" xlink:to="logc_RepaymentUnitsFromRelatedParties_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_RepurchaseOfNotesReceivableFromRelatedParties_lbl0" xml:lang="en-US">The amount of repurchase.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RepurchaseOfNotesReceivableFromRelatedParties" xlink:to="logc_RepurchaseOfNotesReceivableFromRelatedParties_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_RepurchaseUnitsFromRelatedParties_lbl0" xml:lang="en-US">Number of repurchase, units.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RepurchaseUnitsFromRelatedParties" xlink:to="logc_RepurchaseUnitsFromRelatedParties_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_RetainedEarningsAccumulatedDeficitMemberEquity_lbl0" xml:lang="en-US">Amount of member capital in retained earnings (accumulated deficit).</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RetainedEarningsAccumulatedDeficitMemberEquity" xlink:to="logc_RetainedEarningsAccumulatedDeficitMemberEquity_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_ScheduleOfDepreciationAndDepletionExpenseIncludedInStatementsOfOperationsTableTextBlock_lbl0" xml:lang="en-US">Schedule of depreciation and depletion expense included in statements of operations.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfDepreciationAndDepletionExpenseIncludedInStatementsOfOperationsTableTextBlock" xlink:to="logc_ScheduleOfDepreciationAndDepletionExpenseIncludedInStatementsOfOperationsTableTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_ScheduleOfIntangibleAssetsAndRelatedAccumulatedAmortizationTableTextBlock_lbl0" xml:lang="en-US">Tabular disclosure of intangible assets and related accumulated amortization.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfIntangibleAssetsAndRelatedAccumulatedAmortizationTableTextBlock" xlink:to="logc_ScheduleOfIntangibleAssetsAndRelatedAccumulatedAmortizationTableTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_ScheduleOfPrepaidExpensesAndOtherAssetsCurrentTableTextBlock_lbl0" xml:lang="en-US">Schedule of prepaid expenses and other assets current.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfPrepaidExpensesAndOtherAssetsCurrentTableTextBlock" xlink:to="logc_ScheduleOfPrepaidExpensesAndOtherAssetsCurrentTableTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_ScheduleOfUnrecognizedCompensationExpenseTableTextBlock_lbl0" xml:lang="en-US">Tabular disclosure of an equity-based arrangement unrecognized compensation expense.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfUnrecognizedCompensationExpenseTableTextBlock" xlink:to="logc_ScheduleOfUnrecognizedCompensationExpenseTableTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsRepurchasedWeightedAveragesExercisePrice_lbl0" xml:lang="en-US">Weighted average per share amount at which repurchased can acquire shares of common stock by exercise of options.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsRepurchasedWeightedAveragesExercisePrice" xlink:to="logc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsRepurchasedWeightedAveragesExercisePrice_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm1_lbl1" xml:lang="en-US">Weighted-average contractual term remaining for option award outstanding, in &apos;PnYnMnDTnHnMnS&apos; format, for example, &apos;P1Y5M13D&apos; represents reported fact of one year, five months, and thirteen days.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm1" xlink:to="logc_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm1_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_SuretyBondsOutstandingAmount_lbl0" xml:lang="en-US">Surety bonds outstanding amount.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_SuretyBondsOutstandingAmount" xlink:to="logc_SuretyBondsOutstandingAmount_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_TaxDistributions_lbl0" xml:lang="en-US">Represents the amount of Tax distributions.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_TaxDistributions" xlink:to="logc_TaxDistributions_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_UnrecognizedTaxBenefitDuration_lbl0" xml:lang="en-US">Unrecognized tax benefit months.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_UnrecognizedTaxBenefitDuration" xlink:to="logc_UnrecognizedTaxBenefitDuration_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_Unrecognizedcompensationexpensetotal_lbl0" xml:lang="en-US">The amount of unrecognized compensation expense.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_Unrecognizedcompensationexpensetotal" xlink:to="logc_Unrecognizedcompensationexpensetotal_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_Unrecognizedcompensationexpenseyearfour_lbl0" xml:lang="en-US">The amount of unrecognized compensation expense.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_Unrecognizedcompensationexpenseyearfour" xlink:to="logc_Unrecognizedcompensationexpenseyearfour_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_UnreturnedCapitalOfClassAUnitholdersBeforeDistributions_lbl0" xml:lang="en-US">Unreturned capital of Class A unitholders before distributions.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_UnreturnedCapitalOfClassAUnitholdersBeforeDistributions" xlink:to="logc_UnreturnedCapitalOfClassAUnitholdersBeforeDistributions_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_unrecognizedcompensationexpenseyearone_lbl0" xml:lang="en-US">The amount of unrecognized compensation expense.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_unrecognizedcompensationexpenseyearone" xlink:to="logc_unrecognizedcompensationexpenseyearone_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_unrecognizedcompensationexpenseyearthree_lbl0" xml:lang="en-US">The amount of unrecognized compensation expense.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_unrecognizedcompensationexpenseyearthree" xlink:to="logc_unrecognizedcompensationexpenseyearthree_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:label="logc_unrecognizedcompensationexpenseyeartwo_lbl0" xml:lang="en-US">The amount of unrecognized compensation expense.</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_unrecognizedcompensationexpenseyeartwo" xlink:to="logc_unrecognizedcompensationexpenseyeartwo_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_USSaltLLCMember_lbl0" xml:lang="en-US">USSalt LLCMember</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_USSaltLLCMember" xlink:to="logc_USSaltLLCMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsAbstract_lbl0" xml:lang="en-US">Assets [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsAbstract" xlink:to="us-gaap_AssetsAbstract_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_FinanceLeaseCost_lbl1" xml:lang="en-US">Finance Lease Cost</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_FinanceLeaseCost" xlink:to="logc_FinanceLeaseCost_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_SaltReservesMember_lbl0" xml:lang="en-US">Salt Reserves Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_SaltReservesMember" xlink:to="logc_SaltReservesMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PrepaidTaxes_lbl0" xml:lang="en-US">Prepaid Taxes</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PrepaidTaxes" xlink:to="us-gaap_PrepaidTaxes_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfIntangibleAssetsAndRelatedAccumulatedAmortizationTableTextBlock_lbl1" xml:lang="en-US">Schedule Of Intangible Assets And Related Accumulated Amortization Table Text Block</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfIntangibleAssetsAndRelatedAccumulatedAmortizationTableTextBlock" xlink:to="logc_ScheduleOfIntangibleAssetsAndRelatedAccumulatedAmortizationTableTextBlock_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CustomerRelationshipsMember_lbl0" xml:lang="en-US">Customer Relationships [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CustomerRelationshipsMember" xlink:to="us-gaap_CustomerRelationshipsMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EarningsPerShareDiluted_lbl1" xml:lang="en-US">Earnings Per Share, Diluted</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerShareDiluted" xlink:to="us-gaap_EarningsPerShareDiluted_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesNoncurrentAbstract_lbl0" xml:lang="en-US">Liabilities, Noncurrent [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesNoncurrentAbstract" xlink:to="us-gaap_LiabilitiesNoncurrentAbstract_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RetainedEarningsMember_lbl0" xml:lang="en-US">Retained Earnings [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RetainedEarningsMember" xlink:to="us-gaap_RetainedEarningsMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl1" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonClassBMember_lbl0" xml:lang="en-US">Common Class B [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonClassBMember" xlink:to="us-gaap_CommonClassBMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_lbl0" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Risk Free Interest Rate</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod_lbl0" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Forfeitures in Period</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_VariableLeaseCost_lbl0" xml:lang="en-US">Variable Lease, Cost</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_VariableLeaseCost" xlink:to="us-gaap_VariableLeaseCost_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1_lbl0" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Requisite Service Period</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent_lbl1" xml:lang="en-US">Finance Lease, Liability, Current</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityCurrent" xlink:to="us-gaap_FinanceLeaseLiabilityCurrent_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetRetirementObligationRevisionOfEstimate_lbl0" xml:lang="en-US">Asset Retirement Obligation, Revision of Estimate</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligationRevisionOfEstimate" xlink:to="us-gaap_AssetRetirementObligationRevisionOfEstimate_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfChangeInAssetRetirementObligationTableTextBlock_lbl0" xml:lang="en-US">Schedule of Change in Asset Retirement Obligation [Table Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfChangeInAssetRetirementObligationTableTextBlock" xlink:to="us-gaap_ScheduleOfChangeInAssetRetirementObligationTableTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFive_lbl0" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, after Year Five</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFive" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFive_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebtCurrent_lbl1" xml:lang="en-US">Long-Term Debt, Current Maturities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtCurrent" xlink:to="us-gaap_LongTermDebtCurrent_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_LocalPhoneNumber_lbl0" xml:lang="en-US">Local Phone Number</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_LocalPhoneNumber" xlink:to="dei_LocalPhoneNumber_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_PaymentsForRepaymentOfPrincipalOnTermLoan_lbl1" xml:lang="en-US">Payments For Repayment Of Principal On Term Loan</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PaymentsForRepaymentOfPrincipalOnTermLoan" xlink:to="logc_PaymentsForRepaymentOfPrincipalOnTermLoan_lbl1"/>
    <loc xlink:type="locator" xlink:label="logc_PrepaidExpensesDisclosureAbstract" xlink:href="logc-20260226.xsd#logc_PrepaidExpensesDisclosureAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_PrepaidExpensesDisclosureAbstract_lbl" xml:lang="en-US">Prepaid Expenses Disclosure Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PrepaidExpensesDisclosureAbstract" xlink:to="logc_PrepaidExpensesDisclosureAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_NoncashLeaseExpense_lbl1" xml:lang="en-US">Noncash Lease Expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_NoncashLeaseExpense" xlink:to="logc_NoncashLeaseExpense_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1_lbl0" xml:lang="en-US">Intangible Asset, Finite-Lived, Remaining Amortization Period</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1" xlink:to="us-gaap_FiniteLivedIntangibleAssetsRemainingAmortizationPeriod1_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_lbl0" xml:lang="en-US">Line of Credit Facility, Unused Capacity, Commitment Fee Percentage</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:to="us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_lbl0"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfClassBUnitsActivityAbstract" xlink:href="logc-20260226.xsd#logc_ScheduleOfClassBUnitsActivityAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfClassBUnitsActivityAbstract_lbl" xml:lang="en-US">Schedule Of Class BUnits Activity Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfClassBUnitsActivityAbstract" xlink:to="logc_ScheduleOfClassBUnitsActivityAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_lbl0" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Year Two</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_CancellationOfUnitsPurchasedAndCorrespondingSubscriptionNoteReceivable_lbl1" xml:lang="en-US">Cancellation Of Units Purchased And Corresponding Subscription Note Receivable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_CancellationOfUnitsPurchasedAndCorrespondingSubscriptionNoteReceivable" xlink:to="logc_CancellationOfUnitsPurchasedAndCorrespondingSubscriptionNoteReceivable_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherInventoryNoncurrent_lbl0" xml:lang="en-US">Other Inventory, Noncurrent</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherInventoryNoncurrent" xlink:to="us-gaap_OtherInventoryNoncurrent_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsNoncurrent_lbl0" xml:lang="en-US">Assets, Noncurrent</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsNoncurrent" xlink:to="us-gaap_AssetsNoncurrent_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_MembersEquitySubscriptionNoteReceivable_lbl1" xml:lang="en-US">Members Equity Subscription Note Receivable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_MembersEquitySubscriptionNoteReceivable" xlink:to="logc_MembersEquitySubscriptionNoteReceivable_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_OperatingLeaseExpenseAbstract_lbl0" xml:lang="en-US">Operating Lease Expense Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_OperatingLeaseExpenseAbstract" xlink:to="logc_OperatingLeaseExpenseAbstract_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_Security12bTitle_lbl0" xml:lang="en-US">Title of 12(b) Security</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_Security12bTitle" xlink:to="dei_Security12bTitle_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl0" xml:lang="en-US">Segment Reporting [Table Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:to="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_RightsOfferingMember_lbl0" xml:lang="en-US">Rights Offering Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RightsOfferingMember" xlink:to="logc_RightsOfferingMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract_lbl0" xml:lang="en-US">Supplemental Cash Flow Information [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SupplementalCashFlowInformationAbstract" xlink:to="us-gaap_SupplementalCashFlowInformationAbstract_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PartnersCapitalAccountUnitsUnitbasedCompensation_lbl0" xml:lang="en-US">Partners&apos; Capital Account, Unit-Based Payment Arrangement, Number of Units</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PartnersCapitalAccountUnitsUnitbasedCompensation" xlink:to="us-gaap_PartnersCapitalAccountUnitsUnitbasedCompensation_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PrepaidExpenseCurrent_lbl1" xml:lang="en-US">Prepaid Expense, Current</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PrepaidExpenseCurrent" xlink:to="us-gaap_PrepaidExpenseCurrent_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_SolicitingMaterial_lbl0" xml:lang="en-US">Soliciting Material</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_SolicitingMaterial" xlink:to="dei_SolicitingMaterial_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConstructionInProgressMember_lbl0" xml:lang="en-US">Construction in Progress [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConstructionInProgressMember" xlink:to="us-gaap_ConstructionInProgressMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ServiceBasedVestingMember_lbl0" xml:lang="en-US">Service Based Vesting Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ServiceBasedVestingMember" xlink:to="logc_ServiceBasedVestingMember_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InventoryDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InventoryDisclosureAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InventoryDisclosureAbstract_lbl" xml:lang="en-US">Inventory Disclosure [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryDisclosureAbstract" xlink:to="us-gaap_InventoryDisclosureAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl0" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_LossDueToCasualty_lbl1" xml:lang="en-US">Loss Due To Casualty</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_LossDueToCasualty" xlink:to="logc_LossDueToCasualty_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl0" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PrepaidInsurance_lbl0" xml:lang="en-US">Prepaid Insurance</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PrepaidInsurance" xlink:to="us-gaap_PrepaidInsurance_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PartnersCapitalAccountTreasuryUnitsPurchases_lbl0" xml:lang="en-US">Partners&apos; Capital Account, Treasury Units, Purchased</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PartnersCapitalAccountTreasuryUnitsPurchases" xlink:to="us-gaap_PartnersCapitalAccountTreasuryUnitsPurchases_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashAndCashEquivalentsFairValueDisclosure_lbl0" xml:lang="en-US">Cash and Cash Equivalents, Fair Value Disclosure</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:to="us-gaap_CashAndCashEquivalentsFairValueDisclosure_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Depreciation_lbl0" xml:lang="en-US">Depreciation</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Depreciation" xlink:to="us-gaap_Depreciation_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl0" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Three</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_MinimumMember_lbl0" xml:lang="en-US">Minimum [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MinimumMember" xlink:to="srt_MinimumMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_WeightedAverageDiscountRateAbstract_lbl0" xml:lang="en-US">Weighted Average Discount Rate Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_WeightedAverageDiscountRateAbstract" xlink:to="logc_WeightedAverageDiscountRateAbstract_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProceedsFromIssuanceOfLongTermDebt_lbl0" xml:lang="en-US">Proceeds from Issuance of Long-Term Debt</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProceedsFromIssuanceOfLongTermDebt" xlink:to="us-gaap_ProceedsFromIssuanceOfLongTermDebt_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ParentHoldingsAndAggregatorMember_lbl0" xml:lang="en-US">Parent Holdings And Aggregator Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ParentHoldingsAndAggregatorMember" xlink:to="logc_ParentHoldingsAndAggregatorMember_lbl0"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfCashAndCashEquivalentsAbstract" xlink:href="logc-20260226.xsd#logc_ScheduleOfCashAndCashEquivalentsAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfCashAndCashEquivalentsAbstract_lbl" xml:lang="en-US">Schedule Of Cash And Cash Equivalents Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfCashAndCashEquivalentsAbstract" xlink:to="logc_ScheduleOfCashAndCashEquivalentsAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InventoryFinishedGoods_lbl0" xml:lang="en-US">Inventory, Finished Goods, Gross</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryFinishedGoods" xlink:to="us-gaap_InventoryFinishedGoods_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_RepurchaseUnitsFromRelatedParties_lbl1" xml:lang="en-US">Repurchase Units From Related Parties</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RepurchaseUnitsFromRelatedParties" xlink:to="logc_RepurchaseUnitsFromRelatedParties_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl1" xml:lang="en-US">Payments to Acquire Property, Plant, and Equipment</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:to="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseRightOfUseAssetAmortization_lbl0" xml:lang="en-US">Finance Lease, Right-of-Use Asset, Amortization</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseRightOfUseAssetAmortization" xlink:to="us-gaap_FinanceLeaseRightOfUseAssetAmortization_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_IncomeLossAttributableToRedeemableNoncontrollingInterest_lbl1" xml:lang="en-US">Income Loss Attributable To Redeemable Noncontrolling Interest</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_IncomeLossAttributableToRedeemableNoncontrollingInterest" xlink:to="logc_IncomeLossAttributableToRedeemableNoncontrollingInterest_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TradeNamesMember_lbl0" xml:lang="en-US">Trade Names [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TradeNamesMember" xlink:to="us-gaap_TradeNamesMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestPaidNet_lbl0" xml:lang="en-US">Interest Paid, Excluding Capitalized Interest, Operating Activity</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestPaidNet" xlink:to="us-gaap_InterestPaidNet_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InventoryDisclosureTextBlock_lbl0" xml:lang="en-US">Inventory Disclosure [Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryDisclosureTextBlock" xlink:to="us-gaap_InventoryDisclosureTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="country_US_lbl0" xml:lang="en-US">UNITED STATES</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="country_US" xlink:to="country_US_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PartnersCapitalAccountContributions_lbl0" xml:lang="en-US">Partners&apos; Capital Account, Contributions</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PartnersCapitalAccountContributions" xlink:to="us-gaap_PartnersCapitalAccountContributions_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl1" xml:lang="en-US">Property, Plant, and Equipment, after Accumulated Depreciation, Depletion, and Amortization</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentNet" xlink:to="us-gaap_PropertyPlantAndEquipmentNet_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_FinanceLeaseExpenseAbstract_lbl0" xml:lang="en-US">Finance Lease Expense Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_FinanceLeaseExpenseAbstract" xlink:to="logc_FinanceLeaseExpenseAbstract_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MembersEquity_lbl0" xml:lang="en-US">Members&apos; Equity</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MembersEquity" xlink:to="us-gaap_MembersEquity_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilities_lbl0" xml:lang="en-US">Increase (Decrease) in Accrued Liabilities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInAccruedLiabilities" xlink:to="us-gaap_IncreaseDecreaseInAccruedLiabilities_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityIncorporationStateCountryCode_lbl0" xml:lang="en-US">Entity Incorporation, State or Country Code</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityIncorporationStateCountryCode" xlink:to="dei_EntityIncorporationStateCountryCode_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityAddressAddressLine1_lbl0" xml:lang="en-US">Entity Address, Address Line One</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressAddressLine1" xlink:to="dei_EntityAddressAddressLine1_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_RetainedEarningsAccumulatedDeficitMemberEquity_lbl1" xml:lang="en-US">Retained Earnings Accumulated Deficit Member Equity</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RetainedEarningsAccumulatedDeficitMemberEquity" xlink:to="logc_RetainedEarningsAccumulatedDeficitMemberEquity_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_MaximumMember_lbl0" xml:lang="en-US">Maximum [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_MaximumMember" xlink:to="srt_MaximumMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeTaxPolicyTextBlock_lbl0" xml:lang="en-US">Income Tax, Policy [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeTaxPolicyTextBlock" xlink:to="us-gaap_IncomeTaxPolicyTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityAddressAddressLine2_lbl0" xml:lang="en-US">Entity Address, Address Line Two</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressAddressLine2" xlink:to="dei_EntityAddressAddressLine2_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_lbl0" xml:lang="en-US">Right-of-Use Asset Obtained in Exchange for Operating Lease Liability</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:to="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl0" xml:lang="en-US">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Increase (Decrease) in Operating Capital [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:to="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MemberUnitsMember_lbl0" xml:lang="en-US">Member Units [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MemberUnitsMember" xlink:to="us-gaap_MemberUnitsMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_TradeAndOtherAccountsReceivablePolicy_lbl0" xml:lang="en-US">Accounts Receivable [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:to="us-gaap_TradeAndOtherAccountsReceivablePolicy_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl1" xml:lang="en-US">Operating Lease, Liability, Noncurrent</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:to="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentPeriodicPaymentPrincipal_lbl0" xml:lang="en-US">Debt Instrument, Periodic Payment, Principal</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentPeriodicPaymentPrincipal" xlink:to="us-gaap_DebtInstrumentPeriodicPaymentPrincipal_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent_lbl0" xml:lang="en-US">Other Accrued Liabilities, Current</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherAccruedLiabilitiesCurrent" xlink:to="us-gaap_OtherAccruedLiabilitiesCurrent_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_lbl0" xml:lang="en-US">Operating Lease, Weighted Average Discount Rate, Percent</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:to="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfUnrecognizedCompensationExpenseTableTextBlock_lbl1" xml:lang="en-US">Schedule Of Unrecognized Compensation Expense Table Text Block</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfUnrecognizedCompensationExpenseTableTextBlock" xlink:to="logc_ScheduleOfUnrecognizedCompensationExpenseTableTextBlock_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LeaseCost_lbl0" xml:lang="en-US">Lease, Cost</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LeaseCost" xlink:to="us-gaap_LeaseCost_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_lbl0" xml:lang="en-US">Schedule of Accrued Liabilities [Table Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock" xlink:to="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskCreditRisk_lbl0" xml:lang="en-US">Concentration Risk, Credit Risk, Policy [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskCreditRisk" xlink:to="us-gaap_ConcentrationRiskCreditRisk_lbl0"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfDepreciationAndDepletionExpenseIncludedInStatementsOfOperationsAbstract" xlink:href="logc-20260226.xsd#logc_ScheduleOfDepreciationAndDepletionExpenseIncludedInStatementsOfOperationsAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfDepreciationAndDepletionExpenseIncludedInStatementsOfOperationsAbstract_lbl" xml:lang="en-US">Schedule Of Depreciation And Depletion Expense Included In Statements Of Operations Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfDepreciationAndDepletionExpenseIncludedInStatementsOfOperationsAbstract" xlink:to="logc_ScheduleOfDepreciationAndDepletionExpenseIncludedInStatementsOfOperationsAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl0" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl0"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfIntangibleAssetsAndRelatedAccumulatedAmortizationWhichAreIncludedInIntangibleAssetsNetAbstract" xlink:href="logc-20260226.xsd#logc_ScheduleOfIntangibleAssetsAndRelatedAccumulatedAmortizationWhichAreIncludedInIntangibleAssetsNetAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfIntangibleAssetsAndRelatedAccumulatedAmortizationWhichAreIncludedInIntangibleAssetsNetAbstract_lbl" xml:lang="en-US">Schedule Of Intangible Assets And Related Accumulated Amortization Which Are Included In Intangible Assets Net Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfIntangibleAssetsAndRelatedAccumulatedAmortizationWhichAreIncludedInIntangibleAssetsNetAbstract" xlink:to="logc_ScheduleOfIntangibleAssetsAndRelatedAccumulatedAmortizationWhichAreIncludedInIntangibleAssetsNetAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_lbl" xml:lang="en-US">Share-Based Payment Arrangement [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:to="us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_lbl0" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Term</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1" xlink:to="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl0" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_lbl0" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Year One</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember_lbl0" xml:lang="en-US">Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember" xlink:to="us-gaap_SecuredOvernightFinancingRateSofrOvernightIndexSwapRateMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeasePrincipalPayments_lbl0" xml:lang="en-US">Finance Lease, Principal Payments</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeasePrincipalPayments" xlink:to="us-gaap_FinanceLeasePrincipalPayments_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_CustomerOneMember_lbl0" xml:lang="en-US">Customer One Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_CustomerOneMember" xlink:to="logc_CustomerOneMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_UnrecognizedTaxBenefitDuration_lbl1" xml:lang="en-US">Unrecognized Tax Benefit Duration</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_UnrecognizedTaxBenefitDuration" xlink:to="logc_UnrecognizedTaxBenefitDuration_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl0" xml:lang="en-US">Significant Accounting Policies [Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="us-gaap_SignificantAccountingPoliciesTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_SellingGeneralAndAdministrativeExpenseMember_lbl0" xml:lang="en-US">Selling General And Administrative Expense Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_SellingGeneralAndAdministrativeExpenseMember" xlink:to="logc_SellingGeneralAndAdministrativeExpenseMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DepreciationAndAmortization_lbl0" xml:lang="en-US">Depreciation, Depletion and Amortization, Nonproduction</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DepreciationAndAmortization" xlink:to="us-gaap_DepreciationAndAmortization_lbl0"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfUnrecognizedCompensationExpenseAbstract" xlink:href="logc-20260226.xsd#logc_ScheduleOfUnrecognizedCompensationExpenseAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfUnrecognizedCompensationExpenseAbstract_lbl" xml:lang="en-US">Schedule Of Unrecognized Compensation Expense Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfUnrecognizedCompensationExpenseAbstract" xlink:to="logc_ScheduleOfUnrecognizedCompensationExpenseAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Goodwill_lbl0" xml:lang="en-US">Goodwill</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Goodwill" xlink:to="us-gaap_Goodwill_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_AmendmentDescription_lbl0" xml:lang="en-US">Amendment Description</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_AmendmentDescription" xlink:to="dei_AmendmentDescription_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GainLossOnSaleOfPropertyPlantEquipment_lbl0" xml:lang="en-US">Gain (Loss) on Disposition of Property Plant Equipment</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:to="us-gaap_GainLossOnSaleOfPropertyPlantEquipment_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock_lbl0" xml:lang="en-US">Accounts Payable and Accrued Liabilities Disclosure [Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock" xlink:to="us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock_lbl0"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfLeaseTermAndDiscountRateInformationAbstract" xlink:href="logc-20260226.xsd#logc_ScheduleOfLeaseTermAndDiscountRateInformationAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfLeaseTermAndDiscountRateInformationAbstract_lbl" xml:lang="en-US">Schedule Of Lease Term And Discount Rate Information Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfLeaseTermAndDiscountRateInformationAbstract" xlink:to="logc_ScheduleOfLeaseTermAndDiscountRateInformationAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_lbl0" xml:lang="en-US">Goodwill and Intangible Assets, Goodwill, Policy [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:to="us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheThreeMember_lbl0" xml:lang="en-US">Share-Based Payment Arrangement, Tranche Three [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationAwardTrancheThreeMember" xlink:to="us-gaap_ShareBasedCompensationAwardTrancheThreeMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_lbl0" xml:lang="en-US">Long-Term Debt, Maturity, Year Three</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:to="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ImpairmentOfIntangibleAssetsFinitelived_lbl0" xml:lang="en-US">Intangible Asset, Finite-Lived, Impairment Loss</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ImpairmentOfIntangibleAssetsFinitelived" xlink:to="us-gaap_ImpairmentOfIntangibleAssetsFinitelived_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentReportingPolicyPolicyTextBlock_lbl0" xml:lang="en-US">Segment Reporting, Policy [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:to="us-gaap_SegmentReportingPolicyPolicyTextBlock_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RelatedPartyTransactionsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionsAbstract_lbl" xml:lang="en-US">Related Party Transactions [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionsAbstract" xlink:to="us-gaap_RelatedPartyTransactionsAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLife_lbl0" xml:lang="en-US">Property, Plant, and Equipment, Useful Life</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:to="us-gaap_PropertyPlantAndEquipmentUsefulLife_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_NumberOfMajorCustomer_lbl1" xml:lang="en-US">Number Of Major Customer</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_NumberOfMajorCustomer" xlink:to="logc_NumberOfMajorCustomer_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_USSaltIntermediateHoldingsLLCMember_lbl0" xml:lang="en-US">USSalt Intermediate Holdings LLCMember</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_USSaltIntermediateHoldingsLLCMember" xlink:to="logc_USSaltIntermediateHoldingsLLCMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl0" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Two</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_lbl0" xml:lang="en-US">Related Party Transactions Disclosure [Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:to="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_FairValueOfClassSharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedBUnitFairvalueofClassBunit_lbl1" xml:lang="en-US">Fair Value Of Class Sharebased Compensation Arrangement By Sharebased Payment Award Fair Value Assumptions Expected BUnit Fairvalueof Class Bunit</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_FairValueOfClassSharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedBUnitFairvalueofClassBunit" xlink:to="logc_FairValueOfClassSharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedBUnitFairvalueofClassBunit_lbl1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PayablesAndAccrualsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PayablesAndAccrualsAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PayablesAndAccrualsAbstract_lbl" xml:lang="en-US">Payables and Accruals [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PayablesAndAccrualsAbstract" xlink:to="us-gaap_PayablesAndAccrualsAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock_lbl0" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss [Table Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock" xlink:to="us-gaap_AccountsReceivableAllowanceForCreditLossTableTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_EmeraldLakeCapitalLPMember_lbl0" xml:lang="en-US">Emerald Lake Capital LPMember</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_EmeraldLakeCapitalLPMember" xlink:to="logc_EmeraldLakeCapitalLPMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsToAcquireBusinessesGross_lbl0" xml:lang="en-US">Payments to Acquire Businesses, Gross</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsToAcquireBusinessesGross" xlink:to="us-gaap_PaymentsToAcquireBusinessesGross_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_lbl0" xml:lang="en-US">Intangible Asset and Goodwill [Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:to="us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_SuretyBondsOutstandingAmount_lbl1" xml:lang="en-US">Surety Bonds Outstanding Amount</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_SuretyBondsOutstandingAmount" xlink:to="logc_SuretyBondsOutstandingAmount_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree_lbl0" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year Three</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree" xlink:to="us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl0" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_USSaltHoldingsLLCMember_lbl0" xml:lang="en-US">USSalt Holdings LLCMember</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_USSaltHoldingsLLCMember" xlink:to="logc_USSaltHoldingsLLCMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeePercent_lbl0" xml:lang="en-US">Defined Contribution Plan, Maximum Annual Contributions Per Employee, Percent</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeePercent" xlink:to="us-gaap_DefinedContributionPlanMaximumAnnualContributionsPerEmployeePercent_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_RepurchaseOfNotesReceivableFromRelatedParties_lbl1" xml:lang="en-US">Repurchase Of Notes Receivable From Related Parties</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RepurchaseOfNotesReceivableFromRelatedParties" xlink:to="logc_RepurchaseOfNotesReceivableFromRelatedParties_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_PercentageOfNoncontrollingParentInterestRepresentedAggregator_lbl1" xml:lang="en-US">Percentage Of Noncontrolling Parent Interest Represented Aggregator</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PercentageOfNoncontrollingParentInterestRepresentedAggregator" xlink:to="logc_PercentageOfNoncontrollingParentInterestRepresentedAggregator_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ReceivablesPolicyTextBlock_lbl0" xml:lang="en-US">Receivable [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ReceivablesPolicyTextBlock" xlink:to="us-gaap_ReceivablesPolicyTextBlock_lbl0"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfOperatingFinancialResultsAbstract" xlink:href="logc-20260226.xsd#logc_ScheduleOfOperatingFinancialResultsAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfOperatingFinancialResultsAbstract_lbl" xml:lang="en-US">Schedule Of Operating Financial Results Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfOperatingFinancialResultsAbstract" xlink:to="logc_ScheduleOfOperatingFinancialResultsAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfDepreciationAndDepletionExpenseIncludedInStatementsOfOperationsTableTextBlock_lbl1" xml:lang="en-US">Schedule Of Depreciation And Depletion Expense Included In Statements Of Operations Table Text Block</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfDepreciationAndDepletionExpenseIncludedInStatementsOfOperationsTableTextBlock" xlink:to="logc_ScheduleOfDepreciationAndDepletionExpenseIncludedInStatementsOfOperationsTableTextBlock_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_RepaymentUnitsFromRelatedParties_lbl1" xml:lang="en-US">Repayment Units From Related Parties</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RepaymentUnitsFromRelatedParties" xlink:to="logc_RepaymentUnitsFromRelatedParties_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ProfitSharingPlanMember_lbl0" xml:lang="en-US">Profit Sharing Plan Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ProfitSharingPlanMember" xlink:to="logc_ProfitSharingPlanMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl0" xml:lang="en-US">Debt Instrument, Basis Spread on Variable Rate</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:to="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_TermLoanMember_lbl0" xml:lang="en-US">Term Loan Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_TermLoanMember" xlink:to="logc_TermLoanMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice_lbl0" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercisable, Weighted Average Exercise Price</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RevenueFromRightsConcentrationRiskMember_lbl0" xml:lang="en-US">Revenue from Rights Concentration Risk [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenueFromRightsConcentrationRiskMember" xlink:to="us-gaap_RevenueFromRightsConcentrationRiskMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsGross_lbl0" xml:lang="en-US">Intangible Asset, Finite-Lived, before Accumulated Amortization</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsGross" xlink:to="us-gaap_FiniteLivedIntangibleAssetsGross_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ProfessionalServicesAgreementMember_lbl0" xml:lang="en-US">Professional Services Agreement Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ProfessionalServicesAgreementMember" xlink:to="logc_ProfessionalServicesAgreementMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_SubscriptionNoteReceivableMember_lbl0" xml:lang="en-US">Subscription Note Receivable Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_SubscriptionNoteReceivableMember" xlink:to="logc_SubscriptionNoteReceivableMember_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AssetRetirementObligationDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetRetirementObligationDisclosureAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetRetirementObligationDisclosureAbstract_lbl" xml:lang="en-US">Asset Retirement Obligation Disclosure [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligationDisclosureAbstract" xlink:to="us-gaap_AssetRetirementObligationDisclosureAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_PercentageOfAnnualManagementFee_lbl1" xml:lang="en-US">Percentage Of Annual Management Fee</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PercentageOfAnnualManagementFee" xlink:to="logc_PercentageOfAnnualManagementFee_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CompensationRelatedCostsPolicyTextBlock_lbl0" xml:lang="en-US">Compensation Related Costs, Policy [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CompensationRelatedCostsPolicyTextBlock" xlink:to="us-gaap_CompensationRelatedCostsPolicyTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_AdditionsAndChangesInAssetRetirementObligations_lbl1" xml:lang="en-US">Additions And Changes In Asset Retirement Obligations</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_AdditionsAndChangesInAssetRetirementObligations" xlink:to="logc_AdditionsAndChangesInAssetRetirementObligations_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashAndCashEquivalentsPolicyTextBlock_lbl0" xml:lang="en-US">Cash and Cash Equivalents, Policy [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:to="us-gaap_CashAndCashEquivalentsPolicyTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_lbl0" xml:lang="en-US">Property, Plant, and Equipment [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:to="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_OperationAndFinanceLeasesExpiringYear_lbl1" xml:lang="en-US">Operation And Finance Leases Expiring Year</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_OperationAndFinanceLeasesExpiringYear" xlink:to="logc_OperationAndFinanceLeasesExpiringYear_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_AnnualManagementFeeMinimumAmount_lbl1" xml:lang="en-US">Annual Management Fee Minimum Amount</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_AnnualManagementFeeMinimumAmount" xlink:to="logc_AnnualManagementFeeMinimumAmount_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquity_lbl1" xml:lang="en-US">Equity, Attributable to Parent</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_StockholdersEquity_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LandMember_lbl0" xml:lang="en-US">Land [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LandMember" xlink:to="us-gaap_LandMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_WrittenCommunications_lbl0" xml:lang="en-US">Written Communications</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_WrittenCommunications" xlink:to="dei_WrittenCommunications_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl0" xml:lang="en-US">Line of Credit Facility, Maximum Borrowing Capacity</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:to="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LimitedPartnersCapitalAccountUnitsIssued_lbl0" xml:lang="en-US">Limited Partners&apos; Capital Account, Units Issued</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LimitedPartnersCapitalAccountUnitsIssued" xlink:to="us-gaap_LimitedPartnersCapitalAccountUnitsIssued_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_PackagingAndSupplies_lbl1" xml:lang="en-US">Packaging And Supplies</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PackagingAndSupplies" xlink:to="logc_PackagingAndSupplies_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_lbl0" xml:lang="en-US">Operating Lease, Right-of-Use Asset, Periodic Reduction</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:to="us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebt_lbl0" xml:lang="en-US">Long-Term Debt</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebt" xlink:to="us-gaap_LongTermDebt_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl0" xml:lang="en-US">Segment Reporting [Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingDisclosureTextBlock" xlink:to="us-gaap_SegmentReportingDisclosureTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestRateFloorMember_lbl0" xml:lang="en-US">Interest Rate Floor [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestRateFloorMember" xlink:to="us-gaap_InterestRateFloorMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LeaseCostTableTextBlock_lbl0" xml:lang="en-US">Lease, Cost [Table Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LeaseCostTableTextBlock" xlink:to="us-gaap_LeaseCostTableTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_CashPaidForAmountsIncludedInTheMeasurementOfLeaseLiabilitiesAbstract_lbl0" xml:lang="en-US">Cash Paid For Amounts Included In The Measurement Of Lease Liabilities Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_CashPaidForAmountsIncludedInTheMeasurementOfLeaseLiabilitiesAbstract" xlink:to="logc_CashPaidForAmountsIncludedInTheMeasurementOfLeaseLiabilitiesAbstract_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SalesRevenueNetMember_lbl0" xml:lang="en-US">Revenue Benchmark [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SalesRevenueNetMember" xlink:to="us-gaap_SalesRevenueNetMember_lbl0"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfInventoryAbstract" xlink:href="logc-20260226.xsd#logc_ScheduleOfInventoryAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfInventoryAbstract_lbl" xml:lang="en-US">Schedule Of Inventory Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfInventoryAbstract" xlink:to="logc_ScheduleOfInventoryAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfLongTermDebtAbstract" xlink:href="logc-20260226.xsd#logc_ScheduleOfLongTermDebtAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfLongTermDebtAbstract_lbl" xml:lang="en-US">Schedule Of Long Term Debt Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfLongTermDebtAbstract" xlink:to="logc_ScheduleOfLongTermDebtAbstract_lbl"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfAnnualMaturitiesOfThePrincipalAmountOfTotalDebtDueAbstract" xlink:href="logc-20260226.xsd#logc_ScheduleOfAnnualMaturitiesOfThePrincipalAmountOfTotalDebtDueAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfAnnualMaturitiesOfThePrincipalAmountOfTotalDebtDueAbstract_lbl" xml:lang="en-US">Schedule Of Annual Maturities Of The Principal Amount Of Total Debt Due Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfAnnualMaturitiesOfThePrincipalAmountOfTotalDebtDueAbstract" xlink:to="logc_ScheduleOfAnnualMaturitiesOfThePrincipalAmountOfTotalDebtDueAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityAddressPostalZipCode_lbl0" xml:lang="en-US">Entity Address, Postal Zip Code</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressPostalZipCode" xlink:to="dei_EntityAddressPostalZipCode_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BuildingImprovementsMember_lbl0" xml:lang="en-US">Building Improvements [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BuildingImprovementsMember" xlink:to="us-gaap_BuildingImprovementsMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InventoryWriteDown_lbl0" xml:lang="en-US">Inventory Write-down</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryWriteDown" xlink:to="us-gaap_InventoryWriteDown_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl1" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock_lbl0" xml:lang="en-US">Property, Plant, and Equipment [Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock" xlink:to="us-gaap_PropertyPlantAndEquipmentDisclosureTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_lbl0" xml:lang="en-US">Schedule of Accounts, Notes, Loans and Financing Receivable [Table Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:to="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetRetirementObligationsPolicy_lbl0" xml:lang="en-US">Asset Retirement Obligation [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligationsPolicy" xlink:to="us-gaap_AssetRetirementObligationsPolicy_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_DistributionToNoncontrollingParentInterest_lbl1" xml:lang="en-US">Distribution To Noncontrolling Parent Interest</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_DistributionToNoncontrollingParentInterest" xlink:to="logc_DistributionToNoncontrollingParentInterest_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl0" xml:lang="en-US">Business Combination, Consideration Transferred</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationConsiderationTransferred1" xlink:to="us-gaap_BusinessCombinationConsiderationTransferred1_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_EmeraldLakeMember_lbl0" xml:lang="en-US">Emerald Lake Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_EmeraldLakeMember" xlink:to="logc_EmeraldLakeMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ProceedsFromRightsOffering_lbl1" xml:lang="en-US">Proceeds From Rights Offering</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ProceedsFromRightsOffering" xlink:to="logc_ProceedsFromRightsOffering_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_StatementOfIncomeLocationAxis_lbl0" xml:lang="en-US">Statement Of Income Location Axis</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_StatementOfIncomeLocationAxis" xlink:to="logc_StatementOfIncomeLocationAxis_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_IntermediateHoldingsMember_lbl0" xml:lang="en-US">Intermediate Holdings Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_IntermediateHoldingsMember" xlink:to="logc_IntermediateHoldingsMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl1" xml:lang="en-US">Limited Liability Company (LLC) Members&apos; Equity, Including Portion Attributable to Noncontrolling Interest</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:to="us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_LiabilitiesAndMembersEquityAbstract_lbl0" xml:lang="en-US">Liabilities And Members Equity Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_LiabilitiesAndMembersEquityAbstract" xlink:to="logc_LiabilitiesAndMembersEquityAbstract_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueDisclosuresAbstract_lbl" xml:lang="en-US">Fair Value Disclosures [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueDisclosuresAbstract" xlink:to="us-gaap_FairValueDisclosuresAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl0" xml:lang="en-US">Equity [Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl0" xml:lang="en-US">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:to="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm1_lbl2" xml:lang="en-US">Sharebased Compensation Arrangement By Sharebased Payment Award Options Outstanding Weighted Average Remaining Contractual Term1</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm1" xlink:to="logc_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm1_lbl2"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl0" xml:lang="en-US">Sale of Stock, Number of Shares Issued in Transaction</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:to="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl0" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfDebtTableTextBlock_lbl0" xml:lang="en-US">Schedule of Debt [Table Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfDebtTableTextBlock" xlink:to="us-gaap_ScheduleOfDebtTableTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_RepaymentOfPrincipalOfFinanceLeasesObligations_lbl1" xml:lang="en-US">Repayment Of Principal Of Finance Leases Obligations</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RepaymentOfPrincipalOfFinanceLeasesObligations" xlink:to="logc_RepaymentOfPrincipalOfFinanceLeasesObligations_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentTextBlock_lbl0" xml:lang="en-US">Property, Plant, and Equipment [Table Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:to="us-gaap_PropertyPlantAndEquipmentTextBlock_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementOfFinancialPositionAbstract_lbl" xml:lang="en-US">Statement of Financial Position [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementOfFinancialPositionAbstract" xlink:to="us-gaap_StatementOfFinancialPositionAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DefinedContributionPlanCostRecognized_lbl0" xml:lang="en-US">Defined Contribution Plan, Cost</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DefinedContributionPlanCostRecognized" xlink:to="us-gaap_DefinedContributionPlanCostRecognized_lbl0"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfChangesInAssetRetirementObligationAbstract" xlink:href="logc-20260226.xsd#logc_ScheduleOfChangesInAssetRetirementObligationAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfChangesInAssetRetirementObligationAbstract_lbl" xml:lang="en-US">Schedule Of Changes In Asset Retirement Obligation Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfChangesInAssetRetirementObligationAbstract" xlink:to="logc_ScheduleOfChangesInAssetRetirementObligationAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityTaxIdentificationNumber_lbl0" xml:lang="en-US">Entity Tax Identification Number</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityTaxIdentificationNumber" xlink:to="dei_EntityTaxIdentificationNumber_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_Customer1Member_lbl0" xml:lang="en-US">Customer1 Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_Customer1Member" xlink:to="logc_Customer1Member_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl0" xml:lang="en-US">Cash and Cash Equivalent</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CostOfGoodsAndServiceExcludingDepreciationDepletionAndAmortization_lbl0" xml:lang="en-US">Cost of Goods and Service, Excluding Depreciation, Depletion, and Amortization</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CostOfGoodsAndServiceExcludingDepreciationDepletionAndAmortization" xlink:to="us-gaap_CostOfGoodsAndServiceExcludingDepreciationDepletionAndAmortization_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_DocumentType_lbl0" xml:lang="en-US">Document Type</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentType" xlink:to="dei_DocumentType_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_PrepaidExpensesDisclosureTextBlock_lbl1" xml:lang="en-US">Prepaid Expenses Disclosure Text Block</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PrepaidExpensesDisclosureTextBlock" xlink:to="logc_PrepaidExpensesDisclosureTextBlock_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityFileNumber_lbl0" xml:lang="en-US">Entity File Number</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityFileNumber" xlink:to="dei_EntityFileNumber_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseLiability_lbl0" xml:lang="en-US">Finance Lease, Liability</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiability" xlink:to="us-gaap_FinanceLeaseLiability_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl0" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year One</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl0"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfFutureMaturitiesOfLeaseLiabilitiesAbstract" xlink:href="logc-20260226.xsd#logc_ScheduleOfFutureMaturitiesOfLeaseLiabilitiesAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfFutureMaturitiesOfLeaseLiabilitiesAbstract_lbl" xml:lang="en-US">Schedule Of Future Maturities Of Lease Liabilities Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfFutureMaturitiesOfLeaseLiabilitiesAbstract" xlink:to="logc_ScheduleOfFutureMaturitiesOfLeaseLiabilitiesAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_IssuanceOfNotesReceivableFromRelatedParties_lbl1" xml:lang="en-US">Issuance Of Notes Receivable From Related Parties</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_IssuanceOfNotesReceivableFromRelatedParties" xlink:to="logc_IssuanceOfNotesReceivableFromRelatedParties_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_lbl0" xml:lang="en-US">Business Combination, Consideration Transferred, Equity Interest</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:to="us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_DocumentPeriodEndDate_lbl0" xml:lang="en-US">Document Period End Date</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_DocumentPeriodEndDate" xlink:to="dei_DocumentPeriodEndDate_lbl0"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfActivitiesOfClassAUnitsAndSubscriptionNotesReceivableFromEmployeesAndBoardOfDirectAbstract" xlink:href="logc-20260226.xsd#logc_ScheduleOfActivitiesOfClassAUnitsAndSubscriptionNotesReceivableFromEmployeesAndBoardOfDirectAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfActivitiesOfClassAUnitsAndSubscriptionNotesReceivableFromEmployeesAndBoardOfDirectAbstract_lbl" xml:lang="en-US">Schedule Of Activities Of Class AUnits And Subscription Notes Receivable From Employees And Board Of Direct Abstract</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl0" xml:lang="en-US">Increase (Decrease) in Accounts Receivable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:to="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_CollectionOfSubscriptionNoteReceivable_lbl1" xml:lang="en-US">Collection Of Subscription Note Receivable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_CollectionOfSubscriptionNoteReceivable" xlink:to="logc_CollectionOfSubscriptionNoteReceivable_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="srt_NorthAmericaMember_lbl0" xml:lang="en-US">North America [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="srt_NorthAmericaMember" xlink:to="srt_NorthAmericaMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl1" xml:lang="en-US">Finance Lease, Liability, Noncurrent</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:to="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentInterestRateEffectivePercentage_lbl0" xml:lang="en-US">Debt Instrument, Interest Rate, Effective Percentage</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:to="us-gaap_DebtInstrumentInterestRateEffectivePercentage_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtDisclosureAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtDisclosureAbstract_lbl" xml:lang="en-US">Debt Disclosure [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtDisclosureAbstract" xlink:to="us-gaap_DebtDisclosureAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseInterestExpense_lbl1" xml:lang="en-US">Finance Lease, Interest Expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseInterestExpense" xlink:to="us-gaap_FinanceLeaseInterestExpense_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock_lbl0" xml:lang="en-US">Schedule of Related Party Transactions [Table Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:to="us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsNet_lbl0" xml:lang="en-US">Intangible Asset, Finite-Lived, after Accumulated Amortization</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsNet" xlink:to="us-gaap_FiniteLivedIntangibleAssetsNet_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_lbl0" xml:lang="en-US">Long-Term Debt, Maturity, Year Two</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:to="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GainLossOnSaleOfBusiness_lbl0" xml:lang="en-US">Gain (Loss) on Disposition of Business</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GainLossOnSaleOfBusiness" xlink:to="us-gaap_GainLossOnSaleOfBusiness_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_unrecognizedcompensationexpenseyearthree_lbl1" xml:lang="en-US">unrecognizedcompensationexpenseyearthree</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_unrecognizedcompensationexpenseyearthree" xlink:to="logc_unrecognizedcompensationexpenseyearthree_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl0" xml:lang="en-US">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetRetirementObligation_lbl1" xml:lang="en-US">Asset Retirement Obligation</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligation" xlink:to="us-gaap_AssetRetirementObligation_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensation_lbl0" xml:lang="en-US">Share-Based Payment Arrangement, Noncash Expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensation" xlink:to="us-gaap_ShareBasedCompensation_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ProceedsFromCollectionOfSubscriptionNoteReceivable_lbl1" xml:lang="en-US">Proceeds From Collection Of Subscription Note Receivable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ProceedsFromCollectionOfSubscriptionNoteReceivable" xlink:to="logc_ProceedsFromCollectionOfSubscriptionNoteReceivable_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseInterestPaymentOnLiability_lbl0" xml:lang="en-US">Finance Lease, Interest Payment on Liability</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseInterestPaymentOnLiability" xlink:to="us-gaap_FinanceLeaseInterestPaymentOnLiability_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_lbl0" xml:lang="en-US">Schedule of Maturities of Long-Term Debt [Table Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:to="us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent_lbl0" xml:lang="en-US">Defined Contribution Plan, Employer Matching Contribution, Percent of Employees&apos; Gross Pay</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent" xlink:to="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ContextLogicMember_lbl0" xml:lang="en-US">Context Logic Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ContextLogicMember" xlink:to="logc_ContextLogicMember_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_StockholdersEquityNoteAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityNoteAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StockholdersEquityNoteAbstract_lbl" xml:lang="en-US">Stockholders&apos; Equity Note [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StockholdersEquityNoteAbstract" xlink:to="us-gaap_StockholdersEquityNoteAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PartnersCapitalAccountDistributions_lbl0" xml:lang="en-US">Partners&apos; Capital Account, Distributions</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PartnersCapitalAccountDistributions" xlink:to="us-gaap_PartnersCapitalAccountDistributions_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_TradingSymbol_lbl0" xml:lang="en-US">Trading Symbol</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_TradingSymbol" xlink:to="dei_TradingSymbol_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InventoryNet_lbl1" xml:lang="en-US">Inventory, Net</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryNet" xlink:to="us-gaap_InventoryNet_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_CityAreaCode_lbl0" xml:lang="en-US">City Area Code</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_CityAreaCode" xlink:to="dei_CityAreaCode_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeasePayments_lbl0" xml:lang="en-US">Operating Lease, Payments</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeasePayments" xlink:to="us-gaap_OperatingLeasePayments_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NumberOfOperatingSegments_lbl1" xml:lang="en-US">Number of Operating Segments</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NumberOfOperatingSegments" xlink:to="us-gaap_NumberOfOperatingSegments_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate_lbl0" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Dividend Rate</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_UseOfEstimates_lbl0" xml:lang="en-US">Use of Estimates, Policy [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_UseOfEstimates" xlink:to="us-gaap_UseOfEstimates_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock_lbl0" xml:lang="en-US">Schedule of Cash and Cash Equivalents [Table Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:to="us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityAddressCityOrTown_lbl0" xml:lang="en-US">Entity Address, City or Town</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressCityOrTown" xlink:to="dei_EntityAddressCityOrTown_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NonoperatingIncomeExpenseAbstract_lbl0" xml:lang="en-US">Nonoperating Income (Expense) [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NonoperatingIncomeExpenseAbstract" xlink:to="us-gaap_NonoperatingIncomeExpenseAbstract_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths_lbl0" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year One</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive_lbl0" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year Five</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive" xlink:to="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RevolvingCreditFacilityMember_lbl0" xml:lang="en-US">Revolving Credit Facility [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevolvingCreditFacilityMember" xlink:to="us-gaap_RevolvingCreditFacilityMember_lbl0"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfRollForwardOfAllowanceForExpectedCreditLossesAbstract" xlink:href="logc-20260226.xsd#logc_ScheduleOfRollForwardOfAllowanceForExpectedCreditLossesAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfRollForwardOfAllowanceForExpectedCreditLossesAbstract_lbl" xml:lang="en-US">Schedule Of Roll Forward Of Allowance For Expected Credit Losses Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfRollForwardOfAllowanceForExpectedCreditLossesAbstract" xlink:to="logc_ScheduleOfRollForwardOfAllowanceForExpectedCreditLossesAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AmortizationOfFinancingCosts_lbl0" xml:lang="en-US">Amortization of Debt Issuance Costs</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AmortizationOfFinancingCosts" xlink:to="us-gaap_AmortizationOfFinancingCosts_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeLeasesPolicyTextBlock_lbl0" xml:lang="en-US">Lessee, Leases [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeLeasesPolicyTextBlock" xlink:to="us-gaap_LesseeLeasesPolicyTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestCostsCapitalized_lbl0" xml:lang="en-US">Interest Costs Capitalized</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DefinedContributionPlanEmployersMatchingContributionAnnualVestingPercentage_lbl0" xml:lang="en-US">Defined Contribution Plan, Employers Matching Contribution, Annual Vesting Percentage</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DefinedContributionPlanEmployersMatchingContributionAnnualVestingPercentage" xlink:to="us-gaap_DefinedContributionPlanEmployersMatchingContributionAnnualVestingPercentage_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NoncontrollingInterestMember_lbl0" xml:lang="en-US">Noncontrolling Interest [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NoncontrollingInterestMember" xlink:to="us-gaap_NoncontrollingInterestMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SellingExpense_lbl0" xml:lang="en-US">Selling Expense</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1_lbl0" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercisable, Weighted-Average Remaining Contractual Term</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1" xlink:to="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_LeasesRemainingLeaseTerm_lbl1" xml:lang="en-US">Leases Remaining Lease Term</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_LeasesRemainingLeaseTerm" xlink:to="logc_LeasesRemainingLeaseTerm_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_TaxDistributions_lbl1" xml:lang="en-US">Tax Distributions</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_TaxDistributions" xlink:to="logc_TaxDistributions_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsForRepurchaseOfEquity_lbl0" xml:lang="en-US">Payments for Repurchase of Equity</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsForRepurchaseOfEquity" xlink:to="us-gaap_PaymentsForRepurchaseOfEquity_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract_lbl" xml:lang="en-US">Statement of Stockholders&apos; Equity [Abstract]</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive_lbl0" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Year Five</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl1" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl0" xml:lang="en-US">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Grants in Period, Weighted Average Exercise Price</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice" xlink:to="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInOperatingLeaseLiability_lbl0" xml:lang="en-US">Increase (Decrease) in Operating Lease Liability</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:to="us-gaap_IncreaseDecreaseInOperatingLeaseLiability_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_PrepaidHealthBenefits_lbl1" xml:lang="en-US">Prepaid Health Benefits</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PrepaidHealthBenefits" xlink:to="logc_PrepaidHealthBenefits_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfLeaseTermAndDiscountRateInformationRelatedToLeaseTableTextBlock_lbl0" xml:lang="en-US">Schedule Of Lease Term And Discount Rate Information Related To Lease Table Text Block</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfLeaseTermAndDiscountRateInformationRelatedToLeaseTableTextBlock" xlink:to="logc_ScheduleOfLeaseTermAndDiscountRateInformationRelatedToLeaseTableTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_RepaymentOfSubscriptionReceivableFromProceedsOfUnitsRepurchase_lbl1" xml:lang="en-US">Repayment Of Subscription Receivable From Proceeds Of Units Repurchase</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RepaymentOfSubscriptionReceivableFromProceedsOfUnitsRepurchase" xlink:to="logc_RepaymentOfSubscriptionReceivableFromProceedsOfUnitsRepurchase_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RepaymentOfNotesReceivableFromRelatedParties_lbl0" xml:lang="en-US">Repayment of Notes Receivable from Related Parties</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RepaymentOfNotesReceivableFromRelatedParties" xlink:to="us-gaap_RepaymentOfNotesReceivableFromRelatedParties_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeStatementAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncomeStatementAbstract_lbl" xml:lang="en-US">Income Statement [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncomeStatementAbstract" xlink:to="us-gaap_IncomeStatementAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl0" xml:lang="en-US">New Accounting Pronouncements, Policy [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CreditLossAdditionalImprovementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CreditLossAdditionalImprovementsAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CreditLossAdditionalImprovementsAbstract_lbl" xml:lang="en-US">Credit Loss, Additional Improvements [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CreditLossAdditionalImprovementsAbstract" xlink:to="us-gaap_CreditLossAdditionalImprovementsAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_CancellationOfUnitsPurchasedAndTheCorrespondingSubscriptionNotesReceivable_lbl1" xml:lang="en-US">Cancellation Of Units Purchased And The Corresponding Subscription Notes Receivable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_CancellationOfUnitsPurchasedAndTheCorrespondingSubscriptionNotesReceivable" xlink:to="logc_CancellationOfUnitsPurchasedAndTheCorrespondingSubscriptionNotesReceivable_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EarningsPerShareBasic_lbl1" xml:lang="en-US">Earnings Per Share, Basic</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerShareBasic" xlink:to="us-gaap_EarningsPerShareBasic_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsReceivableGrossCurrent_lbl0" xml:lang="en-US">Accounts Receivable, before Allowance for Credit Loss, Current</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableGrossCurrent" xlink:to="us-gaap_AccountsReceivableGrossCurrent_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Assets_lbl0" xml:lang="en-US">Assets</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Assets" xlink:to="us-gaap_Assets_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Liabilities_lbl0" xml:lang="en-US">Liabilities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_Liabilities_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccruedInsuranceCurrent_lbl0" xml:lang="en-US">Accrued Insurance, Current</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccruedInsuranceCurrent" xlink:to="us-gaap_AccruedInsuranceCurrent_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl0" xml:lang="en-US">Subsequent Events [Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventsTextBlock" xlink:to="us-gaap_SubsequentEventsTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityAddressStateOrProvince_lbl0" xml:lang="en-US">Entity Address, State or Province</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityAddressStateOrProvince" xlink:to="dei_EntityAddressStateOrProvince_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetRetirementObligationsNoncurrent_lbl0" xml:lang="en-US">Asset Retirement Obligations, Noncurrent</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligationsNoncurrent" xlink:to="us-gaap_AssetRetirementObligationsNoncurrent_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AmortizationOfIntangibleAssets_lbl0" xml:lang="en-US">Intangible Asset, Finite-Lived, Amortization Expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AmortizationOfIntangibleAssets" xlink:to="us-gaap_AmortizationOfIntangibleAssets_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsReceivableMember_lbl0" xml:lang="en-US">Accounts Receivable [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableMember" xlink:to="us-gaap_AccountsReceivableMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetUsefulLife_lbl0" xml:lang="en-US">Intangible Asset, Finite-Lived, Useful Life</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:to="us-gaap_FiniteLivedIntangibleAssetUsefulLife_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl0" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Gross</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_NoncontrollingParentInterestPolicyTextBlock_lbl1" xml:lang="en-US">Noncontrolling Parent Interest Policy Text Block</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_NoncontrollingParentInterestPolicyTextBlock" xlink:to="logc_NoncontrollingParentInterestPolicyTextBlock_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInInventories_lbl0" xml:lang="en-US">Increase (Decrease) in Inventories</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInInventories" xlink:to="us-gaap_IncreaseDecreaseInInventories_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetRetirementObligationAccretionExpense_lbl1" xml:lang="en-US">Asset Retirement Obligation, Accretion Expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligationAccretionExpense" xlink:to="us-gaap_AssetRetirementObligationAccretionExpense_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EnvironmentalCostsPolicy_lbl0" xml:lang="en-US">Environmental Costs, Policy [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EnvironmentalCostsPolicy" xlink:to="us-gaap_EnvironmentalCostsPolicy_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_lbl0" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss, Current</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:to="us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ForeignCurrencyTransactionGainLossBeforeTax_lbl0" xml:lang="en-US">Gain (Loss), Foreign Currency Transaction, before Tax</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ForeignCurrencyTransactionGainLossBeforeTax" xlink:to="us-gaap_ForeignCurrencyTransactionGainLossBeforeTax_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ClassAUnitsAmountMember_lbl0" xml:lang="en-US">Class AUnits Amount Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ClassAUnitsAmountMember" xlink:to="logc_ClassAUnitsAmountMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InventoryPolicyTextBlock_lbl0" xml:lang="en-US">Inventory, Policy [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InventoryPolicyTextBlock" xlink:to="us-gaap_InventoryPolicyTextBlock_lbl0"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfElementsOfLeaseCostsAbstract" xlink:href="logc-20260226.xsd#logc_ScheduleOfElementsOfLeaseCostsAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfElementsOfLeaseCostsAbstract_lbl" xml:lang="en-US">Schedule Of Elements Of Lease Costs Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfElementsOfLeaseCostsAbstract" xlink:to="logc_ScheduleOfElementsOfLeaseCostsAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_lbl0" xml:lang="en-US">Finance Lease, Weighted Average Remaining Lease Term</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:to="us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ClassAUnitsMember_lbl0" xml:lang="en-US">Class AUnits Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ClassAUnitsMember" xlink:to="logc_ClassAUnitsMember_lbl0"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfPrepaidExpensesAbstract" xlink:href="logc-20260226.xsd#logc_ScheduleOfPrepaidExpensesAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfPrepaidExpensesAbstract_lbl" xml:lang="en-US">Schedule Of Prepaid Expenses Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfPrepaidExpensesAbstract" xlink:to="logc_ScheduleOfPrepaidExpensesAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseLiability_lbl0" xml:lang="en-US">Operating Lease, Liability</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseLiability" xlink:to="us-gaap_OperatingLeaseLiability_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_CancellationOfUnitsPurchasedAndTheCorrespondingSubscriptionNotesReceivableUnits_lbl1" xml:lang="en-US">Cancellation Of Units Purchased And The Corresponding Subscription Notes Receivable Units</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_CancellationOfUnitsPurchasedAndTheCorrespondingSubscriptionNotesReceivableUnits" xlink:to="logc_CancellationOfUnitsPurchasedAndTheCorrespondingSubscriptionNotesReceivableUnits_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CostOfSalesPolicyTextBlock_lbl0" xml:lang="en-US">Cost of Goods and Service [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CostOfSalesPolicyTextBlock" xlink:to="us-gaap_CostOfSalesPolicyTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MachineryAndEquipmentMember_lbl0" xml:lang="en-US">Machinery and Equipment [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MachineryAndEquipmentMember" xlink:to="us-gaap_MachineryAndEquipmentMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_USPHClassBUnitsMember_lbl0" xml:lang="en-US">USPHClass BUnits Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_USPHClassBUnitsMember" xlink:to="logc_USPHClassBUnitsMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl0" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_PropertyPlantAndEquipmentInAccountsPayable_lbl1" xml:lang="en-US">Property Plant And Equipment In Accounts Payable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PropertyPlantAndEquipmentInAccountsPayable" xlink:to="logc_PropertyPlantAndEquipmentInAccountsPayable_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl0" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period, Weighted Average Grant Date Fair Value</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DescriptionOfDefinedContributionPensionAndOtherPostretirementPlans_lbl0" xml:lang="en-US">Defined Contribution Plan, Description</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DescriptionOfDefinedContributionPensionAndOtherPostretirementPlans" xlink:to="us-gaap_DescriptionOfDefinedContributionPensionAndOtherPostretirementPlans_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsPayableCurrent_lbl0" xml:lang="en-US">Accounts Payable, Current</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsPayableCurrent" xlink:to="us-gaap_AccountsPayableCurrent_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl0" xml:lang="en-US">Debt Issuance Costs, Net</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DeferredFinanceCostsNet" xlink:to="us-gaap_DeferredFinanceCostsNet_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_TimeVestingIncentiveUnitsMember_lbl0" xml:lang="en-US">Time Vesting Incentive Units Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_TimeVestingIncentiveUnitsMember" xlink:to="logc_TimeVestingIncentiveUnitsMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonUnitOutstanding_lbl1" xml:lang="en-US">Common Unit, Outstanding</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonUnitOutstanding" xlink:to="us-gaap_CommonUnitOutstanding_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ManagementFeeExpense_lbl0" xml:lang="en-US">Management Fee Expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ManagementFeeExpense" xlink:to="us-gaap_ManagementFeeExpense_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CapitalAdditionsMember_lbl0" xml:lang="en-US">Capital Addition Purchase Commitments [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CapitalAdditionsMember" xlink:to="us-gaap_CapitalAdditionsMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_PaymentsOfCapitalContributions_lbl1" xml:lang="en-US">Payments Of Capital Contributions</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_PaymentsOfCapitalContributions" xlink:to="logc_PaymentsOfCapitalContributions_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl0" xml:lang="en-US">Property, Plant, and Equipment, before Accumulated Depreciation, Depletion, and Amortization</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentGross" xlink:to="us-gaap_PropertyPlantAndEquipmentGross_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PartnersCapitalAccountUnitsContributed_lbl0" xml:lang="en-US">Partners&apos; Capital Account, Units, Contributed</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PartnersCapitalAccountUnitsContributed" xlink:to="us-gaap_PartnersCapitalAccountUnitsContributed_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_MaintenanceMaterials_lbl1" xml:lang="en-US">Maintenance Materials</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_MaintenanceMaterials" xlink:to="logc_MaintenanceMaterials_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet_lbl0" xml:lang="en-US">Debt Instrument, Unamortized Discount (Premium) and Debt Issuance Costs, Net</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet" xlink:to="us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl0" xml:lang="en-US">Employee-related Liabilities, Current</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:to="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByParent_lbl0" xml:lang="en-US">Subsidiary, Ownership Percentage, Parent</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:to="us-gaap_MinorityInterestOwnershipPercentageByParent_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestExpenseNonoperating_lbl0" xml:lang="en-US">Interest Expense, Nonoperating</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestExpenseNonoperating" xlink:to="us-gaap_InterestExpenseNonoperating_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_CostOfRevenueMember_lbl0" xml:lang="en-US">Cost Of Revenue Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_CostOfRevenueMember" xlink:to="logc_CostOfRevenueMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShortTermLeaseCost_lbl0" xml:lang="en-US">Short-Term Lease, Cost</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShortTermLeaseCost" xlink:to="us-gaap_ShortTermLeaseCost_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_AmendmentFlag_lbl0" xml:lang="en-US">Amendment Flag</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_AmendmentFlag" xlink:to="dei_AmendmentFlag_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetRetirementObligationDisclosureTextBlock_lbl0" xml:lang="en-US">Asset Retirement Obligation Disclosure [Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligationDisclosureTextBlock" xlink:to="us-gaap_AssetRetirementObligationDisclosureTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PrimeRateMember_lbl0" xml:lang="en-US">Prime Rate [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PrimeRateMember" xlink:to="us-gaap_PrimeRateMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashMember_lbl0" xml:lang="en-US">Cash [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashMember" xlink:to="us-gaap_CashMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ProvisionForDoubtfulAccounts_lbl0" xml:lang="en-US">Accounts Receivable, Credit Loss Expense (Reversal)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ProvisionForDoubtfulAccounts" xlink:to="us-gaap_ProvisionForDoubtfulAccounts_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_lbl0" xml:lang="en-US">Revenue from Contract with Customer, Excluding Assessed Tax</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:to="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureAbstract_lbl" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:to="us-gaap_CommitmentsAndContingenciesDisclosureAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivable_lbl0" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllowanceForDoubtfulAccountsReceivable" xlink:to="us-gaap_AllowanceForDoubtfulAccountsReceivable_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl0" xml:lang="en-US">Long-Term Debt, Gross</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DebtInstrumentCarryingAmount" xlink:to="us-gaap_DebtInstrumentCarryingAmount_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl0" xml:lang="en-US">Property, Plant, and Equipment, Accumulated Depreciation, Depletion, and Amortization</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:to="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_lbl0" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Four</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_lbl0" xml:lang="en-US">Right-of-Use Asset Obtained in Exchange for Finance Lease Liability</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:to="us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ClassAMemberUnitsMember_lbl0" xml:lang="en-US">Class AMember Units Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ClassAMemberUnitsMember" xlink:to="logc_ClassAMemberUnitsMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingIncomeLoss_lbl0" xml:lang="en-US">Operating Income (Loss)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingIncomeLoss" xlink:to="us-gaap_OperatingIncomeLoss_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive_lbl0" xml:lang="en-US">Finance Lease, Liability, to be Paid, after Year Five</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive" xlink:to="us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_lbl0" xml:lang="en-US">Foreign Currency Transactions and Translations Policy [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock" xlink:to="us-gaap_ForeignCurrencyTransactionsAndTranslationsPolicyTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityCentralIndexKey_lbl0" xml:lang="en-US">Entity Central Index Key</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityCentralIndexKey" xlink:to="dei_EntityCentralIndexKey_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInPrepaidExpense_lbl0" xml:lang="en-US">Increase (Decrease) in Prepaid Expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInPrepaidExpense" xlink:to="us-gaap_IncreaseDecreaseInPrepaidExpense_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_lbl0" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, after Year Five</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SegmentReportingOtherItemAmount_lbl0" xml:lang="en-US">Segment Reporting, Other Segment Item, Amount</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SegmentReportingOtherItemAmount" xlink:to="us-gaap_SegmentReportingOtherItemAmount_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl1" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Number</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PropertyPlantAndEquipmentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PropertyPlantAndEquipmentAbstract_lbl" xml:lang="en-US">Property, Plant, and Equipment [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PropertyPlantAndEquipmentAbstract" xlink:to="us-gaap_PropertyPlantAndEquipmentAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccumulatedAmortizationOfDebtIssuanceCostsLineOfCreditArrangements_lbl0" xml:lang="en-US">Accumulated Amortization of Debt Issuance Costs, Line of Credit Arrangements</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccumulatedAmortizationOfDebtIssuanceCostsLineOfCreditArrangements" xlink:to="us-gaap_AccumulatedAmortizationOfDebtIssuanceCostsLineOfCreditArrangements_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_NewYorkFederalReserveBankRateMember_lbl0" xml:lang="en-US">New York Federal Reserve Bank Rate Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_NewYorkFederalReserveBankRateMember" xlink:to="logc_NewYorkFederalReserveBankRateMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_lbl0" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Diluted</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:to="us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MembersEquityAbstract_lbl0" xml:lang="en-US">Members&apos; Equity [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MembersEquityAbstract" xlink:to="us-gaap_MembersEquityAbstract_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber_lbl0" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercisable, Number</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl0" xml:lang="en-US">Sale of Stock, Price Per Share</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SaleOfStockPricePerShare" xlink:to="us-gaap_SaleOfStockPricePerShare_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityRegistrantName_lbl0" xml:lang="en-US">Entity Registrant Name</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityRegistrantName" xlink:to="dei_EntityRegistrantName_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_lbl0" xml:lang="en-US">Finance Lease, Weighted Average Discount Rate, Percent</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:to="us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense_lbl0" xml:lang="en-US">Unrecognized Tax Benefits, Income Tax Penalties and Interest Expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense" xlink:to="us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestExpense_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CommonClassAMember_lbl0" xml:lang="en-US">Common Class A [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CommonClassAMember" xlink:to="us-gaap_CommonClassAMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate_lbl0" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Volatility Rate</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding_lbl0" xml:lang="en-US">Limited Partners&apos; Capital Account, Units Outstanding</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding" xlink:to="us-gaap_LimitedPartnersCapitalAccountUnitsOutstanding_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_StatementOfCashFlowsAbstract_lbl" xml:lang="en-US">Statement of Cash Flows [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_StatementOfCashFlowsAbstract" xlink:to="us-gaap_StatementOfCashFlowsAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InterestExpense_lbl0" xml:lang="en-US">Interest Expense, Operating and Nonoperating</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InterestExpense" xlink:to="us-gaap_InterestExpense_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_unrecognizedcompensationexpenseyearone_lbl1" xml:lang="en-US">unrecognizedcompensationexpenseyearone</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_unrecognizedcompensationexpenseyearone" xlink:to="logc_unrecognizedcompensationexpenseyearone_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OtherPrepaidExpenseCurrent_lbl0" xml:lang="en-US">Other Prepaid Expense, Current</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OtherPrepaidExpenseCurrent" xlink:to="us-gaap_OtherPrepaidExpenseCurrent_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_SupplementalCashFlowInformationRelatedToLeasesTableTextBlock_lbl0" xml:lang="en-US">Supplemental Cash Flow Information Related To Leases Table Text Block</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_SupplementalCashFlowInformationRelatedToLeasesTableTextBlock" xlink:to="logc_SupplementalCashFlowInformationRelatedToLeasesTableTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermPurchaseCommitmentAmount_lbl0" xml:lang="en-US">Long-Term Purchase Commitment, Amount</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermPurchaseCommitmentAmount" xlink:to="us-gaap_LongTermPurchaseCommitmentAmount_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl1" xml:lang="en-US">Operating Lease, Liability, Current</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseLiabilityCurrent" xlink:to="us-gaap_OperatingLeaseLiabilityCurrent_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MoneyMarketFundsMember_lbl0" xml:lang="en-US">Money Market Funds [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MoneyMarketFundsMember" xlink:to="us-gaap_MoneyMarketFundsMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PartnersCapitalAccountUnitBasedCompensation_lbl0" xml:lang="en-US">Partners&apos; Capital Account, Unit-Based Payment Arrangement, Amount</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PartnersCapitalAccountUnitBasedCompensation" xlink:to="us-gaap_PartnersCapitalAccountUnitBasedCompensation_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NoncashInvestingAndFinancingItemsAbstract_lbl0" xml:lang="en-US">Noncash Investing and Financing Items [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NoncashInvestingAndFinancingItemsAbstract" xlink:to="us-gaap_NoncashInvestingAndFinancingItemsAbstract_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl0" xml:lang="en-US">Selling, General and Administrative Expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SellingGeneralAndAdministrativeExpense" xlink:to="us-gaap_SellingGeneralAndAdministrativeExpense_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_lbl0" xml:lang="en-US">Long-Term Debt, Maturity, Year One</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:to="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl0" xml:lang="en-US">Liabilities, Current [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesCurrentAbstract" xlink:to="us-gaap_LiabilitiesCurrentAbstract_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl1" xml:lang="en-US">Long-Term Debt, Excluding Current Maturities</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtNoncurrent" xlink:to="us-gaap_LongTermDebtNoncurrent_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage_lbl0" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Rights, Percentage</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage" xlink:to="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_unrecognizedcompensationexpenseyeartwo_lbl1" xml:lang="en-US">unrecognizedcompensationexpenseyeartwo</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_unrecognizedcompensationexpenseyeartwo" xlink:to="logc_unrecognizedcompensationexpenseyeartwo_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfPrepaidExpensesAndOtherAssetsCurrentTableTextBlock_lbl1" xml:lang="en-US">Schedule Of Prepaid Expenses And Other Assets Current Table Text Block</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfPrepaidExpensesAndOtherAssetsCurrentTableTextBlock" xlink:to="logc_ScheduleOfPrepaidExpensesAndOtherAssetsCurrentTableTextBlock_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseRightOfUseAsset_lbl0" xml:lang="en-US">Finance Lease, Right-of-Use Asset, after Accumulated Amortization</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseRightOfUseAsset" xlink:to="us-gaap_FinanceLeaseRightOfUseAsset_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdvertisingExpense_lbl0" xml:lang="en-US">Advertising Expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdvertisingExpense" xlink:to="us-gaap_AdvertisingExpense_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_Unrecognizedcompensationexpenseyearfour_lbl1" xml:lang="en-US">Unrecognizedcompensationexpenseyearfour</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_Unrecognizedcompensationexpenseyearfour" xlink:to="logc_Unrecognizedcompensationexpenseyearfour_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdministrativeFeesExpense_lbl0" xml:lang="en-US">Administrative Fees Expense</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdministrativeFeesExpense" xlink:to="us-gaap_AdministrativeFeesExpense_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsAndNontradeReceivableTextBlock_lbl0" xml:lang="en-US">Accounts and Nontrade Receivable [Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsAndNontradeReceivableTextBlock" xlink:to="us-gaap_AccountsAndNontradeReceivableTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_lbl0" xml:lang="en-US">Operating Lease, Weighted Average Remaining Lease Term</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:to="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AdvertisingCostsPolicyTextBlock_lbl0" xml:lang="en-US">Advertising Cost [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AdvertisingCostsPolicyTextBlock" xlink:to="us-gaap_AdvertisingCostsPolicyTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_lbl0" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Five</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract_lbl" xml:lang="en-US">Intangible Asset, Goodwill and Other [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:to="us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LineOfCredit_lbl0" xml:lang="en-US">Long-Term Line of Credit</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCredit" xlink:to="us-gaap_LineOfCredit_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_IssuanceOfNotesReceivableFromRelatedPartiesUnits_lbl1" xml:lang="en-US">Issuance Of Notes Receivable From Related Parties Units</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_IssuanceOfNotesReceivableFromRelatedPartiesUnits" xlink:to="logc_IssuanceOfNotesReceivableFromRelatedPartiesUnits_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ClassBMemberUnitsMember_lbl0" xml:lang="en-US">Class BMember Units Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ClassBMemberUnitsMember" xlink:to="logc_ClassBMemberUnitsMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax_lbl0" xml:lang="en-US">Discontinued Operation, Gain (Loss) on Disposal of Discontinued Operation, Net of Tax</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax" xlink:to="us-gaap_DiscontinuedOperationGainLossOnDisposalOfDiscontinuedOperationNetOfTax_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_UnreturnedCapitalOfClassAUnitholdersBeforeDistributions_lbl1" xml:lang="en-US">Unreturned Capital Of Class AUnitholders Before Distributions</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_UnreturnedCapitalOfClassAUnitholdersBeforeDistributions" xlink:to="logc_UnreturnedCapitalOfClassAUnitholdersBeforeDistributions_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_EstimatedUsefulLivesOfPropertyPlantAndEquipmentTableTextBlock_lbl1" xml:lang="en-US">Estimated Useful Lives Of Property Plant And Equipment Table Text Block</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_EstimatedUsefulLivesOfPropertyPlantAndEquipmentTableTextBlock" xlink:to="logc_EstimatedUsefulLivesOfPropertyPlantAndEquipmentTableTextBlock_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl0" xml:lang="en-US">Earnings Per Share [Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerShareTextBlock" xlink:to="us-gaap_EarningsPerShareTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_Unrecognizedcompensationexpensetotal_lbl1" xml:lang="en-US">Unrecognizedcompensationexpensetotal</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_Unrecognizedcompensationexpensetotal" xlink:to="logc_Unrecognizedcompensationexpensetotal_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfInventoryCurrentTableTextBlock_lbl0" xml:lang="en-US">Schedule of Inventory, Current [Table Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:to="us-gaap_ScheduleOfInventoryCurrentTableTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_DebtIssuanceCostsPolicyTextBlock_lbl1" xml:lang="en-US">Debt Issuance Costs Policy Text Block</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_DebtIssuanceCostsPolicyTextBlock" xlink:to="logc_DebtIssuanceCostsPolicyTextBlock_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NatureOfOperations_lbl0" xml:lang="en-US">Nature of Operations [Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NatureOfOperations" xlink:to="us-gaap_NatureOfOperations_lbl0"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfAccruedLiabilitiesAbstract" xlink:href="logc-20260226.xsd#logc_ScheduleOfAccruedLiabilitiesAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfAccruedLiabilitiesAbstract_lbl" xml:lang="en-US">Schedule Of Accrued Liabilities Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfAccruedLiabilitiesAbstract" xlink:to="logc_ScheduleOfAccruedLiabilitiesAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_Revenues_lbl0" xml:lang="en-US">Revenues</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_Revenues" xlink:to="us-gaap_Revenues_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_lbl0" xml:lang="en-US">Share-Based Payment Arrangement [Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:to="us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetRetirementObligationLiabilitiesIncurred_lbl0" xml:lang="en-US">Asset Retirement Obligation, Liabilities Incurred</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetRetirementObligationLiabilitiesIncurred" xlink:to="us-gaap_AssetRetirementObligationLiabilitiesIncurred_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivablePeriodIncreaseDecrease_lbl0" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss, Period Increase (Decrease)</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllowanceForDoubtfulAccountsReceivablePeriodIncreaseDecrease" xlink:to="us-gaap_AllowanceForDoubtfulAccountsReceivablePeriodIncreaseDecrease_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CompensationAndRetirementDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CompensationAndRetirementDisclosureAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CompensationAndRetirementDisclosureAbstract_lbl" xml:lang="en-US">Retirement Benefits [Abstract]</label>
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    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ConcentrationRiskPercentage1_lbl0" xml:lang="en-US">Concentration Risk, Percentage</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ConcentrationRiskPercentage1" xlink:to="us-gaap_ConcentrationRiskPercentage1_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_PreCommencementIssuerTenderOffer_lbl0" xml:lang="en-US">Pre-commencement Issuer Tender Offer</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_PreCommencementIssuerTenderOffer" xlink:to="dei_PreCommencementIssuerTenderOffer_lbl0"/>
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    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DepreciationDepletionAndAmortization" xlink:to="us-gaap_DepreciationDepletionAndAmortization_lbl0"/>
    <loc xlink:type="locator" xlink:label="us-gaap_EarningsPerShareAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EarningsPerShareAbstract_lbl" xml:lang="en-US">Earnings Per Share [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerShareAbstract" xlink:to="us-gaap_EarningsPerShareAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_InsuranceRecoveries_lbl0" xml:lang="en-US">Insurance Recoveries</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_InsuranceRecoveries" xlink:to="us-gaap_InsuranceRecoveries_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_RevenueRecognitionPolicyTextBlock_lbl0" xml:lang="en-US">Revenue [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_RevenueRecognitionPolicyTextBlock" xlink:to="us-gaap_RevenueRecognitionPolicyTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_AresCapitalCreditAgreementMember_lbl0" xml:lang="en-US">Ares Capital Credit Agreement Member</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_AresCapitalCreditAgreementMember" xlink:to="logc_AresCapitalCreditAgreementMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_OperatingLeaseCost_lbl0" xml:lang="en-US">Operating Lease, Cost</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_OperatingLeaseCost" xlink:to="us-gaap_OperatingLeaseCost_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ManagementFeePayable_lbl0" xml:lang="en-US">Management Fee Payable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ManagementFeePayable" xlink:to="us-gaap_ManagementFeePayable_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_USSaltParentHoldingsLLCMember_lbl0" xml:lang="en-US">USSalt Parent Holdings LLCMember</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_USSaltParentHoldingsLLCMember" xlink:to="logc_USSaltParentHoldingsLLCMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_EarningsPerSharePolicyTextBlock_lbl0" xml:lang="en-US">Earnings Per Share, Policy [Policy Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_EarningsPerSharePolicyTextBlock" xlink:to="us-gaap_EarningsPerSharePolicyTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MembersEquityAttributableToNoncontrollingInterest_lbl0" xml:lang="en-US">Members&apos; Equity Attributable to Noncontrolling Interest</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MembersEquityAttributableToNoncontrollingInterest" xlink:to="us-gaap_MembersEquityAttributableToNoncontrollingInterest_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_EntityEmergingGrowthCompany_lbl0" xml:lang="en-US">Entity Emerging Growth Company</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_EntityEmergingGrowthCompany" xlink:to="dei_EntityEmergingGrowthCompany_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsCurrent_lbl0" xml:lang="en-US">Assets, Current</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsCurrent" xlink:to="us-gaap_AssetsCurrent_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice_lbl0" xml:lang="en-US">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Forfeitures in Period, Weighted Average Exercise Price</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice" xlink:to="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice_lbl0"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfSupplementalCashFlowInformationAbstract" xlink:href="logc-20260226.xsd#logc_ScheduleOfSupplementalCashFlowInformationAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfSupplementalCashFlowInformationAbstract_lbl" xml:lang="en-US">Schedule Of Supplemental Cash Flow Information Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfSupplementalCashFlowInformationAbstract" xlink:to="logc_ScheduleOfSupplementalCashFlowInformationAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl1" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl1" xml:lang="en-US">Accounts Receivable, after Allowance for Credit Loss, Current</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AccountsReceivableNetCurrent" xlink:to="us-gaap_AccountsReceivableNetCurrent_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock_lbl0" xml:lang="en-US">Schedule of Share-Based Payment Award, Stock Options, Valuation Assumptions [Table Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock" xlink:to="us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock_lbl0"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfPlantPropertyAndEquipmentNetAbstract" xlink:href="logc-20260226.xsd#logc_ScheduleOfPlantPropertyAndEquipmentNetAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfPlantPropertyAndEquipmentNetAbstract_lbl" xml:lang="en-US">Schedule Of Plant Property And Equipment Net Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfPlantPropertyAndEquipmentNetAbstract" xlink:to="logc_ScheduleOfPlantPropertyAndEquipmentNetAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_GrossProfit_lbl0" xml:lang="en-US">Gross Profit</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_GrossProfit" xlink:to="us-gaap_GrossProfit_lbl0"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfEstimatedUsefulLivesOfPropertyPlantAndEquipmentAbstract" xlink:href="logc-20260226.xsd#logc_ScheduleOfEstimatedUsefulLivesOfPropertyPlantAndEquipmentAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfEstimatedUsefulLivesOfPropertyPlantAndEquipmentAbstract_lbl" xml:lang="en-US">Schedule Of Estimated Useful Lives Of Property Plant And Equipment Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ScheduleOfEstimatedUsefulLivesOfPropertyPlantAndEquipmentAbstract" xlink:to="logc_ScheduleOfEstimatedUsefulLivesOfPropertyPlantAndEquipmentAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl0" xml:lang="en-US">Intangible Asset, Excluding Goodwill, after Accumulated Amortization</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:to="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock_lbl0" xml:lang="en-US">Retirement Benefits [Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock" xlink:to="us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PartnersCapitalAccountUnitsTreasury_lbl0" xml:lang="en-US">Partners&apos; Capital Account, Units, Treasury Units Purchased</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PartnersCapitalAccountUnitsTreasury" xlink:to="us-gaap_PartnersCapitalAccountUnitsTreasury_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_RightOfUseAssetsObtainedInExchangeForLeaseLiabilitiesAbstract_lbl0" xml:lang="en-US">Right Of Use Assets Obtained In Exchange For Lease Liabilities Abstract</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_RightOfUseAssetsObtainedInExchangeForLeaseLiabilitiesAbstract" xlink:to="logc_RightOfUseAssetsObtainedInExchangeForLeaseLiabilitiesAbstract_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl0" xml:lang="en-US">Intangible Asset, Finite-Lived, Accumulated Amortization</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs_lbl0" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss, Writeoff</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs" xlink:to="us-gaap_AllowanceForDoubtfulAccountsReceivableWriteOffs_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_PaymentsOfCapitalDistribution_lbl0" xml:lang="en-US">Payments of Capital Distribution</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_PaymentsOfCapitalDistribution" xlink:to="us-gaap_PaymentsOfCapitalDistribution_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl0" xml:lang="en-US">Fair Value Disclosures [Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FairValueDisclosuresTextBlock" xlink:to="us-gaap_FairValueDisclosuresTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingRights_lbl0" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Rights</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingRights" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingRights_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl1" xml:lang="en-US">Subsidiary, Ownership Percentage, Noncontrolling Owner</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:to="us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_NetIncomeLoss_lbl2" xml:lang="en-US">Net Income (Loss) Attributable to Parent</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_NetIncomeLoss_lbl2"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_BuildingAndBuildingImprovementsMember_lbl0" xml:lang="en-US">Building and Building Improvements [Member]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_BuildingAndBuildingImprovementsMember" xlink:to="us-gaap_BuildingAndBuildingImprovementsMember_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LineOfCreditFacilityCommitmentFeeAmount_lbl0" xml:lang="en-US">Line of Credit Facility, Commitment Fee Amount</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LineOfCreditFacilityCommitmentFeeAmount" xlink:to="us-gaap_LineOfCreditFacilityCommitmentFeeAmount_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LongTermDebtTextBlock_lbl0" xml:lang="en-US">Long-Term Debt [Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LongTermDebtTextBlock" xlink:to="us-gaap_LongTermDebtTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsRepurchasedWeightedAveragesExercisePrice_lbl1" xml:lang="en-US">Share Based Compensation Arrangements By Share Based Payment Award Options Repurchased Weighted Averages Exercise Price</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsRepurchasedWeightedAveragesExercisePrice" xlink:to="logc_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsRepurchasedWeightedAveragesExercisePrice_lbl1"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDue_lbl0" xml:lang="en-US">Finance Lease, Liability, to be Paid</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityPaymentsDue" xlink:to="us-gaap_FinanceLeaseLiabilityPaymentsDue_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ScheduleOfShareBasedCompensationActivityTableTextBlock_lbl0" xml:lang="en-US">Share-Based Payment Arrangement, Activity [Table Text Block]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ScheduleOfShareBasedCompensationActivityTableTextBlock" xlink:to="us-gaap_ScheduleOfShareBasedCompensationActivityTableTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_LesseeOperatingAndFinanceLeaseLiabilityMaturityTableTextBlock_lbl0" xml:lang="en-US">Lessee Operating And Finance Lease Liability Maturity Table Text Block</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="logc_LesseeOperatingAndFinanceLeaseLiabilityMaturityTableTextBlock" xlink:to="logc_LesseeOperatingAndFinanceLeaseLiabilityMaturityTableTextBlock_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_AssetsCurrentAbstract_lbl0" xml:lang="en-US">Assets, Current [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_AssetsCurrentAbstract" xlink:to="us-gaap_AssetsCurrentAbstract_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl1" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Exercise Price</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:to="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SubsequentEventsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsequentEventsAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_SubsequentEventsAbstract_lbl" xml:lang="en-US">Subsequent Events [Abstract]</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_SubsequentEventsAbstract" xlink:to="us-gaap_SubsequentEventsAbstract_lbl"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="dei_PreCommencementTenderOffer_lbl0" xml:lang="en-US">Pre-commencement Tender Offer</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="dei_PreCommencementTenderOffer" xlink:to="dei_PreCommencementTenderOffer_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch_lbl0" xml:lang="en-US">Defined Contribution Plan, Employer Matching Contribution, Percent of Match</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch" xlink:to="us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_lbl0" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Year Four</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:to="us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour_lbl0" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year Four</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour" xlink:to="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl0" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Including Exchange Rate Effect and Discontinued Operation</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo_lbl0" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year Two</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:to="us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable_lbl0" xml:lang="en-US">Increase (Decrease) in Accounts Payable</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_IncreaseDecreaseInAccountsPayable" xlink:to="us-gaap_IncreaseDecreaseInAccountsPayable_lbl0"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="us-gaap_LiabilitiesCurrent_lbl0" xml:lang="en-US">Liabilities, Current</label>
    <labelArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="us-gaap_LiabilitiesCurrent" xlink:to="us-gaap_LiabilitiesCurrent_lbl0"/>
    <loc xlink:type="locator" xlink:label="logc_ScheduleOfCalculationOfEarningsPerShareBasicAndDilutedEarningsPerUnitAbstract" xlink:href="logc-20260226.xsd#logc_ScheduleOfCalculationOfEarningsPerShareBasicAndDilutedEarningsPerUnitAbstract"/>
    <label xlink:type="resource" xlink:role="http://www.xbrl.org/2003/role/label" xlink:label="logc_ScheduleOfCalculationOfEarningsPerShareBasicAndDilutedEarningsPerUnitAbstract_lbl" xml:lang="en-US">Schedule Of Calculation Of Earnings Per Share Basic And Diluted Earnings Per Unit Abstract</label>
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