XML 176 R57.htm IDEA: XBRL DOCUMENT
v3.25.3

Fair Value Measurements - Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis (Details) - USD ($) $ in Thousands | Sep. 30, 2025 | Dec. 31, 2024 | Dec. 31, 2023
--- | --- | --- | ---
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets |  | $ 9,439 | $ 12,097
Liabilities | $ 133,750 | 60,920 | 12,045
Level 1 [Member] |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets |  | 9,439 | 12,097
Level 3 [Member] |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Liabilities | 133,750 | 60,920 | 12,045
PIPE Warrants [Member] |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Liabilities | 86,359 |  |
PIPE Warrants [Member] | Level 3 [Member] |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Liabilities | 86,359 |  |
NRA Warrants [Member] |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Liabilities | 36,968 |  |
NRA Warrants [Member] | Level 3 [Member] |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Liabilities | 36,968 |  |
Second lien loans |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Liabilities | 10,423 |  |
Second lien loans | Level 3 [Member] |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Liabilities | $ 10,423 |  |
SAFEs [Member] |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Liabilities |  | 59,301 | 10,000
SAFEs [Member] | Level 3 [Member] |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Liabilities |  | 59,301 | 10,000
Redeemable convertible preferred stock warrant liabilities [Member] |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Liabilities |  | 1,619 | 2,045
Redeemable convertible preferred stock warrant liabilities [Member] | Level 3 [Member] |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Liabilities |  | 1,619 | 2,045
Money market funds [Member] |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets |  | 9,439 | 7,042
Money market funds [Member] | Level 1 [Member] |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets |  | $ 9,439 | 7,042
US Treasury Securities [Member] |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets |  |  | 5,055
US Treasury Securities [Member] | Level 1 [Member] |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |  |
Assets |  |  | $ 5,055

X
- Definition Fair value portion of asset recognized for present right to economic benefit. + References Reference 1: http://www.xbrl.org/2003/role/exampleRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 55 -Paragraph 100 -Publisher FASB -URI https://asc.fasb.org/1943274/2147482078/820-10-55-100 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (b) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-2 Reference 3: http://www.xbrl.org/2003/role/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-2 + Details
Name: | us-gaap_AssetsFairValueDisclosure
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | instant

X
- Definition Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table. + References Reference 1: http://www.xbrl.org/2003/role/exampleRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 55 -Paragraph 100 -Publisher FASB -URI https://asc.fasb.org/1943274/2147482078/820-10-55-100 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (b) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-2 Reference 3: http://www.xbrl.org/2003/role/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-2 Reference 4: http://www.xbrl.org/2003/role/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 3 -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-3 + Details
Name: | us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

X
- Definition Fair value of financial and nonfinancial obligations. + References Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-2 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (b) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-2 + Details
Name: | us-gaap_LiabilitiesFairValueDisclosure
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | instant

X
- Details
Name: | us-gaap_FairValueByFairValueHierarchyLevelAxis=us-gaap_FairValueInputsLevel1Member
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_FairValueByFairValueHierarchyLevelAxis=us-gaap_FairValueInputsLevel3Member
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_FairValueByLiabilityClassAxis=kdk_PipeWarrantsMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_FairValueByLiabilityClassAxis=kdk_NraWarrantsMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_FairValueByLiabilityClassAxis=us-gaap_SecuritiesLoanedOrSoldUnderAgreementsToRepurchaseMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_FairValueByLiabilityClassAxis=kdk_SimpleAgreementsForFutureEquityMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_FairValueByLiabilityClassAxis=kdk_RedeemableConvertiblePreferredStockWarrantLiabilitiesMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_FairValueByAssetClassAxis=us-gaap_MoneyMarketFundsMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_FairValueByAssetClassAxis=us-gaap_USTreasurySecuritiesMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |