XML 208 R89.htm IDEA: XBRL DOCUMENT
v3.25.3

Income Taxes (Details) - USD ($) $ in Thousands | 3 Months Ended | 9 Months Ended | 12 Months Ended
--- | --- | --- | ---
Sep. 30, 2025 | Sep. 30, 2024 | Sep. 30, 2025 | Sep. 30, 2024 | Dec. 31, 2024 | Dec. 31, 2023
Income Tax Disclosure [Abstract] |  |  |  |  |  |
Effective Income Tax Rate Reconciliation, Percent | 0.00% | 0.00% | 0.00% | 0.00% |  |
Statutory income tax rate |  |  | 21.00% |  | 21.00% |
Valuation allowance increased |  |  |  |  | $ 20,400 | $ 18,100
Description of ownership change |  |  |  |  | An ownership change generally occurs if one or more stockholders or groups of stockholders that own at least 5% of the Company’s stock increase their ownership by more than 50 percentage points over their lowest ownership percentage (by value) within a rolling three-year period. |
Expected unrecognized tax benefits |  |  |  |  | $ 0 |
Unrecognized tax benefits |  |  |  |  | $ 0 | $ 0

X
- Definition Description of ownership change. + References No definition available. + Details
Name: | kdk_DescriptionOfOwnershipChange
Namespace Prefix: | kdk_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

X
- Definition Expected unrecognized tax benefits. + References No definition available. + Details
Name: | kdk_ExpectedUnrecognizedTaxBenefits
Namespace Prefix: | kdk_
Data Type: | xbrli:monetaryItemType
Balance Type: | na
Period Type: | instant

X
- Definition Percentage of current income tax expense (benefit) and deferred income tax expense (benefit) pertaining to continuing operations. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 740 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 12 -Publisher FASB -URI https://asc.fasb.org/1943274/2147482685/740-10-50-12 Reference 2: http://www.xbrl.org/2003/role/exampleRef -Topic 740 -SubTopic 10 -Name Accounting Standards Codification -Section 55 -Paragraph 231 -Publisher FASB -URI https://asc.fasb.org/1943274/2147482663/740-10-55-231 + Details
Name: | us-gaap_EffectiveIncomeTaxRateContinuingOperations
Namespace Prefix: | us-gaap_
Data Type: | dtr-types:percentItemType
Balance Type: | na
Period Type: | duration

X
- Definition Percentage of domestic federal statutory tax rate applicable to pretax income (loss). + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 235 -SubTopic 10 -Name Accounting Standards Codification -Section S50 -Paragraph 1 -Publisher FASB -URI https://asc.fasb.org/1943274/2147480738/235-10-S50-1 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 740 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 12 -Publisher FASB -URI https://asc.fasb.org/1943274/2147482685/740-10-50-12 Reference 3: http://www.xbrl.org/2003/role/exampleRef -Topic 740 -SubTopic 10 -Name Accounting Standards Codification -Section 55 -Paragraph 231 -Publisher FASB -URI https://asc.fasb.org/1943274/2147482663/740-10-55-231 Reference 4: http://www.xbrl.org/2003/role/disclosureRef -Topic 740 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 1 -Subparagraph (SAB Topic 6.I.1.Q1) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479360/740-10-S99-1 Reference 5: http://www.xbrl.org/2003/role/disclosureRef -Topic 235 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 1 -Subparagraph (SX 210.4-08(h)(2)) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480678/235-10-S99-1 + Details
Name: | us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate
Namespace Prefix: | us-gaap_
Data Type: | dtr-types:percentItemType
Balance Type: | na
Period Type: | duration

X
- References No definition available. + Details
Name: | us-gaap_IncomeTaxDisclosureAbstract
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

X
- Definition Amount of increase (decrease) in unrecognized tax benefits attributable to uncertain tax positions taken in tax returns. + References Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 740 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 15A -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482685/740-10-50-15A + Details
Name: | us-gaap_UnrecognizedTaxBenefitsPeriodIncreaseDecrease
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | na
Period Type: | duration

X
- Definition Amount of increase (decrease) in the valuation allowance for a specified deferred tax asset. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 740 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Publisher FASB -URI https://asc.fasb.org/1943274/2147482685/740-10-50-2 + Details
Name: | us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | duration