XML 190 R71.htm IDEA: XBRL DOCUMENT v3.25.3

Warrant Liabilities - Schedule of redeemable convertible preferred stock warrant liabilities (Details) - $ / shares	Sep. 30, 2025	Dec. 31, 2024
Shares Underlying Warrants	25,376	1,969
PIPE Warrants [Member]
Shares Underlying Warrants	17,769
Exercise Price Per Share	$ 12
Expiration Date	Sep. 24, 2031
NRA Warrants [Member]
Shares Underlying Warrants	7,607
Exercise Price Per Share	$ 12
Expiration Date	Sep. 24, 2031

X

- Definition

Redeemable class of warrant or right, outstanding.

+ References

No definition available.

+ Details

Name:	kdk_RedeemableClassOfWarrantOrRightOutstanding
Namespace Prefix:	kdk_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

X

- Definition

Exercise price per share or per unit of warrants or rights outstanding.

+ 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 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(h)(4))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480678/235-10-S99-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481112/505-10-50-3

+ Details

Name:	us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

X

- Definition

Expiration date of outstanding warrant and right embodying unconditional obligation requiring redemption by transferring asset at specified or determinable date or upon event certain to occur, in YYYY-MM-DD format.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (bbb)(2)(i)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (bbb)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (bbb)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

+ Details

Name:	us-gaap_WarrantsAndRightsOutstandingMaturityDate
Namespace Prefix:	us-gaap_
Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	instant

X

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=kdk_PipeWarrantsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=kdk_NraWarrantsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: