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Accrued Expenses and Other Current Liabilities - Schedule of Accrued Expenses and Other Current Liabilities (Details) - USD ($) $ in Thousands	Sep. 30, 2025	Dec. 31, 2024
Schedule of Accrued Expenses and Other Current Liabilities [Abstract]
Accrued research and development	$ 4,787	$ 1,084
Accrued employee compensation and benefits	2,846	2,041
Accrued professional and consulting	1,015	221
Total	$ 8,648	$ 3,346

X

- Definition

Accrued research and development.

+ References

No definition available.

+ Details

Name:	orka_AccruedResearchAndDevelopment
Namespace Prefix:	orka_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

Carrying value as of the balance sheet date of obligations, excluding pension and other postretirement benefits, incurred through that date and payable for perquisites provided to employees pertaining to services received from them. Used to reflect the current portion of the liabilities (due within one year or within the normal operating cycle if longer).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(20))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

+ Details

Name:	us-gaap_AccruedEmployeeBenefitsCurrent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

Amount of expenses incurred but not yet paid nor invoiced, and liabilities classified as other.

+ References

No definition available.

+ Details

Name:	us-gaap_AccruedLiabilitiesAndOtherLiabilities
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- References

No definition available.

+ Details

Name:	us-gaap_AccruedLiabilitiesAndOtherLiabilitiesAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Carrying value as of the balance sheet date of obligations incurred through that date and payable for professional fees, such as for legal and accounting services received. Used to reflect the current portion of the liabilities (due within one year or within the normal operating cycle if longer).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(20))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

+ Details

Name:	us-gaap_AccruedProfessionalFeesCurrent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant