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Stock-Based Compensation (Details) - Schedule of Award Types of Company’s Stock-Based Compensation Expense - USD ($) $ in Thousands	3 Months Ended	8 Months Ended
	Sep. 30, 2024	Sep. 30, 2024
Schedule of Award Types of Company’s Stock-Based Compensation Expense [Abstract]
Paruka warrant obligation	$ 7,251	$ 7,681
Employee warrants	1,314	1,314
Stock options	427	765
Employee stock purchase plan	9	9
Total	$ 9,001	$ 9,769

X

- Definition

The amount of employee warrants.

+ References

No definition available.

+ Details

Name:	orka_EmployeeWarrants
Namespace Prefix:	orka_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

X

- Definition

Paruka warrant obligation.

+ References

No definition available.

+ Details

Name:	orka_ParukaWarrantObligation
Namespace Prefix:	orka_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

X

- References

No definition available.

+ Details

Name:	orka_ScheduleOfAwardTypesOfCompanySStockBasedCompensationExpenseAbstract
Namespace Prefix:	orka_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Amount of expense for employee benefit and equity-based compensation.

+ References

No definition available.

+ Details

Name:	us-gaap_EmployeeBenefitsAndShareBasedCompensation
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

X

- Definition

Amount of noncash expense for share-based payment arrangement.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 45
-Paragraph 28
-Subparagraph (a)
-SubTopic 10
-Topic 230
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482740/230-10-45-28

+ Details

Name:	us-gaap_ShareBasedCompensation
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

X

- Definition

Value of stock issued as a result of the exercise of stock options.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-SubTopic 10
-Topic 505
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481112/505-10-50-2

Reference 2: 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(29))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 3: 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(30))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 4: 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(31))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 5: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.3-04)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480008/505-10-S99-1

+ Details

Name:	us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration