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v3.25.3

Accrued Collaboration Credit (Details) - USD ($) | 3 Months Ended | 9 Months Ended | 12 Months Ended
--- | --- | --- | ---
Sep. 30, 2025 | Jun. 30, 2025 | Mar. 31, 2025 | Dec. 31, 2024 | Sep. 30, 2024 | Jun. 30, 2024 | Mar. 31, 2024 | Sep. 30, 2025 | Sep. 30, 2024 | Dec. 31, 2024
Accrued Collaboration Credit [Roll Forward] |  |  |  |  |  |  |  |  |  |
Beginning Balance |  |  | $ (981,111) |  |  |  |  | $ (981,111) |  |
Ending Balance | $ (29,057) |  |  | $ (981,111) |  |  |  | (29,057) |  | $ (981,111)
TOI Collaboration Agreement |  |  |  |  |  |  |  |  |  |
Accrued Collaboration Credit [Roll Forward] |  |  |  |  |  |  |  |  |  |
Beginning Balance | (219,625) |  | (981,111) | (1,119,591) | $ (201,536) |  | $ 0 | (981,111) | $ 0 | 0
Prepaid expenses included in reimbursement, not yet incurred | 10,015 | $ 163,277 | 251,304 | 92,546 | (788,934) | $ (450,056) | 0 | 424,596 | (1,238,990) | (1,146,444)
Accrued expenses for work performed, not yet invoiced | 179,141 | 351,681 | $ (9,420) | 45,814 | (126,340) | 248,520 | $ 0 | 521,402 | 122,180 | 167,994
Foreign currency adjustments | 1,413 |  |  |  | (2,781) |  |  | 6,056 | (2,781) |
Ending Balance | $ (29,057) | $ (219,625) |  | $ (981,111) | $ (1,119,591) | $ (201,536) |  | $ (29,057) | $ (1,119,591) | $ (981,111)

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- Definition Accrued Collaboration Credit, Current + References No definition available. + Details
Name: | kprx_AccruedCollaborationCreditCurrent
Namespace Prefix: | kprx_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | instant

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- Definition Accrued Collaboration Credit + References No definition available. + Details
Name: | kprx_AccruedCollaborationCreditRollForward
Namespace Prefix: | kprx_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

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- Definition Collaborative Arrangement, Accrued Expense Adjustments + References No definition available. + Details
Name: | kprx_CollaborativeArrangementAccruedExpenseAdjustments
Namespace Prefix: | kprx_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

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- Definition Collaborative Arrangement, Deferred Collaboration Credit Adjustments + References No definition available. + Details
Name: | kprx_CollaborativeArrangementDeferredCollaborationCreditAdjustments
Namespace Prefix: | kprx_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

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- Definition Collaborative Arrangement, Foreign Currency Adjustments + References No definition available. + Details
Name: | kprx_CollaborativeArrangementForeignCurrencyAdjustments
Namespace Prefix: | kprx_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

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- Details
Name: | us-gaap_TypeOfArrangementAxis=kprx_TOICollaborationAgreementMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |