Fair Value Measurements - Schedule of Level 3 Valuation of the Public Warrants Issued (Details) - Level 3 [Member] - Public Warrants [Member]	Oct. 29, 2025
Implied Class A ordinary share price [Member]
Fair Value Measurement Inputs and Valuation Techniques [Line Items]
Warrants, Measurement Input	9.71
Exercise price [Member]
Fair Value Measurement Inputs and Valuation Techniques [Line Items]
Warrants, Measurement Input	11.5
Expected term to De-SPAC [Member]
Fair Value Measurement Inputs and Valuation Techniques [Line Items]
Warrants, Measurement Input	2
Warrant term [Member]
Fair Value Measurement Inputs and Valuation Techniques [Line Items]
Warrants, Measurement Input	7
Volatility [Member]
Fair Value Measurement Inputs and Valuation Techniques [Line Items]
Warrants, Measurement Input	10
Probability of De-SPAC and market adjustment [Member]
Fair Value Measurement Inputs and Valuation Techniques [Line Items]
Warrants, Measurement Input	40
Risk-free rate (continuous) [Member]
Fair Value Measurement Inputs and Valuation Techniques [Line Items]
Warrants, Measurement Input	3.83

Apex Treasury Corp 10-K