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Fair Value Measurements (Details)
3 Months Ended
Mar. 31, 2024
USD ($)
$ / shares
shares
Mar. 31, 2023
USD ($)
Fair Value Measurements [Abstract]    
Open Market Subscription Agreement expense | $ $ 1,420,405 $ 0
New Adagio Common Stock [Member]    
Fair Value Measurements [Abstract]    
Shares to be issued on Close of Transaction | shares 219,877  
Purchase Price Ratio 1.2  
Fair value per Share at Closing $ 5.25  
New Adagio Common Stock [Member] | Base Share Price [Member]    
Fair Value Measurements [Abstract]    
Measurement input 10  
New Adagio Common Stock [Member] | Adjusted Share Price (1.2X Purchase Price Ratio) [Member]    
Fair Value Measurements [Abstract]    
Measurement input 8.33  
New Adagio Common Stock [Member] | Adjusted Share Price [Member]    
Fair Value Measurements [Abstract]    
Measurement input 7  
New Adagio Common Stock [Member] | Probability of Closing [Member]    
Fair Value Measurements [Abstract]    
Measurement input 0.75  
PIPE Warrants [Member]    
Fair Value Measurements [Abstract]    
PIPE Warrants to be issued on Close of Transaction | shares 183,493  
Fair value per Warrant at Closing $ 1.45  
Coverage Ratio 1.2  
PIPE Warrants [Member] | Base Share Price [Member]    
Fair Value Measurements [Abstract]    
Measurement input 7  
PIPE Warrants [Member] | Strike Price [Member]    
Fair Value Measurements [Abstract]    
Measurement input 10  
PIPE Warrants [Member] | Term [Member]    
Fair Value Measurements [Abstract]    
Term 12 months  
PIPE Warrants [Member] | Average Volatility Rate [Member]    
Fair Value Measurements [Abstract]    
Measurement input 0.70  
PIPE Warrants [Member] | Estimated Expected Warrant Price [Member]    
Fair Value Measurements [Abstract]    
Measurement input 1.21  
Quoted Prices in Active Markets (Level 1) [Member] | U.S. Treasury Securities [Member] | Maximum [Member]    
Investments held in Trust Account [Abstract]    
Investment maturity period 185 days