Commitments and Contingencies, Convertible Security Financing and Convert Registration Rights Agreement (Details)	Feb. 13, 2024 USD ($) $ / shares shares
Convertible Security Financing (Private Placement) and Convert Registration Rights Agreement [Abstract]
Number of trading days under convert registration rights agreement	15 days
New Adagio Convertible Notes [Member]
Convertible Security Financing (Private Placement) and Convert Registration Rights Agreement [Abstract]
Principal amount	$ 12,500,000
Cashless exercise of warrants issued (in shares) | shares	937,500
Number of trading days under convert registration rights agreement	45 days
PIPE Financing [Member]
Convertible Security Financing (Private Placement) and Convert Registration Rights Agreement [Abstract]
Principal amount	$ 45,000,000
PIPE Financing [Member] | 2024 Bridge Financing Notes [Member]
Convertible Security Financing (Private Placement) and Convert Registration Rights Agreement [Abstract]
Convertible promissory note	7,000,000
PIPE Financing [Member] | New Adagio Convertible Notes [Member]
Convertible Security Financing (Private Placement) and Convert Registration Rights Agreement [Abstract]
Principal amount	$ 5,500,000
Cashless exercise of warrants issued (in shares) | shares	412,500
Convertible Security Financing [Member]
Convertible Security Financing (Private Placement) and Convert Registration Rights Agreement [Abstract]
Principal amount	$ 20,000,000
Debt instrument, percentage	13.00%
Conversion price (in dollars per share) | $ / shares	$ 10
Cashless exercise of warrants issued (in shares) | shares	1,500,000
Cash price (in dollars per share) | $ / shares	$ 24
Term of debt	3 years 9 months
Convertible Security Financing [Member] | New Adagio Convertible Notes [Member]
Convertible Security Financing (Private Placement) and Convert Registration Rights Agreement [Abstract]
Principal amount	$ 7,000,000
Cashless exercise of warrants issued (in shares) | shares	525,000
Convertible Security Financing [Member] | Fourth Convertible Promissory Note [Member]
Convertible Security Financing (Private Placement) and Convert Registration Rights Agreement [Abstract]
Principal amount	$ 7,500,000