Mezzanine Equity and Stockholders' Equity (Deficit) - Number of shares outstanding (Details) - shares	Jul. 31, 2024	Dec. 31, 2024	Dec. 31, 2023
Mezzanine Equity and Stockholders' Equity (Deficit)
Total		15,198,232	779,908
Common Stock
Mezzanine Equity and Stockholders' Equity (Deficit)
Shares issued during period (in shares)	3,287,018
Conversion of ARYA convertible promissory Notes (in shares)	355,100
Conversion of ARYA Class A ordinary shares and Class B ordinary shares (in shares)	2,089,000
Conversion of Class A ordinary shares subject to redemption	123,520
Shares issued for acquisition of Legacy Adagio	6,771,769
Additional shares issued and reclassification of Class A ordinary shares subject to non-redemption agreements and open market subscription agreements	761,229
Total	13,387,636
Common Stock | PIPE Investor
Mezzanine Equity and Stockholders' Equity (Deficit)
Shares issued during period (in shares)	3,287,018