Mezzanine Equity and Stockholders' Equity (Deficit) - Voting Rights (Details)	Jun. 30, 2025 item shares
Mezzanine Equity and Stockholders' Equity (Deficit)
Minimum shares of common stock converted from preferred stock \| shares	1,000,000
Number of directors elected by holders of preferred stock	4
Number of directors elected by holders of common stock	1

The minimum number of shares of common stock that can be converted from preferred stock, subject to appropriate adjustment in the event of any stock dividends, stock split, combination or other similar recapitalization with respect to the common stock, which defines the voting rights.

No definition available.

Name:	adgm_ThresholdMinimumNumberOfCommonStockConvertibleFromConvertiblePreferredStockOutstandingForVoting
Namespace Prefix:	adgm_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant