Stockholders’ Equity (Deficit) and Preferred Stock (Details) - USD ($)				12 Months Ended
	Aug. 16, 2024	Jun. 30, 2024	May 31, 2024	Dec. 31, 2024	Dec. 31, 2023
Stockholders’ Equity (Deficit) and Preferred Stock [Line Items]
Cumulative preferred percentage				8.00%
Invested per share (in Dollars per share)				$ 1
Undistributed preferred returns (in Dollars)					$ 5,813,749
Peferred returns per share (in Dollars per share)					$ 0
Share issued of founding companies	1,069,346
RSU [Member]
Stockholders’ Equity (Deficit) and Preferred Stock [Line Items]
Common stock shares issued			404,177
ATG Sellers [Member]
Stockholders’ Equity (Deficit) and Preferred Stock [Line Items]
Combination of shares				1,069,346
Successor [Member]
Stockholders’ Equity (Deficit) and Preferred Stock [Line Items]
Common stock, shares authorized				50,000,000
Common stock par value (in Dollars per share)				$ 0.01
Share issued of founding companies				6,888,128
Series A Preferred Stock [Member]
Stockholders’ Equity (Deficit) and Preferred Stock [Line Items]
Preferred stock, shares authorized				10,000,000
Preferred stock, par value (in Dollars per share)				$ 0.01
Redemption amount (in Dollars)					$ 8,880,672
IPO [Member]
Stockholders’ Equity (Deficit) and Preferred Stock [Line Items]
Price per share (in Dollars per share)		$ 15
Gross proceeds (in Dollars)		$ 20,018,250	$ 215,000,000
Common stocks additional shares				2,149,999
IPO [Member] | Common Stock [Member]
Stockholders’ Equity (Deficit) and Preferred Stock [Line Items]
Common stock shares issued			14,333,333
Price per share (in Dollars per share)			$ 15
Net proceeds (in Dollars)			$ 192,273,599
Over-Allotment Option [Member]
Stockholders’ Equity (Deficit) and Preferred Stock [Line Items]
Gross proceeds (in Dollars)		$ 21,500,000
Shares issued		1,435,000