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Units Outstanding (Details) - shares
9 Months Ended
Jul. 10, 2025
Sep. 30, 2025
Units Outstanding    
Outstanding, beginning balance (in shares)   110,530,329
Units issued (in shares)   1,296,834
Units retired (in shares)   (20,833,912)
Outstanding, ending balance (in shares)   90,993,251
Beneficial ownership of AB Holding units (in shares)   20,833,912
AB Holding Units | Amended Exchange Agreement | EQH    
Units Outstanding    
Units retired (in shares) (19,682,946)  
Beneficial ownership of AB Holding units (in shares) 19,682,946