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Summary of Significant Accounting Policies (Details)
$ / shares in Units, $ in Millions
 1 Months Ended 3 Months Ended 9 Months Ended 12 Months Ended
Sep. 11, 2025
plan
shares
Jan. 31, 2022
acquistion
Sep. 30, 2025
USD ($)
$ / shares
shares
Sep. 30, 2024
USD ($)
Sep. 30, 2025
USD ($)
tranche
$ / shares
shares
Sep. 30, 2024
USD ($)
Dec. 31, 2020
shares
Sep. 10, 2025
class
Dec. 31, 2024
USD ($)
New Accounting Pronouncements or Change in Accounting Principle [Line Items]                  
Customer custodial funds related to GUSD | $     $ 49.3   $ 49.3       $ 58.7
Customer custodial funds due to customers related to GUSD | $     48.7   48.7       $ 58.4
Advertising expense | $     $ 17.9 $ 1.1 $ 28.6 $ 1.7      
Number of equity incentive plans | plan 2                
Number of classes of common units | class               3  
Number of asset acquisitions | acquistion   2              
ESPP                  
New Accounting Pronouncements or Change in Accounting Principle [Line Items]                  
Term of annual increase in shares authorized         10 years        
Annual increase in shares authorized percentage         1.00%        
Stock discount percentage         15.00%        
Accumulated payroll deduction offering period         6 months        
Purchase price of common stock percentage         85.00%        
Maximum annual increase in shares authorized (in shares)         1,500,000        
NSOs                  
New Accounting Pronouncements or Change in Accounting Principle [Line Items]                  
Contractual period         10 years        
Exercise price percentage         100.00%        
Performance period         7 years        
Number of vesting tranches | tranche         4        
NSOs | Share-Based Payment Arrangement, Tranche One                  
New Accounting Pronouncements or Change in Accounting Principle [Line Items]                  
Vesting percentage         50.00%        
NSOs | Share-Based Payment Arrangement, Tranche Two                  
New Accounting Pronouncements or Change in Accounting Principle [Line Items]                  
Vesting percentage         50.00%        
RSUs | Share-Based Payment Arrangement, Tranche One                  
New Accounting Pronouncements or Change in Accounting Principle [Line Items]                  
Vesting percentage         25.00%        
Vesting period         4 years        
RSUs | Share-Based Payment Arrangement, Tranche Two                  
New Accounting Pronouncements or Change in Accounting Principle [Line Items]                  
Vesting percentage         75.00%        
Vesting period         3 years        
Service-Based Incentive Units                  
New Accounting Pronouncements or Change in Accounting Principle [Line Items]                  
Vesting period         4 years        
Service-Based Incentive Units | Share-Based Payment Arrangement, Tranche One                  
New Accounting Pronouncements or Change in Accounting Principle [Line Items]                  
Vesting percentage         25.00%        
Service-Based Incentive Units | Share-Based Payment Arrangement, Tranche Two                  
New Accounting Pronouncements or Change in Accounting Principle [Line Items]                  
Vesting percentage         75.00%        
Vesting period         3 years        
Performance Based Incentive Units                  
New Accounting Pronouncements or Change in Accounting Principle [Line Items]                  
Maximum vesting of granted awards upon achieving certain performance metrics (in shares)             1,300,000    
Service-Based Common Units                  
New Accounting Pronouncements or Change in Accounting Principle [Line Items]                  
Vesting percentage   50.00%              
Vesting period   2 years              
Class A common stock | Common Units                  
New Accounting Pronouncements or Change in Accounting Principle [Line Items]                  
Number of shares resulting from conversion of equity (in shares) 9,800,000                
Class B common stock | Common Units                  
New Accounting Pronouncements or Change in Accounting Principle [Line Items]                  
Number of shares resulting from conversion of equity (in shares) 4,600,000                
Equity Plan                  
New Accounting Pronouncements or Change in Accounting Principle [Line Items]                  
Term of annual increase in shares authorized         10 years        
Annual increase in shares authorized percentage         5.00%        
Empery Common Stock                  
New Accounting Pronouncements or Change in Accounting Principle [Line Items]                  
Number of shares available to purchase from warrant rights (in shares)     900,000   900,000        
Exercise price of warrants (in dollars per share) | $ / shares     $ 10.00   $ 10.00        
Exercisable increments percentage         20.00%        
Exercisable increments, volume-weighted average price per share increasing increments per share (in dollars per share) | $ / shares         $ 5.00        
Percentage of warrant vesting conditions met     40.00%   40.00%        
Empery Common Stock | Minimum                  
New Accounting Pronouncements or Change in Accounting Principle [Line Items]                  
Exercisable increments, volume-weighted average price per share (in dollars per share) | $ / shares         $ 10.00        
Empery Common Stock | Maximum                  
New Accounting Pronouncements or Change in Accounting Principle [Line Items]                  
Exercisable increments, volume-weighted average price per share (in dollars per share) | $ / shares         $ 30.00