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Summary of Significant Accounting Policies - Stock-Based Compensation (Details)
 12 Months Ended
Sep. 30, 2025
Minimum  
New Accounting Pronouncements or Change in Accounting Principle [Line Items]  
Shares and options vesting period 1 year
Maximum  
New Accounting Pronouncements or Change in Accounting Principle [Line Items]  
Shares and options vesting period 4 years