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Stock-Based Compensation (Fair Value Assumptions) (Details) - Stock Options - $ / shares
12 Months Ended
Sep. 30, 2025
Sep. 30, 2024
Sep. 30, 2023
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Weighted average per option grant date fair value $ 16.24 $ 12.45 $ 19.87
Assumptions Used For Options Grants [Abstract]      
Risk free interest rate, minimum 3.93% 3.78% 3.50%
Risk free interest rate, maximum 4.38% 4.86% 4.15%
Expected term 6 years 6 years 6 years
Expected volatility rate, minimum 48.00% 48.00%  
Expected volatility rate, maximum   48.00% 46.00%
Weighted average volatility 48.00% 46.00% 46.00%
Expected dividend yield 0.00% 0.00% 0.00%