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Stock-Based Compensation - Valuation Assumptions (Details)
12 Months Ended
Sep. 30, 2025
Sep. 30, 2024
Sep. 30, 2023
Performance Shares      
Stock Based Compensation Activity [Line Items]      
Risk-free interest rate 4.01% 4.21% 4.04%
Expected volatility of the Company’s stock 28.50% 27.20% 33.50%
Employee Stock Option      
Stock Based Compensation Activity [Line Items]      
Expected life of option (years) 5 years 8 months 12 days 5 years 8 months 12 days 5 years 9 months 18 days
Risk-free interest rate 4.07% 3.86% 3.59%
Expected volatility of the Company’s stock 30.20% 29.80% 29.40%
Expected dividend yield on the Company’s stock 1.83% 2.77% 2.10%