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Share-Based Compensation - Narrative (Details) - USD ($) $ / shares in Units, $ in Millions | 12 Months Ended
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Sep. 30, 2025 | Sep. 30, 2024 | Sep. 30, 2023
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Share-based compensation arrangement by share-based payment award, number of shares authorized (in shares) | 5,400,000 |  |
Stock options authorized (in shares) | 4,400,000 |  |
Allocated share-based compensation expense | $ 49.0 | $ 37.2 | $ 28.0
Weighted average grant date fair value, granted (in dollar per share) | $ 27.93 | $ 26.77 | $ 22.14
Employee service share-based compensation, non vested awards, total compensation cost not yet recognized, stock options | $ 45.9 |  |
Employee service share-based compensation, non vested awards, total compensation cost not yet recognized, period for recognition | 2 years 7 months 6 days |  |
Share-based compensation arrangement by share-based payment award, options, exercises in period, total intrinsic value | $ 22.4 | $ 9.8 | $ 4.2
Restricted Stock Units |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Employee service share-based compensation, nonvested awards, total compensation cost not yet recognized | $ 63.7 |  |
Employee service share-based compensation, nonvested awards, total compensation cost not yet recognized, period for recognition, restricted stock | 1 year 2 months 26 days |  |
Number of shares outstanding, granted (in shares) | 749,809 |  |
Performance Shares |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Employee service share-based compensation, nonvested awards, total compensation cost not yet recognized | $ 15.0 |  |
Number of shares outstanding, granted (in shares) | 225,000 |  |
Performance Shares | Minimum |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Number of shares outstanding, granted (in shares) | 0 |  |
Performance Shares | Maximum |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Number of shares outstanding, granted (in shares) | 337,500 |  |

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- Definition Weighted average period over which unrecognized compensation is expected to be recognized for equity-based compensation plans, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days for restricted stock plan. + References No definition available. + Details
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- Definition Line items represent financial concepts included in a table. 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