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Share-Based Compensation - Narrative (Details) - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
	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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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.

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