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Stock-Based Compensation - Stock-based Compensation Expense (Details) - USD ($) $ in Millions | 3 Months Ended | 9 Months Ended
--- | --- | ---
Jun. 30, 2025 | Jun. 30, 2024 | Jun. 30, 2025 | Jun. 30, 2024
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items] |  |  |  |
Total Stock-Based Compensation Expense | $ 5.9 | $ 6.5 | $ 22.2 | $ 20.4
Tax benefit associated with stock-based compensation costs recognized | 0.9 | 0.6 | 3.1 | 1.8
Equity Awards |  |  |  |
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items] |  |  |  |
Total Stock-Based Compensation Expense | 5.9 | 6.3 | 22.1 | 20.1
Liability Awards |  |  |  |
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items] |  |  |  |
Total Stock-Based Compensation Expense | 0.0 | 0.2 | 0.1 | 0.3
Time-Vested Restricted Stock Units (TVUs) |  |  |  |
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items] |  |  |  |
Total Stock-Based Compensation Expense | 5.1 | 4.8 | 16.9 | 15.4
Performance-Based Restricted Stock Units (PSUs) |  |  |  |
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items] |  |  |  |
Total Stock-Based Compensation Expense | 0.5 | 0.7 | 3.8 | 2.0
Stock Appreciation Rights (SARs) |  |  |  |
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items] |  |  |  |
Total Stock-Based Compensation Expense | 0.3 | 1.0 | 1.5 | 3.0
Cost of products sold |  |  |  |
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items] |  |  |  |
Total Stock-Based Compensation Expense | 0.7 | 0.6 | 1.9 | 2.6
Selling and administrative expense |  |  |  |
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items] |  |  |  |
Total Stock-Based Compensation Expense | 5.1 | 5.3 | 17.2 | 16.1
Research and development expense |  |  |  |
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items] |  |  |  |
Total Stock-Based Compensation Expense | 0.1 | 0.6 | 0.3 | 1.7
Other operating expense |  |  |  |
Share-based Payment Arrangement, Expensed and Capitalized, Amount [Line Items] |  |  |  |
Total Stock-Based Compensation Expense | $ 0.0 | $ 0.0 | $ 2.8 | $ 0.0

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