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Goodwill and Intangible Assets - Schedule of Goodwill and Acquired Intangible Assets (Details) - USD ($) $ in Thousands | Jun. 30, 2026 | Sep. 30, 2025
--- | --- | ---
Intangible Asset, Finite-Lived [Line Items] |  |
Goodwill (not amortized) | $ 3,398,303 | $ 3,493,316
Intangible assets with finite lives (amortized), Gross Carrying Amount | 1,694,193 | 1,853,441
Intangible assets with finite lives (amortized), Accumulated Amortization | 928,394 | 1,028,778
Intangible assets with finite lives (amortized), Net Book Value | 765,799 | 824,663
Intangible Assets, Net (Including Goodwill) | 4,164,102 | 4,317,979
Purchased software |  |
Intangible Asset, Finite-Lived [Line Items] |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 547,640 | 639,104
Intangible assets with finite lives (amortized), Accumulated Amortization | 401,974 | 472,357
Intangible assets with finite lives (amortized), Net Book Value | 145,666 | 166,747
Capitalized Software |  |
Intangible Asset, Finite-Lived [Line Items] |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 22,877 | 22,877
Intangible assets with finite lives (amortized), Accumulated Amortization | 22,877 | 22,877
Intangible assets with finite lives (amortized), Net Book Value | 0 | 0
Customer Lists and Relationships |  |
Intangible Asset, Finite-Lived [Line Items] |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 1,088,385 | 1,149,262
Intangible assets with finite lives (amortized), Accumulated Amortization | 480,308 | 505,202
Intangible assets with finite lives (amortized), Net Book Value | 608,077 | 644,060
Trademarks and Trade Names |  |
Intangible Asset, Finite-Lived [Line Items] |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 31,822 | 38,179
Intangible assets with finite lives (amortized), Accumulated Amortization | 19,766 | 24,323
Intangible assets with finite lives (amortized), Net Book Value | 12,056 | 13,856
Other |  |
Intangible Asset, Finite-Lived [Line Items] |  |
Intangible assets with finite lives (amortized), Gross Carrying Amount | 3,469 | 4,019
Intangible assets with finite lives (amortized), Accumulated Amortization | 3,469 | 4,019
Intangible assets with finite lives (amortized), Net Book Value | $ 0 | $ 0

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