Basis of Presentation and Significant Accounting Policies - Goodwill and Indefinite-lived Intangible Assets (Details) - USD ($)	12 Months Ended
Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Goodwill and Indefinite-lived Intangible Assets
Impairment losses in connection with the goodwill	$ 0	$ 0	$ 0
Impairment of intangible assets with indefinite lives	$ 0	$ 0	$ 0

Amount of impairment loss from asset representing future economic benefit arising from other asset acquired in business combination or from joint venture formation or both, that is not individually identified and separately recognized.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
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-Topic 230
-Publisher FASB
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Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Topic 350
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Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 350
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Reference 4: http://www.xbrl.org/2003/role/exampleRef
-Topic 820
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-Topic 350
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Reference 6: http://www.xbrl.org/2003/role/disclosureRef
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Name:	us-gaap_GoodwillImpairmentLoss
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration