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Income Taxes - Schedule of Deferred Income Taxes, Net (Parenthetical) (Details)
$ in Millions
12 Months Ended
Sep. 30, 2024
USD ($)
Income Tax Disclosure [Line Items]  
NOL carryforwards, U.S. state $ 0.4
NOL carryforwards, Ireland $ 4.4
State [Member]  
Income Tax Disclosure [Line Items]  
Net operating loss carryforwards, beginning of expiration year Jan. 01, 2029
R&D Credit Carryforwards [Member] | Federal and State [Member] | 2028 [Member]  
Income Tax Disclosure [Line Items]  
Net operating loss carryforwards, beginning of expiration year Jan. 01, 2029