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Concentrations of Credit Risk - Additional Information (Detail)	3 Months Ended		12 Months Ended
	Dec. 31, 2024 USD ($) Vendor	Dec. 31, 2023	Sep. 30, 2024 USD ($)	Sep. 30, 2023 USD ($)	Sep. 30, 2022
Concentration Risk [Line Items]
Restricted cash	$ 3,004,000		$ 3,009,000	$ 3,132,000
Outstanding letters of credit to be collateralized by amounts on deposit	3,000,000		3,000,000	3,100,000
Allowance for doubtful accounts	$ 0		$ 0	$ 0
Number of vendors represents more than ten percentage of purchases | Vendor	2
AAR [Member]
Concentration Risk [Line Items]
Percentage of purchases during year	18.00%
Standard Aero Holdings, Inc. [Member]
Concentration Risk [Line Items]
Percentage of purchases during year	13.00%
Sales Revenue, Net [Member] | American Airlines Inc. [Member] | Customer Concentration Risk [Member]
Concentration Risk [Line Items]
Concentration risk, percentage	0.00%	0.00%	0.00%	23.00%	45.00%
Sales Revenue, Net [Member] | United CPA [Member] | Customer Concentration Risk [Member]
Concentration Risk [Line Items]
Concentration risk, percentage	34.40%		35.80%	48.70%
Sales Revenue, Net [Member] | United [Member] | Customer Concentration Risk [Member]
Concentration Risk [Line Items]
Concentration risk, percentage	98.00%	96.00%	97.00%	73.00%	48.00%

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