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Warrants - Narrative (Details) |  |  | 1 Months Ended | 3 Months Ended | 9 Months Ended | 12 Months Ended |  |  |
--- | --- | --- | --- | --- | --- | --- | --- | --- | ---
Aug. 24, 2024 USD ($) $ / shares | Jul. 25, 2024 USD ($) $ / shares yr shares | Jul. 31, 2024 $ / shares shares | Sep. 30, 2024 USD ($) | Sep. 30, 2023 USD ($) | Sep. 30, 2024 USD ($) | Sep. 30, 2023 USD ($) | Dec. 31, 2018 $ / shares shares | Aug. 31, 2024 $ / shares | Feb. 29, 2024 shares | Dec. 31, 2023 USD ($) shares
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Exercise price of warrants (in dollars per share) | $ / shares |  |  |  |  |  |  |  | $ 14.40 |  |  |
Warrants outstanding, term |  |  |  |  |  |  |  | 10 years |  |  |
Warrant liability | $ |  |  |  | $ 457 |  | $ 457 |  |  |  |  | $ 35,453
Loss on issuance of common stock | $ |  |  |  | 2,132,800 | $ 0 | 2,132,800 | $ 0 |  |  |  |
Change in fair value of warrant liability | $ |  |  |  |  |  | $ (4,033,996) | $ (9,350) |  |  |  |
Reclass of warrant liability | $ | $ (1,900,000) |  |  | $ (1,866,200) |  |  |  |  |  |  |
Measurement Input, Expected Dividend Rate |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Derivative liability, measurement input |  | 0 |  |  |  |  |  |  |  |  |
Measurement Input, Price Volatility |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Derivative liability, measurement input |  | 1.19 |  |  |  |  |  |  |  |  |
Minimum | Measurement Input, Share Price |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Derivative liability, measurement input | $ / shares |  | 1.14 |  |  |  |  |  |  |  |  |
Minimum | Measurement Input, Risk Free Interest Rate |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Derivative liability, measurement input |  | 0.0413 |  |  |  |  |  |  |  |  |
Minimum | Measurement Input, Volume Weighted Average Price |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Derivative liability, measurement input | $ / shares |  | 1.14 |  |  |  |  |  |  |  |  |
Minimum | Measurement Input, Strike Price |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Derivative liability, measurement input | $ / shares |  | 1.50 |  |  |  |  |  |  |  |  |
Minimum | Measurement Input, Expected Term |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Derivative liability, measurement input | yr |  | 5.00 |  |  |  |  |  |  |  |  |
Maximum | Measurement Input, Share Price |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Derivative liability, measurement input | $ / shares |  | 1.40 |  |  |  |  |  |  |  |  |
Maximum | Measurement Input, Risk Free Interest Rate |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Derivative liability, measurement input |  | 0.0414 |  |  |  |  |  |  |  |  |
Maximum | Measurement Input, Strike Price |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Derivative liability, measurement input | $ / shares |  | 1.40 |  |  |  |  |  |  |  |  |
Maximum | Measurement Input, Expected Term |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Derivative liability, measurement input | yr |  | 4.92 |  |  |  |  |  |  |  |  |
Class A Warrant |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Exercise price of warrants (in dollars per share) | $ / shares |  | $ 1.50 | $ 1.50 |  |  |  |  |  | $ 0.7043 |  |
Warrants outstanding, term |  | 5 years |  |  |  |  |  |  |  |  |
Warrants issued to underwriters (in shares) | shares |  | 13,330,000 | 13,330,000 |  |  |  |  |  |  |  |
Reset price, number of days following issuance |  | 30 days | 30 days |  |  |  |  |  |  |  |
Warrant reset price, percentage of volume weighted average price |  | 1 |  |  |  |  |  |  |  |  |
Class of warrant or right, volume weighted average price, number of trading days |  | 5 days |  |  |  |  |  |  |  |  |
Reset price, floor (in dollars per share) | $ / shares |  | $ 0.32 |  |  |  |  |  |  |  |  |
Warrant reset price, floor, percentage of closing stock price |  | 0.20 |  |  |  |  |  |  |  |  |
Reset price (in dollars per share) | $ / shares | $ 0.7043 |  |  |  |  |  |  |  |  |  |
Class of warrant or right, expiration term |  | 5 years |  |  |  |  |  |  |  |  |
Class of warrant or right, ownership limitation percentage |  | 4.99% |  |  |  |  |  |  |  |  |
Class of warrant or right, ownership limitation, election of the holder |  | 9.99% |  |  |  |  |  |  |  |  |
Warrant liability | $ |  | $ 12,100,000 |  |  |  |  |  |  |  |  |
Loss on issuance of common stock | $ |  | 2,100,000 |  |  |  |  |  |  |  |  |
Change in fair value of warrant liability | $ | $ 4,000,000.0 |  |  |  |  |  |  |  |  |  |
Underwriter |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Warrants outstanding, term |  |  |  | 5 years |  | 5 years |  |  |  |  |
Over-Allotment Option | Underwriter |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Warrants issued to underwriters (in shares) | shares |  |  | 266,600 |  |  |  |  |  |  | 22,223 | 2,000
Follow-On Public Offering |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Gross proceeds from follow-on public offering | $ |  | $ 10,000,000.0 |  |  |  |  |  |  |  |  |
Common Stock |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Convertible debt, warrants issued (in shares) | shares |  |  |  |  |  |  |  | 1,596 |  |  |
Warrant |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right [Line Items] |  |  |  |  |  |  |  |  |  |  |
Fair value of warrants | $ |  |  |  | $ 457 |  | $ 457 |  |  |  |  | $ 35,453

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