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Stockholders' Equity - Additional Information (Details) - USD ($) |  |  |  |  | 3 Months Ended | 9 Months Ended |  |  |  |  |
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
Aug. 01, 2025 | Jun. 16, 2025 | Mar. 06, 2025 | Feb. 14, 2025 | Sep. 30, 2025 | Sep. 30, 2025 | Sep. 30, 2024 | Jun. 30, 2025 | Mar. 31, 2025 | Dec. 31, 2024 | Feb. 14, 2024 | Dec. 31, 2023
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Common stock, shares authorized |  |  |  | 600,000,000 | 600,000,000 | 600,000,000 |  |  |  | 600,000,000 |  |
Common stock, par value |  |  |  | $ 0.0001 | $ 0.0001 | $ 0.0001 |  |  |  | $ 0.0001 |  |
Common stock, shares issued |  |  |  |  | 48,720,405 | 48,720,405 | 5,800,000 |  |  | 5,836,882 |  |
Common stock, shares outstanding |  |  |  |  | 48,018,545 | 48,018,545 | 5,800,000 |  |  | 5,836,882 |  |
Common Stock, Voting Rights |  |  |  |  |  | one vote per share |  |  |  |  |  |
Preferred stock , shares authorized |  |  |  |  | 20,000,000 | 20,000,000 |  |  |  | 20,000,000 | 20,000,000 |
Preferred stock, par value |  |  |  |  | $ 0.0001 | $ 0.0001 |  |  |  | $ 0.0001 | $ 0.0001 |
Preferred stock , shares issued |  |  |  |  | 0 | 0 |  |  |  | 10,204,880 |  |
Preferred stock , shares outstanding |  |  |  |  | 0 | 0 |  |  |  | 10,204,880 |  |
Warrants exercisable price per share |  |  |  |  |  |  |  |  | $ 15 |  |  |
Warrants outstanding |  |  |  |  |  |  | 0 |  |  |  |  |
Common stock were reserved for issuance |  |  |  |  | 750,000 | 750,000 |  |  |  |  |  |
Sale of common stock |  |  |  |  |  | 1,150,000 |  |  |  |  |  |
Gross proceeds from sale of common stock |  |  |  |  |  | $ 3,478,137 | $ 0 |  |  |  |  |
2025 Equity Line of Credit [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Common stock, par value |  | $ 0.0001 |  |  |  |  |  |  |  |  |  |
Sale of common stock |  |  |  |  | 1,150,000 |  |  |  |  |  |  |
Gross proceeds from sale of common stock |  |  |  |  | $ 3,480,000 |  |  |  |  |  |  |
Equity line of credit facility, term |  | 24 months |  |  |  |  |  |  |  |  |  |
Beneficial ownership limitation percentage |  | 9.99% |  |  |  |  |  |  |  |  |  |
2025 Equity Line of Credit [Member] | Put Option [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Fair value of the put option |  | $ 0 |  |  |  |  |  |  |  |  |  |
Put option settlement date, description |  | The fair value of the put option was determined to be zero as the shares to be issued and the purchase price is settled within one to two business days. |  |  |  |  |  |  |  |  |  |
2025 Equity Line of Credit [Member] | Maximum [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Percentage of volume weighted average price |  | 97.00% |  |  |  |  |  |  |  |  |  |
2025 Equity Line of Credit [Member] | Minimum [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Percentage of volume weighted average price |  | 92.00% |  |  |  |  |  |  |  |  |  |
Common Stock [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Common stock, shares outstanding |  |  |  |  | 48,720,405 | 48,720,405 | 5,836,882 |  |  | 5,836,882 |  | 7,072,300
Shares issued |  |  |  |  |  | 1,151,071 |  |  |  |  |  |
Common Stock [Member] | 2025 Equity Line of Credit [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Shares issued |  | 250,000,000 |  |  |  |  |  |  |  |  |  |
2025 Employee Share Purchase Plan [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Common stock were reserved for issuance | 1,216,254 |  |  |  |  |  |  |  |  |  |  |
Percentage of eligible compensation per employee to purchase shares of common stock | 15.00% |  |  |  |  |  |  |  |  |  |  |
Initial offering period | the ESPP, each consisting of consecutive six-month offering periods with the initial offering period beginning on September 1, 2025 and ending on February 28, 2026. |  |  |  |  |  |  |  |  |  |  |
Commencement date | Mar. 01, 2026 |  |  |  |  |  |  |  |  |  |  |
Employee purchase price, percentage of fair market value of common stock | 85.00% |  |  |  |  |  |  |  |  |  |  |
Employee share purchase plan, purchase date |  |  |  |  | Feb. 28, 2026 | Feb. 28, 2026 |  |  |  |  |  |
March 2025 Investor Note [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Common stock, par value |  |  | $ 15 |  |  |  |  |  |  |  |  |
Number of warrants related to legacy |  |  | 925,590 |  |  |  |  |  |  |  |  |
Warrants exercisable price per share |  |  |  |  | $ 15 | $ 15 |  |  |  |  |  |
Warrants outstanding |  |  |  |  | 925,590 | 925,590 |  |  |  |  |  |
Shares issued |  |  | 750,000 |  |  |  |  |  |  |  |  |
Series A [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Number of warrants related to legacy |  |  |  |  |  |  |  | 869,565 |  |  |  |
Warrants exercisable price per share |  |  |  |  |  |  |  | $ 12.5 |  |  |  |
Series A [Member] | June 2025 Amended Investor Note [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Number of warrants related to legacy |  |  |  |  | 869,565 | 869,565 |  |  |  |  |  |
Warrants exercisable price per share |  |  |  |  | $ 12.5 | $ 12.5 |  |  |  |  |  |
Series C [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Number of warrants related to legacy |  |  |  |  |  |  |  | 869,565 |  |  |  |
Warrants exercisable price per share |  |  |  |  |  |  |  | $ 9 |  |  |  |
Series C [Member] | June 2025 Amended Investor Note [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Number of warrants related to legacy |  |  |  |  | 869,565 | 869,565 |  |  |  |  |  |
Warrants exercisable price per share |  |  |  |  | $ 9 | $ 9 |  |  |  |  |  |
FTAC Emerald [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Common stock, shares outstanding |  |  |  |  | 14,237,038 | 14,237,038 |  |  |  |  |  |
Number of warrants related to legacy |  |  |  |  | 12,434,658 | 12,434,658 |  |  |  |  |  |
Warrants exercisable price per share |  |  |  |  | $ 11.5 | $ 11.5 |  |  |  |  |  |
FTAC Emerald [Member] | Common Stock [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Sale of common stock |  |  |  | 34,100,000 |  |  |  |  |  |  |  |
Convertible Preferred Stock [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Stock [Line Items] |  |  |  |  |  |  |  |  |  |  |  |
Preferred stock , shares issued |  |  |  |  |  |  | 10,200,000 |  |  |  |  |
Preferred stock , shares outstanding |  |  |  |  |  |  | 10,200,000 |  |  |  |  |

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