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Recapitalization - Additional Information (Details) - USD ($) $ / shares in Units, $ in Millions |  | 9 Months Ended |  |  |
--- | --- | --- | --- | --- | ---
Feb. 14, 2025 | Sep. 30, 2025 | Dec. 31, 2024 | Sep. 30, 2024 | Dec. 31, 2023
Share Repurchase Program [Line Items] |  |  |  |  |
Sale of common stock |  | 1,150,000 |  |  |
Common stock, shares outstanding |  | 48,018,545 | 5,836,882 | 5,800,000 |
Common stock, par value | $ 0.0001 | $ 0.0001 | $ 0.0001 |  |
Transaction costs incurred | $ 14.0 |  |  |  |
Common Stock [Member] |  |  |  |  |
Share Repurchase Program [Line Items] |  |  |  |  |
Common stock, shares outstanding |  | 48,720,405 | 5,836,882 | 5,836,882 | 7,072,300
FTAC Emerald [Member] |  |  |  |  |
Share Repurchase Program [Line Items] |  |  |  |  |
Common stock, shares outstanding |  | 14,237,038 |  |  |
Net cash proceeds | $ 0.8 |  |  |  |
FTAC Emerald [Member] | Class A [Member] |  |  |  |  |
Share Repurchase Program [Line Items] |  |  |  |  |
Common stock, shares outstanding | 10,932,855 | 10,932,855 |  |  |
Common stock, par value | $ 0.0001 |  |  |  |
Common stock redeemed | $ 3.3 |  |  |  |
FTAC Emerald [Member] | Common Stock [Member] |  |  |  |  |
Share Repurchase Program [Line Items] |  |  |  |  |
Number of common shares issued and outstanding equity interests | $ 372.0 |  |  |  |
Sale of common stock | 34,100,000 |  |  |  |
FTAC Emerald [Member] | Common Stock [Member] | SAFEs [Member] |  |  |  |  |
Share Repurchase Program [Line Items] |  |  |  |  |
Sale of common stock | 34,100,000 |  |  |  |

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