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Stockholders' Equity/(Deficit) - Additional Information (Detail) |  |  |  |  |  | 3 Months Ended | 9 Months Ended |  |  |  |  |
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Jun. 27, 2025 USD ($) | Apr. 30, 2025 $ / shares shares | Mar. 27, 2025 shares | Dec. 23, 2024 USD ($) $ / shares shares | Jun. 10, 2022 USD ($) shares | Sep. 30, 2025 USD ($) $ / shares shares | Sep. 30, 2024 USD ($) | Sep. 30, 2025 USD ($) $ / shares shares | Sep. 30, 2024 USD ($) | Dec. 31, 2024 USD ($) shares | Dec. 31, 2023 $ / shares shares | Dec. 28, 2023 USD ($) | Dec. 01, 2023 USD ($) | Mar. 06, 2023 $ / shares shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |
Common Stock, Value, Issued | $ |  |  |  |  |  | $ 5,039 |  | $ 5,039 |  | $ 2,883 |  |  |  |
APIC at a fair value | $ |  |  |  | $ 1,500,000 |  |  |  |  |  |  |  |  |  |
Share-based compensation expense | $ |  |  |  |  |  | $ 45,742 | $ 101,785 | $ 137,226 | $ 1,666,318 |  |  |  |  |
Common stock, shares issued |  |  |  |  |  | 50,384,898 |  | 50,384,898 |  | 28,825,333 |  |  |  |
Offering cost paid on sale of common stock | $ |  |  |  |  |  |  |  | $ 97,135 | $ 0 |  |  |  |  |
Restricted Stock Units |  |  |  |  |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |
Number of Shares, Granted |  |  |  |  |  |  |  | 44,879 |  |  |  |  |  |
SPA |  |  |  |  |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |
Shares issued and sold |  | 7,220,141 |  | 7,377,912 |  | 4,373,893 |  | 6,975,488 |  |  |  |  |  |
Purchase price per share | $ / shares |  | $ 1.1 |  | $ 0.55 |  |  |  |  |  |  |  |  |  |
Aggregate purchase price | $ |  |  |  | $ 4,100,000 |  | $ 4,800,000 |  | $ 7,700,000 |  |  |  |  |  |
Remaining options to purchase outstanding |  |  |  |  |  | 0 |  | 0 |  |  |  |  |  |
Oceanica Equity Exchange Agreements |  |  |  |  |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |
Accrued aggregate of adminstrators and officers |  |  |  |  |  |  |  | 1,911,666 |  |  |  |  |  |
Compensation quota aggregate amount of additional fair value | $ |  |  |  |  |  |  |  | $ 2,029,575 |  |  |  |  |  |
Compensation quota, incremental value | $ | $ 2,029,575 |  |  |  |  |  |  |  |  |  |  |  |  |
Oceanica Equity Exchange Agreements | Odyssey's Common Stock [Member] |  |  |  |  |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |
Common stock, shares issued |  |  |  |  |  | 1,841,137 |  | 1,841,137 |  |  |  |  |  |
December 2023 Warrants |  |  |  |  |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |
Debt instrument face amount | $ |  |  |  |  |  |  |  |  |  |  |  | $ 2,250,000 | $ 3,750,000 |
March 2023 Warrants |  |  |  |  |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |
Class of warrants or rights exercise price of warrants or rights | $ / shares |  |  |  |  |  |  |  |  |  |  |  |  |  | $ 1.1
2022 Warrants |  |  |  |  |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |
Class of warrant or right, Number of securities called by warrants or rights |  |  |  |  | 4,939,515 |  |  |  |  |  |  |  |  |
Warrants, expiration beginning date |  |  |  |  | Dec. 10, 2022 |  |  |  |  |  |  |  |  |
Warrants, expiration date |  |  |  |  | Jun. 10, 2027 |  |  |  |  |  |  |  |  |
Common stock, shares issued |  |  |  |  | 4,939,515 |  |  |  |  |  |  |  |  |
Offering cost paid on sale of common stock | $ |  |  |  |  | $ 1,800,000 |  |  |  |  |  |  |  |  |
Net proceeds received from sale | $ |  |  |  |  | $ 14,700,000 |  |  |  |  |  |  |  |  |
2022 Warrants | Measurement Input, Exercise Price [Member] |  |  |  |  |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |
Long-term debt measurement input |  |  |  |  | 3.35 |  |  |  |  |  |  |  |  |
2022 Warrants | Measurement Input, Share Price [Member] |  |  |  |  |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |
Long-term debt measurement input |  |  |  |  | 3.35 |  |  |  |  |  |  |  |  |
First tranche | December 2023 Warrants |  |  |  |  |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |
Class of warrants or rights exercise price of warrants or rights | $ / shares |  |  |  |  |  |  |  |  |  |  | $ 1.23 |  |  |
Second tranche | December 2023 Warrants |  |  |  |  |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |
Class of warrants or rights exercise price of warrants or rights | $ / shares |  |  |  |  |  |  |  |  |  |  | $ 2.05 |  |  |
Maximum [Member] | March 2023 Warrants |  |  |  |  |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |
Class of warrant or right, Number of securities called by warrants or rights |  |  |  |  |  |  |  |  |  |  |  |  |  | 3,703,704
Maximum [Member] | First tranche | December 2023 Warrants |  |  |  |  |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |
Class of warrant or right, Number of securities called by warrants or rights |  |  |  |  |  |  |  |  |  |  | 1,411,765 |  |  |
Maximum [Member] | Second tranche | December 2023 Warrants |  |  |  |  |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |
Class of warrant or right, Number of securities called by warrants or rights |  |  |  |  |  |  |  |  |  |  | 211,565 |  |  |
Consultant |  |  |  |  |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |
Common stock, shares issued |  |  |  |  |  | 261,500 |  | 261,500 |  |  |  |  |  |
Common Stock | Oceanica Equity Exchange Agreements |  |  |  |  |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |
Exchange value per share | $ / shares |  |  |  |  |  | $ 1.12 |  | $ 1.12 |  |  |  |  |  |
Common Stock | Director [Member] |  |  |  |  |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |
Number of stock options granted |  |  | 7,500 |  |  |  |  |  |  |  |  |  |  |
Member Interests | Oceanica Equity Exchange Agreements |  |  |  |  |  |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |
Exchange value per share | $ / shares |  |  |  |  |  | $ 0.017 |  | $ 0.017 |  |  |  |  |  |

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