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Fair Value Measurements | 3 Months Ended | 12 Months Ended
--- | --- | ---
Mar. 31, 2025 | Dec. 31, 2024
Fair Value Measurements |  |
Fair Value Measurements | Note 9.Fair Value Measurements Recurring Fair Value Measurements The following table presents information about the Company’s assets and liabilities that are measured at fair value at March 31, 2025, and December 31, 2024, and indicates the fair value hierarchy of the valuation inputs the Company utilized to determine such fair value: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | March 31, 2025
​ |  | (Level 1) |  | (Level 2) |  | (Level 3)
Assets: |  | ​ | ​ |  | ​ | ​ |  | ​ |
Marketable securities held in trust account | ​ | $ | 433,645 | ​ | $ | — | ​ | $ | —
Liabilities: | ​ |  | ​ | ​ |  | ​ | ​ |  |
Public Warrants | ​ | $ | — | ​ | $ | 2,270,100 | ​ | $ | —
Private Placement Warrants | ​ | $ | — | ​ | $ | 2,310,000 | ​ | $ | —
​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | December 31, 2024
​ |  | (Level 1) |  | (Level 2) |  | (Level 3)
Assets: | ​ |  |  | ​ |  |  | ​ |  |
Marketable securities held in trust account |  | $ | 429,151 |  | $ | — |  | $ | —
Liabilities: | ​ |  | ​ | ​ |  | ​ | ​ |  | ​
Public Warrants |  | $ | — |  | $ | 2,300,000 |  | $ | —
Private Placement Warrants |  | $ | — |  | $ | 2,339,000 |  | $ | —
​ The following table presents the changes in the fair value of the Company’s liabilities classified as Level 2 as of March 31, 2025 and December 31, 2024: ​
​ | ​ | ​ | ​
​ |  | Warrant Liabilities
Level 2 Derivative warrant liabilities as of December 31, 2023 | ​ | $ | 293,000
Change in fair value of Private Placement Warrant liability | ​ |  | 2,046,000
Transfer of Public Warrant liability to Level 2 | ​ |  | 2,300,000
Level 2 Derivative warrant liabilities as of December 31, 2024 | ​ |  | 4,639,000
Change in fair value of warrant liabilities | ​ |  | (58,900)
Level 2 Derivative warrant liabilities as of March 31, 2025 | ​ | $ | 4,580,100
​ The Public Warrants were reclassified from Level 1 to Level 2 as a result of the delisting of the Company’s Class A common stock and Public Warrants from the NYSE on March 21, 2024. At March 31, 2025, and December 31, 2024, the Company’s warrant liability was valued at $4,580,100 and $4,639,000. Under the guidance in ASC 815-40, the Public Warrants and the Private Placement Warrants do not meet the criteria for equity treatment. As such, the Public Warrants and the Private Placement Warrants must be recorded on the balance sheet at fair value. This valuation is subject to re-measurement at each balance sheet date. With each re-measurement, the valuations will be adjusted to fair value, with the change in fair value recognized in the Company’s condensed consolidated statement of operations. The following table presents fair value information for the three months ended March 31, 2025, and 2024, of the Company’s financial assets and liabilities that were accounted for at fair value on a recurring basis and indicates the fair value hierarchy of the valuation techniques the Company utilized to determine such fair value. The Company’s Private Placement Warrant liability is based on a valuation model utilizing management judgment and pricing inputs from observable and unobservable markets with less volume and transaction frequency than active markets. Significant deviations from these estimates and inputs could result in a material change in fair value. ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | For the Three Months Ended March 31, 2025
​ | ​ | ​ | ​ | Private | ​ | ​ | ​
​ | ​ | Public | ​ | Placement | ​ | Warrant
​ |  | Warrants |  | Warrants |  | Liability
Derivative warrant liabilities as of December 31, 2024 | ​ | $ | 2,300,000 | ​ | $ | 2,339,000 | ​ | $ | 4,639,000
Change in fair value |  | ​ | (29,900) | ​ | ​ | (29,000) | ​ | ​ | (58,900)
Derivative warrant liabilities as of March 31, 2025 | ​ | $ | 2,270,100 | ​ | $ | 2,310,000 | ​ | $ | 4,580,100
​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | For the Three Months Ended March 31, 2024
​ | ​ | ​ | ​ | Private | ​ | ​ | ​
​ | ​ | Public | ​ | Placement | ​ | Warrant
​ |  | Warrants |  | Warrants |  | Liability
Derivative warrant liabilities as of December 31, 2023 | ​ | $ | 287,500 | ​ | $ | 293,000 | ​ | $ | 580,500
Change in fair value | ​ | ​ | (221,950) | ​ | ​ | (226,000) | ​ | ​ | (447,950)
Derivative warrant liabilities as of March 31, 2024 | ​ | $ | 65,550 | ​ | $ | 67,000 | ​ | $ | 132,550
​ Measurement The Company established the initial fair value for the warrants on December 14, 2021, the date of the consummation of the Company’s IPO. The Company allocated the proceeds received from (i) the sale of Units (which is inclusive of one share of Class A common stock and one-half of one Public Warrant), (ii) the sale of Private Placement Warrants, and (iii) the issuance of Class B common stock, first to the warrants based on their fair values as determined at initial measurement, with the remaining proceeds allocated to Class A common stock subject to possible redemption (temporary equity), Class A common stock (permanent equity) and Class B common stock (permanent equity) based on their relative fair values at the initial measurement date. As of March 31, 2025, the Public Warrants have detached from the Units and are separately tradable on the over-the-counter markets. The closing price of the Public Warrants was utilized in determining the fair value of the Public Warrants as of March 31, 2025. The key inputs into the Monte Carlo simulation formula used to value the Private Placement Warrants were as follows at March 31, 2025 and 2024: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | March 31, | ​
Inputs: |  | 2025 |  | 2024 |
Common stock price | ​ | $ | 11.36 | ​ | $ | 10.80 |
Exercise price | ​ | $ | 11.50 | ​ | $ | 11.50 | ​
Risk-free rate of interest | ​ |  | 3.94 | % |  | 4.16 | %
Volatility | ​ |  | 0.00 | % |  | 0.00 | %
Term | ​ |  | 5.24 | ​ |  | 5.71 | ​
Warrant to buy one share | ​ | $ | 0.01 | ​ | $ | 0.01 | ​
Dividend yield | ​ |  | 0.00 | % |  | 0.00 | %
​ Non-recurring Fair Value Measurements On May 25, 2023, the Company and the Sponsor entered into Non-Redemption Agreements with unaffiliated third parties (see Note 8). The Company accounts for the excess fair value of the Class B shares transferred from the Sponsor to the unaffiliated third parties as a capital contribution by the Sponsor and recorded a non-redemption agreement expense in accordance with SAB Topic 5T. The Company estimated the fair value of the 500,000 Class B shares transferred upon the consummation of the First Extension at $387,000, or $0.77 per share. In connection with the subsequent extensions to March 14, 2024, the Sponsor transferred an additional 999,996 Class B shares to the unaffiliated third parties under the terms of the Non-Redemption Agreements. The Company estimated the fair value of the 999,996 Class B shares transferred at $0.82 to $0.83 per share. The fair value of the Class B shares was determined by multiplying the underlying stock price of the Company’s Class A common stock by the estimated probability of an Initial Business Combination and applying a discount for lack of marketability (“DLOM”). The Company utilized June 9, 2023, the date of the consummation of the First Extension, as the measurement date for the transfer of the 500,000 Class B shares and September 30, 2023, October 11, 2023, November 14, 2023, December 13, 2023, January 12, 2024 and February 14, 2024 as the measurement dates for the transfer of the 166,666 Class B shares (999,996 Class B shares in the aggregate) transferred in connection with the subsequent extensions, respectively. The following are the key inputs into the calculations at the measurement dates: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | June 9, |  | September 30, | ​ | October 11, |  | November 14, | ​ | December 13, | ​ | January 12, |  | February 12, | ​
Inputs: |  | 2023 |  | 2023 |  | 2023 |  | 2023 |  | 2023 |  | 2024 |  | 2024 | ​
Common stock price | ​ | $ | 10.54 | ​ | $ | 10.56 | ​ | $ | 10.57 | ​ | $ | 10.60 | ​ | $ | 10.62 | ​ | $ | 10.65 | ​ | $ | 10.73 | ​
Estimated probability of an Initial Business Combination | ​ |  | 10.00 | % | ​ | 10.00 | % |  | 10.00 | % | ​ | 10.00 | % | ​ | 10.00 | % | ​ | 10.00 | % | ​ | 10.00 | %
Estimated volatility | ​ |  | 76.56 | % | ​ | 65.96 | % |  | 64.90 | % | ​ | 63.91 | % | ​ | 65.52 | % | ​ | 66.02 | % | ​ | 64.40 | %
Risk-free rate | ​ |  | 5.10 | % | ​ | 5.39 | % |  | 5.31 | % | ​ | 5.17 | % | ​ | 4.88 | % | ​ | 4.60 | % | ​ | 4.88 | %
Time to expiration | ​ |  | 1.00 | ​ | ​ | 1.00 | ​ |  | 1.00 | ​ | ​ | 1.00 | ​ | ​ | 1.00 | ​ |  | 1.00 | ​ | ​ | 1.00 | ​
​ | Note 9.Fair Value Measurements Recurring Fair Value Measurements The following table presents information about the Company’s assets and liabilities that are measured at fair value at December 31, 2024 and 2023, and indicates the fair value hierarchy of the valuation inputs the Company utilized to determine such fair value: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | December 31, 2024
​ |  | (Level 1) |  | (Level 2) |  | (Level 3)
Assets |  | ​ |  |  | ​ |  |  | ​ |
Marketable securities held in trust account | ​ | $ | 429,151 | ​ | $ | — | ​ | $ | —
Liabilities | ​ |  | ​ | ​ |  | ​ | ​ |  |
Public Warrants | ​ | $ | — | ​ | $ | 2,300,000 | ​ | $ | —
Private Placement Warrants | ​ | $ | — | ​ | $ | 2,339,000 | ​ | $ | —
​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | December 31, 2023
​ |  | (Level 1) |  | (Level 2) |  | (Level 3)
Assets | ​ |  |  | ​ |  |  | ​ |  |
Marketable securities held in trust account |  | $ | 44,709,805 |  | $ | — |  | $ | —
Liabilities | ​ |  | ​ | ​ |  | ​ | ​ |  |
Public Warrants |  | $ | 287,500 |  | $ | — |  | $ | —
Private Placement Warrants |  | $ | — |  | $ | 293,000 |  | $ | —
​ The following table presents the changes in the fair value of the Company’s liabilities classified as Level 2 as of December 31, 2024 and 2023. ​
​ | ​ | ​ | ​
​ |  | Warrant Liabilities
Level 2 Derivative warrant liabilities as of December 31, 2023 | ​ | $ | 293,000
Change in fair value of Private Placement Warrant liability |  | ​ | 2,046,000
Transfer of Public Warrant liability to Level 2 |  | ​ | 2,300,000
Level 2 Derivative warrant liabilities as of December 31, 2024 | ​ | $ | 4,639,000
​ The Public Warrants were reclassified from Level 1 to Level 2 as a result of the delisting of the Company’s Class A common stock and Public Warrants from the NYSE on March 21, 2024. ​ At December 31, 2024 and 2023, the Company’s warrant liability was valued at $4,639,000 and $580,500, respectively. Under the guidance in ASC 815-40, the Public Warrants and the Private Placement Warrants do not meet the criteria for equity treatment. As such, the Public Warrants and the Private Placement Warrants must be recorded on the balance sheet at fair value. The fair value of the Public Warrants and Private Placement Warrants are subject to re-measurement at each balance sheet date. With each re-measurement, the Public Warrants and Private Placement Warrants are adjusted to fair value, with the change in fair value recognized in the Company’s statement of operations. The following table presents fair value information for the Company’s financial assets and liabilities that were accounted for at fair value on a recurring basis as of December 31, 2024 and 2023, and indicates the fair value hierarchy of the valuation techniques the Company utilized to determine such fair value. The Company’s warrant liability is based on a valuation model utilizing management judgment and pricing inputs from observable and unobservable markets with less volume and transaction frequency than active markets. Significant deviations from these estimates and inputs could result in a material change in fair value. ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | ​ | ​ | Private | ​ | ​ | ​ | ​ | Share
​ | ​ | Public | ​ | Placement | ​ | Warrant | ​ | Redemptions
​ |  | Warrants |  | Warrants |  | Liability |  | Payable
Derivative warrant liabilities as of December 31, 2022 | ​ | ​ | 261,050 | ​ | ​ | 266,000 | ​ | ​ | 527,050 | ​ | ​ | —
Establishment of share repurchase liability | ​ | ​ | — | ​ | ​ | — | ​ | ​ | — | ​ | ​ | 197,694,657
Share repurchase payment | ​ | ​ | — | ​ | ​ | — | ​ | ​ | — | ​ | ​ | (197,694,657)
Change in fair value |  | ​ | 26,450 |  | ​ | 27,000 | ​ | ​ | 53,450 |  | ​ | —
Derivative warrant liabilities as of December 31, 2023 |  | ​ | 287,500 |  | ​ | 293,000 | ​ | ​ | 580,500 |  | ​ | —
Change in fair value | ​ | ​ | 2,012,500 | ​ | ​ | 2,046,000 | ​ | ​ | 4,058,500 | ​ | ​ | —
Derivative warrant liabilities as of December 31, 2024 | ​ | $ | 2,300,000 | ​ | $ | 2,339,000 | ​ | $ | 4,639,000 | ​ | $ | —
​ Measurement The Company established the initial fair value for the warrants on December 14, 2021, the date of the consummation of the Company’s IPO. The Company allocated the proceeds received from (i) the sale of Units (which is inclusive of one share of Class A common stock and one-half of one Public Warrant), (ii) the sale of Private Placement Warrants, and (iii) the issuance of Class B common stock, first to the warrants based on their fair values as determined at initial measurement, with the remaining proceeds allocated to Class A common stock subject to possible redemption (temporary equity), Class A common stock (permanent equity) and Class B common stock (permanent equity) based on their relative fair values at the initial measurement date. As of December 31, 2024, the Public Warrants have detached from the Units and are separately tradable on the over-the-counter markets. The closing price of the Public Warrants was utilized in determining the fair value of the Public Warrants as of December 31, 2024. The key inputs into the Monte Carlo simulation formula used to value the Private Placement Warrants were as follows at December 31, 2024 and 2023: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | ​ | December 31, | ​
Inputs: |  | ​ | 2024 |  | ​ | 2023 |
Common stock price | ​ | $ | 11.14 | ​ | $ | 10.64 |
Exercise price | ​ | $ | 11.50 | ​ | $ | 11.50 | ​
Risk-free rate of interest | ​ |  | 4.37 | % |  | 3.81 | %
Volatility | ​ |  | 0.00 | % |  | 0.00 | %
Term | ​ |  | 5.75 | ​ |  | 5.21 | ​
Warrant to buy one share (adjusted for the probability of dissolution) | ​ | $ | 0.20 | ​ | $ | 0.03 | ​
Dividend yield | ​ |  | 0.00 | % |  | 0.00 | %
​ Non-recurring Fair Value Measurements On May 25, 2023, the Company and the Sponsor entered into Non-Redemption Agreements with unaffiliated third parties (see Note 8). The Company accounts for the excess fair value of the Class B shares transferred from the Sponsor to the unaffiliated third parties as a capital contribution by the Sponsor and recorded a financing expense in accordance with SAB Topic 5T. The Company estimated the fair value of the 500,000 Class B shares transferred upon the consummation of the First Extension of the deadline to complete a business combination from June 14, 2023 to September 14, 2023 at $387,000, or $0.77 per share. In connection with the subsequent extensions to March 14, 2024, the Sponsor transferred an additional 999,996 Class B shares to the unaffiliated third parties under the terms of the Non-Redemption Agreements. The Company estimated the fair value of the 999,996 Class B shares transferred at $0.82 to $0.83 per share. The fair value of the Class B shares was determined by multiplying the underlying stock price of the Company’s Class A common stock by the estimated probability of an Initial Business Combination and applying a discount for lack of marketability (“DLOM”). The Company utilized June 9, 2023, the date of the consummation of the First Extension, as the measurement date for the transfer of the 500,000 Class B shares and September 30, 2023, October 11, 2023, November 14, 2023, December 13, 2023, January 12, 2024 and February 14, 2024 as the measurement dates for the transfer of the 166,666 Class B shares (999,996 Class B shares in the aggregate) transferred in connection with the subsequent extensions, respectively. The following are the key inputs into the calculations at the measurement dates: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | June 9, |  | September 30, |  | October 11, |  | November 14, |  | December 13, |  | January 12, |  | February 12, | ​
Inputs: | ​ | 2023 | ​ | 2023 | ​ | 2023 | ​ | 2023 | ​ | 2023 |  | 2024 | ​ | 2024 | ​
Common stock price | ​ | $ | 10.54 | ​ | $ | 10.56 | ​ | $ | 10.57 | ​ | $ | 10.60 | ​ | $ | 10.62 | ​ | $ | 10.65 | ​ | $ | 10.73 | ​
Estimated probability of an Initial Business Combination | ​ |  | 10.00 | % |  | 10.00 | % |  | 10.00 | % |  | 10.00 | % |  | 10.00 | % | ​ | 10.00 | % | ​ | 10.00 | %
Estimated volatility | ​ |  | 76.56 | % |  | 65.96 | % |  | 64.90 | % |  | 63.91 | % |  | 65.52 | % | ​ | 66.02 | % | ​ | 64.40 | %
Risk-free rate | ​ |  | 5.10 | % |  | 5.39 | % |  | 5.31 | % |  | 5.17 | % |  | 4.88 | % | ​ | 4.60 | % | ​ | 4.88 | %
Time to expiration | ​ |  | 1.00 | ​ |  | 1.00 | ​ |  | 1.00 | ​ |  | 1.00 | ​ |  | 1.00 | ​ | ​ | 1.00 | ​ | ​ | 1.00 | ​
​

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- Definition The entire disclosure for the fair value of financial instruments (as defined), including financial assets and financial liabilities (collectively, as defined), and the measurements of those instruments as well as disclosures related to the fair value of non-financial assets and liabilities. Such disclosures about the financial instruments, assets, and liabilities would include: (1) the fair value of the required items together with their carrying amounts (as appropriate); (2) for items for which it is not practicable to estimate fair value, disclosure would include: (a) information pertinent to estimating fair value (including, carrying amount, effective interest rate, and maturity, and (b) the reasons why it is not practicable to estimate fair value; (3) significant concentrations of credit risk including: (a) information about the activity, region, or economic characteristics identifying a concentration, (b) the maximum amount of loss the entity is exposed to based on the gross fair value of the related item, (c) policy for requiring collateral or other security and information as to accessing such collateral or security, and (d) the nature and brief description of such collateral or security; (4) quantitative information about market risks and how such risks are managed; (5) for items measured on both a recurring and nonrecurring basis information regarding the inputs used to develop the fair value measurement; and (6) for items presented in the financial statement for which fair value measurement is elected: (a) information necessary to understand the reasons for the election, (b) discussion of the effect of fair value changes on earnings, (c) a description of [similar groups] items for which the election is made and the relation thereof to the balance sheet, the aggregate carrying value of items included in the balance sheet that are not eligible for the election; (7) all other required (as defined) and desired information. + References Reference 1: http://www.xbrl.org/2003/role/exampleRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 55 -Paragraph 107 -Publisher FASB -URI https://asc.fasb.org/1943274/2147482078/820-10-55-107 Reference 2: http://www.xbrl.org/2003/role/exampleRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 55 -Paragraph 100 -Publisher FASB -URI https://asc.fasb.org/1943274/2147482078/820-10-55-100 Reference 3: http://www.xbrl.org/2003/role/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c)(3) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-2 Reference 4: http://www.xbrl.org/2003/role/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 6A -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-6A Reference 5: http://www.xbrl.org/2003/role/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2E -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-2E Reference 6: http://www.xbrl.org/2003/role/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 6A -Subparagraph (h) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-6A Reference 7: http://www.xbrl.org/2003/role/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 6A -Subparagraph (f) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-6A Reference 8: http://www.xbrl.org/2003/role/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 6A -Subparagraph (e) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-6A Reference 9: http://www.xbrl.org/2003/role/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 6A -Subparagraph (d) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-6A Reference 10: http://www.xbrl.org/2003/role/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (h) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-2 Reference 11: http://www.xbrl.org/2003/role/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (g) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-2 Reference 12: http://www.xbrl.org/2003/role/disclosureRef -Topic 940 -SubTopic 820 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org/1943274/2147478119/940-820-50-1 + Details
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