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Fair Value Measurement | 6 Months Ended | 12 Months Ended
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Jun. 30, 2025 | Dec. 31, 2024
Fair Value Measurement [Line Items] |  |
Fair Value Measurement | Note 3 — Fair Value Measurement Assets and liabilities recorded at fair value on a recurring basis in the balance sheets are categorized based upon the level of judgment associated with the inputs used to measure their fair values. Fair value represents the price that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants at the measurement date. Valuation techniques used to measure fair value must maximize the use of observable inputs and minimize the use of unobservable inputs. The authoritative guidance on fair value measurements establishes a three-tier fair value hierarchy for disclosure of fair value measurements as follows:
| Level 1 — | Inputs are unadjusted, quoted prices in active markets for identical assets or liabilities at the measurement date;
| Level 2 — | Inputs are observable, unadjusted quoted prices in active markets for similar assets or liabilities, unadjusted quoted prices for identical or similar assets or liabilities in markets that are not active, or other inputs that are observable or can be corroborated by observable market data for substantially the full term of the related assets or liabilities; and
| Level 3 — | Unobservable inputs that are significant to the measurement of the fair value of the assets or liabilities that are supported by little or no market data.
In determining fair value, the Company utilizes valuation techniques that maximize the use of observable inputs and minimize the use of unobservable inputs to the extent possible as well as considers counterparty credit risk in its assessment of fair value. Assets and liabilities measured at fair value are classified in their entirety based on the lowest level of input that is significant to the fair value measurement. The Company’s assessment of the significance of a particular input to the fair value measurement in its entirety requires management to make judgments and consider factors specific to the asset or liability. As of June 30, 2025 and December 31, 2024, the Company had no financial assets measured at fair value on a recurring basis. As of June 30, 2025, the Company’s financial liabilities measured at fair value on a recurring basis, were as follows (in thousands):
|  | Fair value as of June 30, 2025 |
|  | Level 1 |  |  | Level 2 |  |  | Level 3 |  |  | Total |
Liabilities: |  |  |  |  |  |  |  |  |  |  |  |
Convertible Notes at fair value |  | $ | — |  |  | $ | — |  |  | $ | 2,543 |  |  | $ | 2,543 |
Total liabilities measured at fair value |  | $ | — |  |  | $ | — |  |  | $ | 2,543 |  |  | $ | 2,543 |
|  | Fair value as of December 31, 2024 |
|  | Level 1 |  |  | Level 2 |  |  | Level 3 |  |  | Total |
Liabilities: |  |  |  |  |  |  |  |  |  |  |  |
Convertible Notes at fair value |  | $ | — |  |  | $ | — |  |  | $ | 2,234 |  |  | $ | 2,234 |
Total liabilities measured at fair value |  | $ | — |  |  | $ | — |  |  | $ | 2,234 |  |  | $ | 2,234 |
The following table sets forth a summary of the changes in the fair value of the Company’s Level 3 financial instruments for the three and six months ended June 30, 2025 and 2024 (in thousands):
|  | Tasly convertible debt at fair value |
Fair value as of January 1, 2024 |  | $ | 1,714 |
Issuance of Convertible Notes |  |  | 16 |
Accrued stated interest |  |  | 48 |
Change in fair value included in other income and gain on change in the fair value of Tasly convertible debt |  |  | (4 | )
Fair value as of March 31, 2024 |  | $ | 1,774 |
Accrued stated interest |  |  | 49 |
Change in fair value included in other income and loss on change in the fair value of Tasly convertible debt |  |  | 15 |
Fair value as of June 30, 2024 |  | $ | 1,838 |
Fair value as of January 1, 2025 |  | $ | 2,234 |
Accrued stated interest |  |  | 95 |
Change in fair value included in other income and loss on change in the fair value of Tasly convertible debt |  |  | 61 |
Fair value as of March 31, 2025 |  | $ | 2,390 |
Accrued stated interest |  |  | 96 |
Change in fair value included in other income and loss on change in the fair value of Tasly convertible debt |  |  | 57 |
Fair value as of June 30, 2025 |  | $ | 2,543 |
The Company elected to measure its Tasly convertible debt at fair value (Note 5) with changes in fair value reported in earnings as they occur. The Convertible Debt fair values were determined using the discounted cash flow methodology based on probability weighted scenarios of the convertible notes conversion. At issuance of the first $1 million on June 26, 2023 the time to event was 0.28 years and the discount rate applied was 14.54%. At issuance of the next $0.3 million on July 20, 2023, the time to event was 0.22 years and the discount rate applied was 13.82%. At issuance of the additional $0.3 million on August 15, 2023, the time to event was 0.15 years and the discount rate applied was 13.70%. The final amount which was less than $0.02 million was issued on February 6, 2024; the time to event was 0.66 years and the discount rate applied was 13.69%. On June 30, 2025, the time event was .03 years and the discount rate applied was 12.66%. Based on this method, the Fair value of the convertible debt at the date of inception was $1.6 million, the fair value at June 30, 2025 was $2.1 million. | Note 3 — Fair Value Measurement Assets and liabilities recorded at fair value on a recurring basis in the balance sheets are categorized based upon the level of judgment associated with the inputs used to measure their fair values. Fair value represents the price that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants at the measurement date. Valuation techniques used to measure fair value must maximize the use of observable inputs and minimize the use of unobservable inputs. The authoritative guidance on fair value measurements establishes a three-tier fair value hierarchy for disclosure of fair value measurements as follows:
| Level 1 — | Inputs are unadjusted, quoted prices in active markets for identical assets or liabilities at the measurement date;
| Level 2 — | Inputs are observable, unadjusted quoted prices in active markets for similar assets or liabilities, unadjusted quoted prices for identical or similar assets or liabilities in markets that are not active, or other inputs that are observable or can be corroborated by observable market data for substantially the full term of the related assets or liabilities; and
| Level 3 — | Unobservable inputs that are significant to the measurement of the fair value of the assets or liabilities that are supported by little or no market data.
In determining fair value, the Company utilizes valuation techniques that maximize the use of observable inputs and minimize the use of unobservable inputs to the extent possible as well as considers counterparty credit risk in its assessment of fair value. Assets and liabilities measured at fair value are classified in their entirety based on the lowest level of input that is significant to the fair value measurement. The Company’s assessment of the significance of a particular input to the fair value measurement in its entirety requires management to make judgments and consider factors specific to the asset or liability. As of December 31, 2024 and 2023, the Company had no financial assets measured at fair value on a recurring basis. As of December 31, 2024 and 2023, the Company’s financial liabilities measured at fair value on a recurring basis, were as follows (in thousands):
|  | Fair value as of December 31, 2024 |
|  | Level 1 |  |  | Level 2 |  |  | Level 3 |  |  | Total |
Liabilities: |  |  |  |  |  |  |  |  |  |  |  |
Convertible Notes at fair value |  | $ | — |  |  | $ | — |  |  | $ | 2,235 |  |  | $ | 2,235 |
Total liabilities measured at fair value |  | $ | — |  |  | $ | — |  |  | $ | 2,235 |  |  | $ | 2,235 |
|  | Fair value as of December 31, 2023 |
|  | Level 1 |  |  | Level 2 |  |  | Level 3 |  |  | Total |
Liabilities: |  |  |  |  |  |  |  |  |  |  |  |
Convertible Notes at fair value |  | $ | — |  |  | $ | — |  |  | $ | 1,714 |  |  | $ | 1,714 |
Total assets measured at fair value |  | $ | — |  |  | $ | — |  |  | $ | 1,714 |  |  | $ | 1,714 |
The following table sets forth a summary of the changes in the fair value of the Company’s Level 3 financial instruments for the years ended December 31, 2024 and 2023 (in thousands):
|  | Tasly convertible debt at fair value |
Fair value as of January 1, 2023 |  | $ | — |
Issuance of Convertible Notes |  |  | 1,600 |
Accrued stated interest |  |  | 92 |
Change in fair value included in other income and loss on change in the fair value of Tasly convertible debt |  |  | 22 |
Fair value as of December 31, 2023 |  | $ | 1,714 |
Fair value as of January 1, 2024 |  | $ | 1,714 |
Issuance of Convertible Notes |  |  | 16 |
Accrued stated interest |  |  | 194 |
Change in fair value included in other income and loss on change in the fair value of Tasly convertible debt |  |  | 311 |
Fair value as of December 31, 2024 |  | $ | 2,235 |
The Company elected to measure its Tasly convertible debt at fair value (Note 5) with changes in fair value reported in earnings as they occur. The Convertible Debt fair values were determined using the discounted cash flow methodology based on probability weighted scenarios of the convertible notes conversion. At issuance of the first $1 million on June 26, 2023 the time to event was 0.28 years and the discount rate applied was 14.54%. At issuance of the next $0.3 million on July 20, 2023, the time to event was 0.22 years and the discount rate applied was 13.82%. At issuance of the additional $0.3 million on August 15, 2023, the time to event was 0.15 years and the discount rate applied was 13.70%. The final amount which was less than $0.02 million was issued on February 6, 2024; the time to event was 0.66 years and the discount rate applied was 13.69%. On December 31, 2024 the time event was 0.41 years and the discount rate applied was 11.78%. The fair value of the convertible debt as of December 31, 2023 was $1.71 million and the fair value as of December 31, 2024 was $2.2 million.
NorthView Acquisition Corp [Member] |  |
Fair Value Measurement [Line Items] |  |
Fair Value Measurement | Note 8 — Fair Value Measurements Fair value is defined as the price that would be received for sale of an asset or paid for transfer of a liability, in an orderly transaction between market participants at the measurement date. GAAP establishes a three-tier fair value hierarchy, which prioritizes the inputs used in measuring fair value. The hierarchy gives the highest priority to unadjusted quoted prices in active markets for identical assets or liabilities (Level 1 measurements) and the lowest priority to unobservable inputs (Level 3 measurements). The Company’s financial instruments are classified as either Level 1, Level 2 or Level 3. These tiers include:
| ● | Level 1, defined as observable inputs such as quoted prices (unadjusted) for identical instruments in active markets;
| ● | Level 2, defined as inputs other than quoted prices in active markets that are either directly or indirectly observable such as quoted prices for similar instruments in active markets or quoted prices for identical or similar instruments in markets that are not active; and
| ● | Level 3, defined as unobservable inputs in which little or no market data exists, therefore requiring an entity to develop its own assumptions, such as valuations derived from valuation techniques in which one or more significant inputs or significant value drivers are unobservable.
The following tables present information about the Company’s assets and liabilities that are measured at fair value on June 30, 2025 and December 31, 2024, and indicates the fair value hierarchy of the valuation inputs the Company utilized to determine such fair value:
|  | June 30, 2025 |  |  | Quoted Prices In Active Markets (Level 1) |  |  | Significant Other Observable Inputs (Level 2) |  |  | Significant Other Unobservable Inputs (Level 3) |
Assets: |  |  |  |  |  |  |  |  |  |  |  |
Cash held in trust |  | $ | 1,935,561 |  |  | $ | 1,274,549 |  |  | $ | — |  |  | $ | — |
Liabilities: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Warrant liabilities – Public Warrants |  | $ | 3,795,000 |  |  | $ | — |  |  | $ | 3,795,000 |  |  | $ | — |
Warrant liabilities – Private Placement Warrants |  |  | 2,939,000 |  |  |  | — |  |  |  | — |  |  |  | 2,939,000 |
Warrant liabilities – Representative’s Warrants |  |  | 227,700 |  |  |  | — |  |  |  | — |  |  |  | 227,700 |
Convertible Promissory Note – Related Party |  |  | 10,288,111 |  |  |  | — |  |  |  | — |  |  |  | 10,288,111 |
Securities Purchase Agreement |  |  | 193,878 |  |  |  | — |  |  |  | — |  |  |  | 193,878 |
Total |  | $ | 17,443,689 |  |  | $ | — |  |  | $ | 3,795,000 |  |  | $ | 13,648,689 |
|  | December 31, 2024 |  |  | Quoted Prices In Active Markets (Level 1) |  |  | Significant Other Observable Inputs (Level 2) |  |  | Significant Other Unobservable Inputs (Level 3) |
Assets: |  |  |  |  |  |  |  |  |  |  |  |
Cash held in trust |  | $ | 8,330,835 |  |  | $ | 8,330,835 |  |  | $ | — |  |  | $ | — |
Liabilities: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Warrant liabilities – Public Warrants |  | $ | 379,500 |  |  | $ | — |  |  | $ | 379,500 |  |  | $ | — |
Warrant liabilities – Private Placement Warrants |  |  | 293,900 |  |  |  | — |  |  |  | — |  |  |  | 293,900 |
Warrant liabilities – Representative’s Warrants |  |  | 22,770 |  |  |  | — |  |  |  | — |  |  |  | 22,770 |
Convertible Promissory Note – Related Party |  |  | 8,908,052 |  |  |  | — |  |  |  | — |  |  |  | 8,908,052 |
Total |  | $ | 9,604,222 |  |  | $ | — |  |  | $ | 379,500 |  |  | $ | 9,224,722 |
The Public Warrants, the Private Placement Warrants and the Representative’s Warrants were accounted for as liabilities in accordance with ASC 815-40 and are presented within liabilities on the condensed consolidated balance sheets. The warrant liabilities are measured at fair value at inception and on a recurring basis, with changes in fair value presented within change in fair value of warrant liabilities in the condensed consolidated statements of operations. The Company utilized a Monte Carlo simulation model for the initial valuation of the Public Warrants. The subsequent measurement of the Public Warrants at June 30, 2025 and December 31, 2024 was classified as Level 2 due to the lack of an active market. As of June 30, 2025 and December 31, 2024, the aggregate value of Public Warrants was $3,795,000 and $379,500, respectively. The Company uses a Monte Carlo simulation model to value the Private Placement Warrants and the Representative’s Warrants. The Private Placement Warrants and the Representative’s Warrants were classified within Level 3 of the fair value hierarchy due to the use of unobservable inputs. Inherent in pricing models are assumptions related to expected share-price volatility, expected life and risk-free interest rate. The Company estimates the volatility of its common stock based on historical volatility that matches the expected remaining life of the warrants. The risk-free interest rate is based on the U.S. Treasury zero-coupon yield curve on the grant date for a maturity similar to the expected remaining life of the warrants. The expected life of the warrants is assumed to be equivalent to their remaining contractual term. The key inputs into the Monte Carlo simulation model for the warrant liabilities were as follows at June 30, 2025 and December 31, 2024:
|  | June 30, 2025 |  |  | December 31, 2024 |
Input |  |  |  |  |  |
Risk-free interest rate |  |  | 4.22 | % |  |  | 4.18 | %
Expected term (years) |  |  | 0.61 |  |  |  | 0.89 |
Expected volatility |  |  | De minimis | % |  |  | De minimis | %
Exercise price |  | $ | 11.50 |  |  | $ | 11.50 |
Fair value of Common stock |  | $ | 12.52 |  |  | $ | 12.12 |
The key inputs into the Monte Carlo simulation model for the convertible promissory note were as follows at June 30, 2025 and December 31, 2024:
|  | June 30, 2025 |  |  | December 31, 2024 |
Input |  |  |  |  |  |
Risk-free interest rate |  |  | 4.28 | % |  |  | 4.18 | %
Expected term (years) |  |  | 0.05 |  |  |  | 0.27 |
Expected volatility |  |  | De minimis | % |  |  | De minimis | %
Exercise price |  | $ | 11.50 |  |  | $ | 11.50 |
Fair value of Common stock |  | $ | 12.52 |  |  | $ | 12.12 |
The key inputs into the Monte Carlo simulation model for the securities purchase agreement were as follows at June 30, 2025 and December 31, 2024:
|  | June 30, 2025 |  |  | December 31, 2024 |
Input |  |  |  |  |  |
Risk-free interest rate |  |  | 3.83 | % |  |  | — |
Expected term (years) |  |  | 1.59 |  |  |  | — |
Expected volatility |  |  | 4.84 | % |  |  | — |
Exercise price |  | $ | 11.50 |  |  |  | — |
Fair value of Common stock |  | $ | 12.52 |  |  |  | — |
The following table provides a summary of the changes in the fair value of the Company’s Level 3 financial instruments that are measured at fair value on a recurring basis for the three and six months ended June 30, 2025 and 2024:
|  | Private Placement Warrants |  |  | Representative’s Warrants |  |  | Warrant Liability |
Fair value at December 31, 2024 |  | $ | 293,900 |  |  | $ | 22,770 |  |  | $ | 316,670 |
Change in fair value of warrant liabilities |  |  | 146,950 |  |  |  | 11,385 |  |  |  | 158,335 |
Fair value at March 31, 2025 |  |  | 440,850 |  |  |  | 34,155 |  |  |  | 475,005 |
Change in fair value of warrant liabilities |  |  | 2,498,150 |  |  |  | 193,545 |  |  |  | 2,691,695 |
Fair value at June 30, 2025 |  | $ | 2,939,000 |  |  | $ | 227,700 |  |  | $ | 3,166,700 |
|  | Private Placement Warrants |  |  | Representative’s Warrants |  |  | Warrant Liability |
Fair value at December 31, 2023 |  | $ | 66,128 |  |  | $ | 5,123 |  |  | $ | 71,251 |
Change in fair value of warrant liabilities |  |  | 213,077 |  |  |  | 16,509 |  |  |  | 229,586 |
Fair value at March 31, 2024 |  |  | 279,205 |  |  |  | 21,632 |  |  |  | 300,837 |
Change in fair value of warrant liabilities |  |  | 124,908 |  |  |  | 9,676 |  |  |  | 134,584 |
Fair value at June 30, 2024 |  | $ | 404,113 |  |  | $ | 31,308 |  |  | $ | 435,421 |
|  | Convertible Promissory Note – related party |
Fair value at December 31, 2024 |  | $ | 8,908,052 |
Change in fair value of convertible promissory note |  |  | 225,330 |
Fair value at March 31, 2025 |  |  | 9,133,382 |
Change in fair value of convertible promissory note |  |  | 1,154,729 |
Fair value at June 30, 2025 |  | $ | 10,288,111 |
|  | Convertible Promissory Note |
Fair value at December 31, 2023 |  | $ | 944,118 |
Principal proceeds |  |  | 378,185 |
Change in fair value of convertible promissory note |  |  | (60,077 | )
Fair value at March 31, 2024 |  |  | 1,262,226 |
Proceeds received through convertible promissory note |  |  | 330,796 |
Change in fair value of convertible promissory note |  |  | (66,021 | )
Fair value at June 30, 2024 |  | $ | 1,527,001 |
The fair value of the Company’s convertible promissory note is valued using a compound option formula on the convertible feature and a present value of the host contract. The valuation technique requires inputs that are both unobservable and significant to the overall fair value measurement. These inputs reflect management’s own assumption about the assumptions a market participant would use in pricing the working capital loan. The convertible promissory note was classified within Level 3 of the fair value hierarchy due to the use of unobservable inputs. Inherent in pricing models are assumptions related to expected share-price volatility, expected life and risk-free interest rate. The Company estimates the volatility of its common stock based on historical volatility that matches the expected remaining life of the note. The risk-free interest rate is based on the U.S. Treasury zero-coupon yield curve on the grant date for a maturity similar to the expected remaining life of the note. The expected life of the note is assumed to be equivalent to their remaining contractual term.
|  | Securities Purchase Agreement |
Fair value at February 11, 2025 |  | $ | — |
Change in fair value of securities purchase agreement |  |  | 23,487 |
Fair value at March 31, 2025 |  |  | 23,487 |
Change in fair value of securities purchase agreement |  |  | 170,391 |
Fair value at June 30, 2025 |  | $ | 193,878 |
The Company utilizes a Monte Carlo model to estimate the fair value of the conversion feature within the securities purchase agreement, which is required to be recorded at its initial fair value on the date of issuance, and each balance sheet date thereafter. Changes in the estimated fair value of the conversion feature are recognized as non-cash gains or losses in the accompanying condensed consolidated statements of operations. The key assumptions in the model relate to expected share-price volatility, risk-free interest rate, exercise price, expected term and the probability of occurrence of the transaction. The expected volatility was based on the average volatility of special purpose acquisition companies that are searching for an acquisition target. The risk-free interest rate is based on the U.S. Treasury zero-coupon yield curve on the grant date for a maturity similar to the expected remaining life of the note. The expected life of the note is assumed to be equivalent to their remaining contractual term. | Note 8 — Fair Value Measurements Fair value is defined as the price that would be received for sale of an asset or paid for transfer of a liability, in an orderly transaction between market participants at the measurement date. GAAP establishes a three-tier fair value hierarchy, which prioritizes the inputs used in measuring fair value. The hierarchy gives the highest priority to unadjusted quoted prices in active markets for identical assets or liabilities (Level 1 measurements) and the lowest priority to unobservable inputs (Level 3 measurements). The Company’s financial instruments are classified as either Level 1, Level 2 or Level 3. These tiers include:
| ● | Level 1, defined as observable inputs such as quoted prices (unadjusted) for identical instruments in active markets;
| ● | Level 2, defined as inputs other than quoted prices in active markets that are either directly or indirectly observable such as quoted prices for similar instruments in active markets or quoted prices for identical or similar instruments in markets that are not active; and
| ● | Level 3, defined as unobservable inputs in which little or no market data exists, therefore requiring an entity to develop its own assumptions, such as valuations derived from valuation techniques in which one or more significant inputs or significant value drivers are unobservable.
The following tables present information about the Company’s assets and liabilities that are measured at fair value on 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 |  |  | Quoted Prices In Active Markets (Level 1) |  |  | Significant Other Observable Inputs (Level 2) |  |  | Significant Other Unobservable Inputs (Level 3) |
Assets: |  |  |  |  |  |  |  |  |  |  |  |
Cash and marketable securities held in trust |  | $ | 8,330,835 |  |  | $ | 8,330,835 |  |  | $ | — |  |  | $ | — |
Liabilities: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Warrant liabilities – Public Warrants |  | $ | 379,500 |  |  | $ | — |  |  | $ | 379,500 |  |  | $ | — |
Warrant liabilities – Private Placement Warrants |  |  | 293,900 |  |  |  | — |  |  |  | — |  |  |  | 293,900 |
Warrant liabilities – Representative’s Warrants |  |  | 22,770 |  |  |  | — |  |  |  | — |  |  |  | 22,770 |
Convertible promissory note |  |  | 8,908,052 |  |  |  | — |  |  |  | — |  |  |  | 8,908,052 |
Total |  | $ | 9,604,222 |  |  | $ | — |  |  | $ | 379,500 |  |  | $ | 9,224,722 |
|  | December 31, 2023 |  |  | Quoted Prices In Active Markets (Level 1) |  |  | Significant Other Observable Inputs (Level 2) |  |  | Significant Other Unobservable Inputs (Level 3) |
Assets: |  |  |  |  |  |  |  |  |  |  |  |
Cash and marketable securities held in trust |  | $ | 10,873,406 |  |  | $ | 10,873,406 |  |  | $ | — |  |  | $ | — |
Liabilities: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Warrant liabilities – Public Warrants |  | $ | 85,388 |  |  | $ | 85,388 |  |  | $ | — |  |  | $ | — |
Warrant liabilities – Private Placement Warrants |  |  | 66,128 |  |  |  | — |  |  |  | — |  |  |  | 66,128 |
Warrant liabilities – Representative’s Warrants |  |  | 5,123 |  |  |  | — |  |  |  | — |  |  |  | 5,123 |
Convertible promissory note |  |  | 944,118 |  |  |  | — |  |  |  | — |  |  |  | 944,118 |
Total |  | $ | 1,100,757 |  |  | $ | 85,388 |  |  | $ | — |  |  | $ | 1,015,369 |
The Public Warrants, the Private Placement Warrants and the Representative’s Warrants were accounted for as liabilities in accordance with ASC 815-40 and are presented within liabilities on the consolidated balance sheets. The warrant liabilities are measured at fair value at inception and on a recurring basis, with changes in fair value presented within change in fair value of warrant liabilities in the consolidated statements of operations. The Company utilized a Monte Carlo simulation model for the initial valuation of the Public Warrants. The subsequent measurement of the Public Warrants at December 31, 2024 was classified as Level 2 due to the lack of an active market. At December 31, 2023, the Public Warrants was classified as Level 1 due to the use of an observable market quote in an active market. As of December 31, 2024 and 2023, the aggregate value of Public Warrants was $379,500 and $85,388, respectively. The Company uses a Monte Carlo simulation model to value the Private Placement Warrants and the Representative’s Warrants. The Private Placement Warrants and the Representative’s Warrants were classified within Level 3 of the fair value hierarchy due to the use of unobservable inputs. Inherent in pricing models are assumptions related to expected share-price volatility, expected life and risk-free interest rate. The Company estimates the volatility of its common stock based on historical volatility that matches the expected remaining life of the warrants. The risk-free interest rate is based on the U.S. Treasury zero-coupon yield curve on the grant date for a maturity similar to the expected remaining life of the warrants. The expected life of the warrants is assumed to be equivalent to their remaining contractual term. The key inputs into the Monte Carlo simulation model for the warrant liabilities were as follows at December 31, 2024 and 2023:
|  | December 31, 2024 |  |  | December 31, 2023 |
Input |  |  |  |  |  |
Risk-free interest rate |  |  | 4.18 | % |  |  | 5.06 | %
Expected term (years) |  |  | 0.89 |  |  |  | 0.71 |
Expected volatility |  |  | De minimis | % |  |  | De minimis | %
Exercise price |  | $ | 11.50 |  |  | $ | 11.50 |
Fair value of Common stock |  | $ | 12.12 |  |  | $ | 11.16 |
The key inputs into the Monte Carlo simulation model for the convertible promissory note were as follows at December 31, 2024 and 2023:
|  | December 31, 2024 |  |  | December 31, 2023 |
Input |  |  |  |  |  |
Risk-free interest rate |  |  | 4.18 | % |  |  | 5.48 | %
Expected term (years) |  |  | 0.27 |  |  |  | 0.19 |
Expected volatility |  |  | De minimis | % |  |  | De minimis | %
Exercise price |  | $ | 11.50 |  |  | $ | 11.50 |
Fair value of Common stock |  | $ | 12.12 |  |  | $ | 11.16 |
The following table provides a summary of the changes in the fair value of the Company’s Level 3 financial instruments that are measured at fair value on a recurring basis for the years ended December 31, 2024 and 2023:
|  | Private Placement Warrants |  |  | Representative’s Warrants |  |  | Warrant Liability |
Fair value at December 31, 2023 |  | $ | 66,128 |  |  | $ | 5,123 |  |  | $ | 71,251 |
Change in fair value of warrant liabilities |  |  | 227,772 |  |  |  | 17,647 |  |  |  | 245,419 |
Fair value at December 31, 2024 |  | $ | 293,900 |  |  | $ | 22,770 |  |  | $ | 316,670 |
|  | Private Placement Warrants |  |  | Representative’s Warrants |  |  | Warrant Liability |
Fair value at December 31, 2022 |  | $ | 377,857 |  |  | $ | 29,274 |  |  | $ | 407,131 |
Change in fair value of warrant liabilities |  |  | (311,729 | ) |  |  | (24,151 | ) |  |  | (335,880 | )
Fair value at December 31, 2023 |  | $ | 66,128 |  |  | $ | 5,123 |  |  | $ | 71,251 |
|  | Convertible Promissory Note |
Fair value at December 31, 2023 |  | $ | 944,118 |
Principal borrowing |  |  | 797,981 |
Change in fair value of convertible promissory note |  |  | 7,165,953 |
Fair value at December 31, 2024 |  | $ | 8,908,052 |
|  | Convertible Promissory Note |
Fair value at December 31, 2022 |  | $ | — |
Principal borrowing |  |  | 1,121,815 |
Change in fair value of convertible promissory note |  |  | (177,697 | )
Fair value at December 31, 2023 |  | $ | 944,118 |
The fair value of the Company’s convertible promissory note is valued using a compound option formula on the convertible feature and a present value of the host contract. The valuation technique requires inputs that are both unobservable and significant to the overall fair value measurement. These inputs reflect management’s own assumption about the assumptions a market participant would use in pricing the working capital loan. The convertible promissory note was classified within Level 3 of the fair value hierarchy due to the use of unobservable inputs. Inherent in pricing models are assumptions related to expected share-price volatility, expected life and risk-free interest rate. The Company estimates the volatility of its common stock based on historical volatility that matches the expected remaining life of the note. The risk-free interest rate is based on the U.S. Treasury zero-coupon yield curve on the grant date for a maturity similar to the expected remaining life of the note. The expected life of the note is assumed to be equivalent to their remaining contractual term.

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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/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (bbb)(1) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-2 Reference 2: 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 3: 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 4: 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 5: 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 6: 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 7: 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 8: 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 9: 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 10: 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 11: 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 12: 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 13: 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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