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Stock Awards and Stock-based Compensation | 3 Months Ended | 12 Months Ended
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Mar. 31, 2023 | Dec. 31, 2022
Stock Awards and Stock-Based Compensation |  |
Stock Awards and Stock-Based Compensation | 7. Stock Awards and Stock-Based Compensation From time to time, the Company may issue stock awards in the form of Class A Common Stock grants, Restricted Stock Units (RSUs), or Class A Common Stock options with vesting/service terms. Stock awards are valued on the grant date using the Company’s common stock share price quoted on an active market. Stock options are valued using the Black-Scholes-Merton pricing model to determine the fair value of the options. We generally issue our awards in terms of a fixed monthly value, resulting in a variable number of shares being issued, or in terms of a fixed monthly share number. During the three months ended March 31, 2023 and 2022, the Company entered into agreements with advisory board members and other external advisors to issue cash payments and stock awards in exchange for services rendered to the Company monthly. The total granted stock-based awards to advisory board members and other external advisors during the three months ended March 31, 2023 and 2022 included grants totaling, $0 and $3 thousand, respectively, options totaling $0, and RSUs totaling $3 thousand and $17 thousand, respectively. In addition to issuing stock awards to advisory board members and other external advisors, during the three months ended March 31, 2023 and 2022, the Company granted stock-based awards to multiple employees. The total granted stock-based awards to employees during the three months ended March 31, 2023 and 2022 included grants totaling, $26 thousand and $149 thousand, respectively, options totaling $4 thousand and $29 thousand, respectively, and RSUs totaling $29 thousand and $89 thousand, respectively. The following table summarizes stock option activity for the three months ended March 31, 2023: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | ​ |  | ​ | ​ |  | Weighted |  | ​ | ​
​ | ​ | ​ | ​ | Weighted | ​ | Average | ​ | ​ | ​
​ | ​ | ​ | ​ | Average | ​ | Remaining | ​ | ​ | ​
​ |  | Options |  | Exercise Price |  | Contractual |  | Aggregate
​ | ​ | Outstanding | ​ | Per Share | ​ | Life (years) | ​ | Intrinsic Value
Balance as of January 1, 2022 |  | 395,002 | ​ | $ | 6.40 |  | 2.42 | ​ | $ | 5,365,737
Options granted |  | 7,443 | ​ |  | 3.20 |  | ​ | ​ |  | ​
Options exercised |  | (15,121) | ​ |  | 6.30 |  | ​ | ​ |  | ​
Options canceled and forfeited | ​ | (215) | ​ | ​ | 4.40 | ​ | ​ | ​ | ​ | ​
Balance as of December 31, 2022 | ​ | 387,109 | ​ | ​ | 6.40 | ​ | 1.45 | ​ | ​ | 0
Options granted | ​ | 2,647 | ​ | ​ | 3.01 | ​ | ​ | ​ | ​ | ​
Options exercised | ​ | (1,230) | ​ | ​ | 3.25 | ​ | ​ | ​ | ​ | ​
Options canceled and forfeited |  | (756) | ​ |  | 7.94 |  | ​ | ​ |  | ​
Balance as of March 31, 2023 |  | 387,770 | ​ |  | 6.37 |  | 1.21 | ​ |  | 0
Options vested and exercisable as of March 31, 2023 |  | 387,770 | ​ | $ | 6.37 |  | 1.21 | ​ | $ | 0
​ The aggregate intrinsic value of options outstanding, exercisable, and vested and exercisable is calculated as the difference between the exercise price of the underlying options and the fair value of the Company’s common stock. The aggregate intrinsic value of options exercised during the three months ended March 31, 2023 and 2022 is $0 and $37 thousand, respectively. The weighted average grant-date fair value of options granted during the three months ended March 31, 2023 and 2022 was $2.00 and $16.72 per share, respectively. The total grant-date fair value of options that vested during the three months ended March 31, 2023 and 2022 was $4 thousand and $29 thousand, respectively. As of March 31, 2023, the Company had 387,770 stock options outstanding of which all are fully vested options. As of March 31, 2023, the Company had 70,641 common stock grants outstanding of which 62,965 were vested but not issued and 7,676 were not yet vested. All granted and outstanding common stock grants will fully vest by March 31, 2024. The Company had unrecognized stock-based compensation related to common stock grants of $15 thousand as of March 31, 2023. As of March 31, 2023, the Company had 276,590 RSUs outstanding of which 241,945 were vested but not issued and 34,645 were not yet vested. All granted and outstanding RSUs will fully vest by January 2, 2024. The Company had unrecognized stock-based compensation related to RSUs of $22 thousand as of March 31, 2023. A summary of outstanding RSU activity is as follows: ​
​ | ​ | ​
​ |  | RSU Outstanding Number of Shares
Balance as of January 1, 2022 | ​ | 126,900
Granted | ​ | 211,700
Vested (issued) | ​ | (46,036)
Forfeited | ​ | —
Balance as of December 31, 2022 | ​ | 292,564
Granted | ​ | 4,627
Vested (issued) | ​ | —
Forfeited | ​ | (20,601)
Balance as of March 31, 2023 | ​ | 276,590
​ The following assumptions were used to calculate the fair value of options granted during the three months ended March 31, 2023: ​
​ | ​ | ​ | ​ | ​
Fair value of Class A Common Stock |  | $ | 2.65—3.57 | ​
Exercise price | ​ | $ | 2.93 — 3.09 | ​
Risk free interest rate | ​ | ​ | 3.91 — 4.23 | %
Expected dividend yield | ​ | ​ | 0.00 | %
Expected volatility | ​ | ​ | 92.90 — 96.45 | %
Expected term | ​ | ​ | 3 Years | ​
​ Stock-based compensation expense Our consolidated statements of operations include stock-based compensation expense as follows: ​
​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Three months ended March 31,
​ |  | 2023 |  | 2022
Cost of services | ​ | $ | 494 | ​ | $ | 2,174
Research and development | ​ | ​ | 18,855 | ​ | ​ | 59,860
Selling, general, and administrative | ​ | ​ | 40,225 | ​ | ​ | 225,752
Total stock-based compensation expense | ​ | $ | 59,574 | ​ | $ | 287,786
​ | 10. Stock Awards and Stock-Based Compensation From time to time, the Company may issue stock awards in the form of Class A Shares of Common Stock grants, Restricted Stock Units (RSUs), or Class A Shares of Common Stock options with vesting/service terms. Stock awards are valued on the grant date using the Company’s common stock share price quoted on an active market. Stock options are valued using the Black-Scholes-Merton pricing model to determine the fair value of the options. We generally issue our awards in terms of a fixed monthly value, resulting in a variable number of shares being issued, or in terms of a fixed monthly share number. During the years ended December 31, 2022 and 2021, the Company entered into agreements with advisory board members and other external advisors to issue cash payments and stock awards in exchange for services rendered to the Company monthly. The total granted stock-based awards to advisory board members and other external advisors during the years ended December 31, 2022, and 2021 included grants totaling, $49 thousand and $141 thousand, respectively, options totaling $0 and $114, respectively, and RSUs totaling $190 thousand and $297 thousand, respectively. In addition to issuing stock awards to advisory board members and other external advisors, during the years ended December 31, 2022, and 2021, the Company granted stock-based awards to multiple employees. The total granted stock-based awards to employees during the years ended December 31, 2022, and 2021 included grants totaling, $307 thousand and $369 thousand, respectively, options totaling $57 thousand and $500 thousand, respectively, and RSUs totaling $1.80 million and $1.47 million, respectively. The following table summarizes stock option activity for the year ended December 31, 2022 and 2021: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | ​ | ​ |  | ​ | ​ |  | Weighted |  | ​ | ​
​ | ​ | ​ | ​ | ​ | Weighted | ​ | Average | ​ | ​ | ​
​ | ​ | ​ | ​ | ​ | Average | ​ | Remaining | ​ | ​ | ​
​ | ​ | Options | ​ | Exercise Price | ​ | Contractual | ​ | Aggregate
​ | ​ | Outstanding | ​ | Per Share | ​ | Life (years) | ​ | Intrinsic Value
Balance as of January 1, 2021 | ​ | ​ | 346,806 | ​ | $ | 6.30 |  | 3.21 | ​ | $ | 527,450
Options granted | ​ |  | 52,347 | ​ |  | 7.55 |  |  | ​ |  |
Options exercised | ​ |  | — | ​ |  | — |  |  | ​ |  |
Options canceled and forfeited | ​ |  | (4,151) | ​ |  | 3.85 |  |  | ​ |  |
Balance as of December 31, 2021 | ​ | ​ | 395,002 | ​ | ​ | 6.40 |  | 2.42 | ​ | ​ | 5,365,737
Options granted | ​ | ​ | 7,443 | ​ | ​ | 3.20 | ​ | ​ | ​ | ​ | ​
Options exercised | ​ | ​ | (15,121) | ​ | ​ | 6.30 | ​ | ​ | ​ | ​ | ​
Options canceled and forfeited | ​ | ​ | (215) | ​ | ​ | 4.40 | ​ | ​ | ​ | ​ | ​
Balance as of December 31, 2022 | ​ | ​ | 387,109 | ​ | ​ | 6.40 | ​ | 1.45 | ​ | ​ | 0
Options vested and exercisable as of December 31, 2022 | ​ | ​ | 387,109 | ​ | $ | 6.40 |  | 1.45 | ​ | $ | 0
​ The aggregate intrinsic value of options outstanding, exercisable, and vested and exercisable is calculated as the difference between the exercise price of the underlying options and the fair value of the Company’s common stock. The aggregate intrinsic value of options exercised during the year ended December 31, 2022 and 2021 is $0. The weighted average grant-date fair value of options granted during the years ended December 31, 2022, and 2021 was $7.65 and $ 9.55 per share, respectively. The total grant-date fair value of options that vested during the years ended December 31, 2022 and 2021 was $57 thousand and $500 thousand, respectively. As of December 31, 2022, the Company had 387,109 stock options outstanding of which all are fully vested options. As of December 31, 2022, the Company had 64,699 common stock grants outstanding of which 57,197 were vested but not issued and 7,502 were not yet vested. All granted and outstanding common stock grants will fully vest by August 31, 2023. The Company had unrecognized stock- based compensation related to common stock grants of $23 thousand as of December 31, 2022. As of December 31, 2022, the Company had 292,565 RSUs outstanding of which 44,234 were vested but not issued and 248,331 were not yet vested. All granted and outstanding RSUs will fully vest by January 2, 2024. The Company had unrecognized stock-based compensation related to RSUs of $176 thousand as of December 31, 2022. A summary of outstanding RSU activity is as follows: ​
​ | ​ | ​
​ |  | RSU Outstanding Number of Shares
Balance as of January 1, 2021 |  | —
Granted |  | 126,900
Vested (issued) |  | —
Forfeited |  | —
Balance as of December 31, 2021 |  | 126,900
Granted |  | 211,700
Vested (issued) |  | (46,036)
Forfeited |  | —
Balance as of December 31, 2022 |  | 292,564
​ The following assumptions were used to calculate the fair value of options granted during the year ended December 31, 2022:
​ | ​ | ​ | ​
Fair value of Class A Shares of Common Stock | $ | 3.05 – 22.90 | ​
Exercise price | $ | 3.10 – 3.75 | ​
Risk free interest rate |  | 1.25 - 4.38 | %
Expected dividend yield |  | 0 | %
Expected volatility |  | 52.80 – 104.50 | %
Expected term |  | 3 Years | ​
​ Stock-based compensation expense Our consolidated statements of operations include stock-based compensation expense as follows: ​
​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | For the years ended December 31,
​ | ​ | 2022 |  | 2021
Cost of services provided | ​ | $ | 21,721 | ​ | $ | 160,504
Research and development expense | ​ |  | 292,084 | ​ |  | 493,336
Selling, general, and administrative | ​ |  | 2,085,258 | ​ |  | 2,126,799
Total stock-based compensation expense | ​ | $ | 2,399,063 | ​ | $ | 2,780,639
​

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