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Stock Options | 3 Months Ended | 12 Months Ended
--- | --- | ---
Mar. 31, 2023 | Dec. 31, 2022
Stock Options |  |
Stock Options |
5. | Stock Options
The Company has adopted a stock option plan covering the issuance of up to 4,000,000 shares of Common Stock to qualified individuals. Options granted under this plan vest over four years and expire ten years from the date of the grant. The following table summarizes stock option activity for the three months ended March 31, 2023: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | Option |  | Weighted-Average |  | Weighted-Average
​ | ​ | Number of | ​ | Exercise | ​ | Remaining
​ |  | Shares |  | Price Per Share |  | Contractual Term
Options outstanding as of January 1, 2023 |  | 4,851,666 | ​ | $ | 1.91 |  | 8.4
Granted |  | 58,000 | ​ |  | 1.81 |  |
Exercised |  | — | ​ |  | — |  |
Canceled |  | — | ​ |  | — |  |
Options outstanding as of March 31, 2023 |  | 4,909,666 | ​ | $ | 1.91 |  | 8.2
Options exercisable as of March 31, 2023 |  | 1,906,098 | ​ | $ | 1.68 |  | 7.1
​ Stock-based compensation expense resulting from granted stock options was $368,140 and $76,973 for the three months ended March 31, 2023 and 2022, respectively. Unrecognized stock-based compensation expense of $6,843,566 at March 31, 2023 will be recognized in future periods as the related stock options continue to vest over a weighted-average period of 3.32 years. | 9.Stock Options The Company has adopted a stock option plan covering the issuance of up to 4,000,000 shares of Common Stock to qualified individuals. Options granted under this plan vest over four years and expire ten years from the date of the grant. The following table summarizes stock option activity for the years ended December 31, 2022 and 2021: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | Option |  | Option |  | Weighted-Average
​ | ​ | Number of | ​ | Exercise | ​ | Exercise
​ |  | Shares |  | Price Per Share |  | Price Per Share
Options outstanding at January 1, 2021 |  | 2,709,964 | ​ | $0.30 - $2.00 |  | $ | 1.48
Granted |  | 335,300 | ​ | $3.13 - $3.76 |  | $ | 3.17
Exercised |  | — | ​ | — |  |  | —
Canceled |  | (286,000) | ​ | $0.30 - $3.13 |  | $ | 1.70
Options outstanding at December 31, 2021 |  | 2,759,264 | ​ | $0.30 - $3.76 |  | $ | 1.66
Granted | ​ | 2,149,152 | ​ | $1.67 - $5.00 | ​ | $ | 2.19
Exercised | ​ | — | ​ | — | ​ | ​ | —
Canceled | ​ | (56,750) | ​ | $0.30 - $2.00 | ​ | $ | 0.49
Options outstanding at December 31, 2022 | ​ | 4,851,666 | ​ | $0.30 - $5.00 | ​ | $ | 1.91
Options exercisable at December 31, 2022 |  | 1,592,088 | ​ | $0.30 - $3.76 |  | $ | 1.49
​ Stock-based compensation expense resulting from granted stock options was $743,274 and $205,629 for the years ended December 31, 2022 and 2021, respectively. Unrecognized stock-based compensation expense of $6,900,425 at December 31, 2022 will be recognized in future periods as the related stock options continue to vest. The weighted-average remaining contractual life of previously granted stock options was 8.40 years at December 31, 2022. The grant-date fair values of stock options granted in 2022 and 2021 was $3.16 and $1.53, respectively, and were estimated using a Black-Scholes valuation model with the following assumptions: ​
​ | ​ | ​ | ​ | ​ | ​
​ |  | December 31, |  | December 31, |
​ | ​ | 2022 | ​ | 2021 |
Expected term |  | 7.21 | years | 7.0 | years
Volatility |  | 27.03 | % | 30.3 | %
Dividend rate |  | 0.0 | % | 0.0 | %
Discount rate |  | 3.32 | % | 1.2 | %
​ ​

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