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Basis of Presentation and Summary of Significant Accounting Policies (Details) - USD ($) |  | 2 Months Ended | 3 Months Ended | 6 Months Ended | 9 Months Ended | 11 Months Ended | 12 Months Ended |
--- | --- | --- | --- | --- | --- | --- | --- | ---
Jan. 31, 2021 | Mar. 31, 2021 | Sep. 30, 2022 | Sep. 30, 2021 | Sep. 30, 2021 | Sep. 30, 2022 | Sep. 30, 2021 | Dec. 31, 2021 | Dec. 31, 2021 | Dec. 31, 2020 | Dec. 31, 2019
Cash equivalents |  |  | $ 0 |  |  | $ 0 |  | $ 0 | $ 0 |  |
Effective tax rate |  |  |  |  |  | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% |
Statutory tax rate (as a percent) | 21.00% | 21.00% | 21.00% |  | 21.00% | 21.00% |  | 21.00% | 21.00% | 28.00% |
Common stock subject to possible redemption, outstanding |  |  | 29,521,810 | 29,521,810 | 29,521,810 | 29,521,810 | 29,521,810 | 29,521,810 | 29,521,810 | 25,729,542 | 23,695,330
Aggregate purchase of stock |  |  |  |  |  | 34,117,671 | 33,867,263 |  | 34,175,113 | 30,720,703 |
AMCI ACQUISITION CORP. II |  |  |  |  |  |  |  |  |  |  |
Effective tax rate | 0.00% | 0.00% | 0.88% | 0.00% | 0.00% | 0.91% |  |  |  |  |
Class A Common stock |  |  |  |  |  |  |  |  |  |  |
Common stock subject to possible redemption, outstanding |  |  |  |  |  |  |  | 15,000,000 | 15,000,000 |  |
Aggregate purchase of stock |  |  |  |  |  | 11,000,000 |  | 11,000,000 |  |  |
Class A Common stock | AMCI ACQUISITION CORP. II |  |  |  |  |  |  |  |  |  |  |
Common stock subject to possible redemption, outstanding |  |  |  |  |  |  |  | 15,000,000 | 15,000,000 |  |
Class A Common stock | IPO [Member] |  |  |  |  |  |  |  |  |  |  |
Common stock subject to possible redemption, outstanding |  |  |  |  |  |  |  | 15,000,000 | 15,000,000 |  |
Class A Common Stock Subject to Redemption |  |  |  |  |  |  |  |  |  |  |
Common stock subject to possible redemption, outstanding |  |  | 15,000,000 |  |  | 15,000,000 |  | 15,000,000 | 15,000,000 |  |
Class A Common Stock Subject to Redemption | AMCI ACQUISITION CORP. II |  |  |  |  |  |  |  |  |  |  |
Common stock subject to possible redemption, outstanding |  |  | 15,000,000 |  |  | 15,000,000 |  | 15,000,000 | 15,000,000 |  |
Class A Common Stock Subject to Redemption | IPO [Member] |  |  |  |  |  |  |  |  |  |  |
Common stock subject to possible redemption, outstanding |  |  | 15,000,000 |  |  | 15,000,000 |  |  |  |  |

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