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Summary of Significant Accounting Policies - Restatement (Details)
$ / shares in Units, $ in Thousands
 2 Months Ended 9 Months Ended 12 Months Ended
Apr. 04, 2021
USD ($)
Sep. 30, 2022
USD ($)
$ / shares
Sep. 30, 2021
USD ($)
$ / shares
Dec. 31, 2021
USD ($)
$ / shares
Dec. 31, 2020
USD ($)
$ / shares
Error Corrections and Prior Period Adjustments Restatement [Line Items]          
Equity method investments   $ 11,047   $ 24,752 $ 23,217
Accumulated deficit   (434,863)   (379,889) (333,200)
Gain from equity method investees, net   2,346 $ 2,371 (1,606) (1,644)
Revenue from related party transactions   2,116 2,348 3,253 4,203
Contract assets   14,848   11,700 6,186
Other accrued liabilities   8,064   7,059 2,897
Revenue from contracts with customers       18,871 12,987
Consolidated Balance Sheet          
Contract assets   14,848   11,700 6,186
Total current assets   88,815   148,675 76,589
Equity method investments   11,047   24,752 23,217
Total assets   135,590   193,011 118,980
Other accrued liabilities   8,064   7,059 2,897
Total current liabilities   49,047   49,290 15,204
Total liabilities   62,599   67,297 35,788
Accumulated deficit   (434,863)   (379,889) (333,200)
Total shareholders’ deficit   (407,640) (339,740) (354,917) (311,216)
Total liabilities, contingently redeemable preferred stock, and shareholders' deficit   135,590   193,011 118,980
Consolidated Statement of Operations and Comprehensive Loss          
Revenue from contracts with customers       18,871 12,987
Revenues   2,116 2,348 3,253 4,203
Revenues   25,781 18,327 25,461 18,353
Cost of revenues from contracts with customers (exclusive of depreciation shown below)       (13,167) (8,185)
Total cost and operating expenses       (76,480) (58,054)
Loss from operations   (56,223) (35,244) (51,019) (39,701)
Loss before income taxes   (57,320) (32,962) (48,634) (39,880)
Gain from equity method investees, net   2,346 2,371 1,945 2,167
Net income (loss)   (54,974) (30,591) (46,689) (37,713)
Net loss allocated to common shareholders   (83,899) (57,659) (83,447) (69,004)
Net loss allocated to common shareholders       (83,447) (69,004)
Comprehensive loss   $ (55,741) $ (30,620) $ (46,594) $ (37,088)
Net loss per common share - basic (usd per share) | $ / shares   $ (39,790) $ (30,190) $ (42.59) $ (42.34)
Net loss per common share - diluted (usd per share) | $ / shares   $ (39,790) $ (30,190) $ (42.59) $ (42.34)
Consolidated Statement of Changes in Redeemable Convertible Preferred Stock and Shareholders’ Equity (Deficit)          
Balance at the beginning   $ (354,917) $ (311,216) $ (311,216) $ (276,592)
Net loss   (54,974) (30,591) (46,689) (37,713)
Balance at the end   (407,640) (339,740) (354,917) (311,216)
Consolidated Statement of Cash Flows          
Net loss   (54,974) (30,591) (46,689) (37,713)
Non-cash recognition of licensing revenue   (1,620) (1,516) (2,022) (1,018)
Gain from equity method investees, net   2,346 2,371 1,945 2,167
Contract assets   (3,270) (3,838) (5,514) (5,605)
Accounts payable and accrued salaries and wages   463 717 1,256 690
Net cash used in operating activities   (71,336) (26,718) (42,591) (39,271)
Gain on dilution       503  
LanzaJet          
Error Corrections and Prior Period Adjustments Restatement [Line Items]          
Equity method investments       12,433 13,651
Revenue from contracts with customers   1,620 1,516 2,025 1,018
Consolidated Balance Sheet          
Equity method investments       12,433 13,651
Consolidated Statement of Operations and Comprehensive Loss          
Revenue from contracts with customers   1,620 1,516 2,025 1,018
Consolidated Statement of Cash Flows          
Gain on dilution $ 503        
Intra-entity | LanzaJet          
Error Corrections and Prior Period Adjustments Restatement [Line Items]          
Revenue from contracts with customers   (395) (497) 662 549
Consolidated Statement of Operations and Comprehensive Loss          
Revenue from contracts with customers   (395) (497) 662 549
Accumulated Deficit          
Consolidated Balance Sheet          
Total shareholders’ deficit   (434,863) (363,791) (379,889) (333,200)
Consolidated Statement of Operations and Comprehensive Loss          
Net income (loss)   (54,974) (30,591) (46,689) (37,713)
Consolidated Statement of Changes in Redeemable Convertible Preferred Stock and Shareholders’ Equity (Deficit)          
Balance at the beginning   (379,889) (333,200) (333,200) (295,487)
Net loss   (54,974) (30,591) (46,689) (37,713)
Balance at the end   (434,863) (363,791) (379,889) (333,200)
Consolidated Statement of Cash Flows          
Net loss   (54,974) (30,591) (46,689) (37,713)
Related Party Supply Agreement          
Error Corrections and Prior Period Adjustments Restatement [Line Items]          
Related party fees       1,223 242
As Previously Reported          
Error Corrections and Prior Period Adjustments Restatement [Line Items]          
Equity method investments       26,479 24,023
Accumulated deficit       (378,162) (332,394)
Revenue from related party transactions       3,915 4,752
Contract assets         6,064
Other accrued liabilities         2,775
Revenue from contracts with customers       18,993 12,865
Consolidated Balance Sheet          
Contract assets         6,064
Total current assets         76,467
Equity method investments       26,479 24,023
Total assets       194,738 119,664
Other accrued liabilities         2,775
Total current liabilities         15,082
Total liabilities         35,666
Accumulated deficit       (378,162) (332,394)
Total shareholders’ deficit       (353,190) (310,410)
Total liabilities, contingently redeemable preferred stock, and shareholders' deficit       194,738 119,664
Consolidated Statement of Operations and Comprehensive Loss          
Revenue from contracts with customers       18,993 12,865
Revenues       3,915 4,752
Revenues       26,245 18,780
Cost of revenues from contracts with customers (exclusive of depreciation shown below)       (13,289) (8,063)
Total cost and operating expenses       (76,602) (57,932)
Loss from operations       (50,357) (39,152)
Loss before income taxes       (47,972) (39,331)
Gain from equity method investees, net       2,204 2,424
Net income (loss)       (45,768) (36,907)
Net loss allocated to common shareholders       (82,526) (68,198)
Net loss allocated to common shareholders       (82,526) (68,198)
Comprehensive loss       $ (45,673) $ (36,282)
Net loss per common share - basic (usd per share) | $ / shares       $ (42.12) $ (41.84)
Net loss per common share - diluted (usd per share) | $ / shares       $ (42.12) $ (41.84)
Consolidated Statement of Changes in Redeemable Convertible Preferred Stock and Shareholders’ Equity (Deficit)          
Balance at the beginning   (353,190) (310,410) $ (310,410) $ (276,592)
Net loss       (45,768) (36,907)
Balance at the end       (353,190) (310,410)
Consolidated Statement of Cash Flows          
Net loss       (45,768) (36,907)
Non-cash recognition of licensing revenue       (2,684) (1,567)
Gain from equity method investees, net       2,204 2,424
Contract assets       (5,636) (5,483)
Accounts payable and accrued salaries and wages       1,378 568
Net cash used in operating activities       (42,591) (39,271)
Gain on dilution       181  
As Previously Reported | Accumulated Deficit          
Consolidated Balance Sheet          
Total shareholders’ deficit       (378,162) (332,394)
Consolidated Statement of Changes in Redeemable Convertible Preferred Stock and Shareholders’ Equity (Deficit)          
Balance at the beginning   (378,162) (332,394) (332,394) (295,487)
Balance at the end       (378,162) (332,394)
Adjustments          
Error Corrections and Prior Period Adjustments Restatement [Line Items]          
Equity method investments       (1,727) (806)
Accumulated deficit       (1,727) (806)
Revenue from related party transactions       (662) (549)
Contract assets         122
Other accrued liabilities         122
Revenue from contracts with customers       (122) 122
Cost of revenue         122
Consolidated Balance Sheet          
Contract assets         122
Total current assets         122
Equity method investments       (1,727) (806)
Total assets       (1,727) (684)
Other accrued liabilities         122
Total current liabilities         122
Total liabilities         122
Accumulated deficit       (1,727) (806)
Total shareholders’ deficit       (1,727) (806)
Total liabilities, contingently redeemable preferred stock, and shareholders' deficit       (1,727) (684)
Consolidated Statement of Operations and Comprehensive Loss          
Revenue from contracts with customers       (122) 122
Revenues       (662) (549)
Revenues       (784) (427)
Cost of revenues from contracts with customers (exclusive of depreciation shown below)       122 (122)
Total cost and operating expenses       122 (122)
Loss from operations       (662) (549)
Loss before income taxes       (662) (549)
Gain from equity method investees, net       (259) (257)
Net income (loss)       (921) (806)
Net loss allocated to common shareholders       (921) (806)
Net loss allocated to common shareholders       (921) (806)
Comprehensive loss       $ (921) $ (806)
Net loss per common share - basic (usd per share) | $ / shares       $ (0.47) $ (0.50)
Net loss per common share - diluted (usd per share) | $ / shares       $ (0.47) $ (0.50)
Consolidated Statement of Changes in Redeemable Convertible Preferred Stock and Shareholders’ Equity (Deficit)          
Balance at the beginning   (1,727) (806) $ (806) $ 0
Net loss       (921) (806)
Balance at the end       (1,727) (806)
Consolidated Statement of Cash Flows          
Net loss       (921) (806)
Non-cash recognition of licensing revenue       662 549
Gain from equity method investees, net       (259) (257)
Contract assets       122 (122)
Accounts payable and accrued salaries and wages       (122) 122
Net cash used in operating activities       0 0
Adjustments | Accumulated Deficit          
Consolidated Balance Sheet          
Total shareholders’ deficit       (1,727) (806)
Consolidated Statement of Changes in Redeemable Convertible Preferred Stock and Shareholders’ Equity (Deficit)          
Balance at the beginning   $ (1,727) $ (806) (806) 0
Balance at the end       (1,727) (806)
Adjustments | Error Correction, Equity Method Investments, Intangibles And Fixed Assets          
Error Corrections and Prior Period Adjustments Restatement [Line Items]          
Equity method investments       580 257
Accumulated deficit       (580) (257)
Gain from equity method investees, net       (580) (257)
Consolidated Balance Sheet          
Equity method investments       580 257
Accumulated deficit       (580) (257)
Adjustments | Error Correction, Equity Method Investment, Contributed Intellectual Asset          
Error Corrections and Prior Period Adjustments Restatement [Line Items]          
Equity method investments       662 549
Accumulated deficit       (662) (549)
Revenue from related party transactions       (662) (549)
Consolidated Balance Sheet          
Equity method investments       662 549
Accumulated deficit       (662) (549)
Consolidated Statement of Operations and Comprehensive Loss          
Revenues       (662) $ (549)
Adjustments | Error Correction, Equity Method Investment, Gain On Dilution          
Error Corrections and Prior Period Adjustments Restatement [Line Items]          
Equity method investments       322  
Accumulated deficit       322  
Gain from equity method investees, net       322  
Consolidated Balance Sheet          
Equity method investments       322  
Accumulated deficit       $ 322