Fair Value Measurements - Summary of Fair Value Measurements (Detail) - Fair Value, Recurring [Member] - USD ($)	Sep. 30, 2022	Dec. 31, 2021
Fair Value, Inputs, Level 1 [Member] \| US Treasury Securities [Member] \| U.S. Treasury Securities (Matures on 12/15/22)
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Amortized Cost	$ 299,444,382
Gross Holding Loss	207,256
Fair Value	299,651,638
Fair Value, Inputs, Level 1 [Member] \| US Treasury Securities [Member] \| U.S. Treasury Securities (Matures on 12/22/22)
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Amortized Cost	303,762,232
Gross Holding Loss	194,489
Fair Value	303,567,743
Fair Value, Inputs, Level 1 [Member] \| Money Market Funds [Member]
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Fair Value		$ 600,166,685
Fair Value, Inputs, Level 1 [Member] \| Public Warrant [Member]
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Fair Value		9,480,000
Fair Value, Inputs, Level 3 [Member] \| FPA Derivative [Member]
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Fair Value		107,000
Fair Value, Inputs, Level 3 [Member] \| FPA Derivative Liability [Member]
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Fair Value	25,000
Fair Value, Inputs, Level 2 [Member] \| Public Warrant [Member]
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Fair Value	1,800,000
Fair Value, Inputs, Level 2 [Member] \| Private Placement Warrant [Member]
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Fair Value	$ 1,400,000	$ 7,373,334

Hudson Executive Investment Corp. III 10-Q