Description of Organization and Business Operations - Additional Information (Detail)				2 Months Ended	9 Months Ended
	Jul. 28, 2021 USD ($) Offering $ / shares	Feb. 11, 2021 USD ($) $ / shares shares	Dec. 23, 2020 USD ($)	Feb. 16, 2021 USD ($)	Sep. 30, 2021 USD ($) $ / shares shares	Jun. 30, 2021 $ / shares	Mar. 31, 2021 $ / shares	Dec. 31, 2020 USD ($) $ / shares
Description Of Organization And Business Operations [Line Items]
Entity incorporation, date of incorporation					Dec. 23, 2020
Shares issued price per share \| $ / shares					$ 10.00
Gross proceeds from the initial public offering		$ 552,000,000.0
Deferred offering costs		31,100,000						$ 93,774
Deferred underwriting commissions		$ 19,300,000
Warrants issued during period \| shares					23,160,000
Proceeds received from initial public offering, gross					$ 552,000,000
Interest used to pay franchise and income tax, reduces dissolution expenses					$ 100,000
Redemption percentage of public shares if business combination is not completed within specific period					100.00%
Period from closing of public offering to complete business combination scenario one					24 months
Date from closing of public offering to complete business combination scenario one					Feb. 11, 2023
Period from closing of public offering to complete business combination scenario two					27 months
Date from closing of public offering to complete business combination scenario two					May 11, 2023
Minimum percentage of fair market value of business combination assets held in trust account					80.00%
Redemption of shares, minimum net tangible assets to complete business combination					$ 5,000,001
Threshold number of trading days that common stock spice equals or exceeds					20 days
Threshold number of consecutive trading days that common stock spice equals or exceeds					30 days
Cash					$ 497,039
Working capital deficit					$ 5,300,000
Proceeds from issuance of common stock to the Sponsor			$ 25,000
Proceeds received under loan from the Sponsor				$ 182,000
Debt instrument repayment date					Feb. 17, 2021
Sponsor \| Working Capital Loans
Description Of Organization And Business Operations [Line Items]
Debt outstanding					$ 0			$ 0
Amendment to Letter Agreement
Description Of Organization And Business Operations [Line Items]
Letter agreement date	Feb. 08, 2021
Reported last sale price \| $ / shares	$ 12.00
Threshold number of trading days that common stock spice equals or exceeds	20 years
Threshold number of consecutive trading days that common stock spice equals or exceeds	30 days
Threshold days commencing after closing date	120 days
Threshold days to transfer warrants after closing date	30 days
Amendment to Letter Agreement
Description Of Organization And Business Operations [Line Items]
Threshold days commencing after closing date	15 days
Registerable securities aggregate value	$ 50,000,000
Registration rights agreement date	Feb. 08, 2021
Number of underwritten offerings \| Offering	3
Amendment to Letter Agreement \| Madeleine Charging
Description Of Organization And Business Operations [Line Items]
Reported last sale price \| $ / shares	$ 12.00
Threshold number of trading days that common stock spice equals or exceeds	20 years
Threshold number of consecutive trading days that common stock spice equals or exceeds	30 years
Threshold days commencing after closing date	120 days
Amendment to Letter Agreement \| E8 Investor
Description Of Organization And Business Operations [Line Items]
Threshold months to transfer securities after closing date	18 months
Class A Common Stock
Description Of Organization And Business Operations [Line Items]
Common stock, par or stated value per share \| $ / shares		$ 0.0001			$ 0.0001	$ 0.0001	$ 0.0001	$ 0.0001
Reported last sale price \| $ / shares					$ 12.00
Proceeds from issuance of common stock to the Sponsor					$ 552,000,000
Initial Public Offering
Description Of Organization And Business Operations [Line Items]
Stock issued during period (in shares) \| shares		55,200,000
Shares issued price per share \| $ / shares		$ 10.00
Proceeds received from initial public offering, gross		$ 552,000,000.0
Initial Public Offering \| Class A Common Stock
Description Of Organization And Business Operations [Line Items]
Stock issued during period (in shares) \| shares		55,200,000
Common stock, par or stated value per share \| $ / shares		$ 0.0001
Over-Allotment Option
Description Of Organization And Business Operations [Line Items]
Stock issued during period (in shares) \| shares		7,200,000
Over-Allotment Option \| Class A Common Stock
Description Of Organization And Business Operations [Line Items]
Stock issued during period (in shares) \| shares		7,200,000
Shares issued price per share \| $ / shares		$ 10.00
Private Placement Warrants
Description Of Organization And Business Operations [Line Items]
Warrants issued during period \| shares		9,360,000
Warrants issued price per share \| $ / shares		$ 1.50
Proceeds received from private placement		$ 14,000,000.0

Spartan Acquisition Corp. III 10-Q/A