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S-K 1604(c) De-SPAC Dilution
 6 Months Ended
Jun. 30, 2025
USD ($)
shares
De-SPAC, Net Tangible Book Value [Line Items]  
De-SPAC, Net Tangible Book Value, Adjusted $ 298,952,339 [1]
De-SPAC, Number of Shares Used [Line Items]  
De-SPAC, Number of Shares Used to Determine Net Tangible Book Value, Adjusted | shares 36,685,391 [1]
Shareholder Redemptions [Member]  
De-SPAC, Number of Shares Used [Line Items]  
De-SPAC, Number of Shares Used to Determine Net Tangible Book Value, Adjusted | shares 24,679,856 [1]
SPAC Sponsor Compensation [Member]  
De-SPAC, Number of Shares Used [Line Items]  
De-SPAC, Number of Shares Used to Determine Net Tangible Book Value, Adjusted | shares 6,250,000 [1]
PIPE Financing [Member]  
De-SPAC, Number of Shares Used [Line Items]  
De-SPAC, Number of Shares Used to Determine Net Tangible Book Value, Adjusted | shares 5,755,535 [1]
No Redemption [Member]  
De-SPAC, Net Tangible Book Value [Line Items]  
De-SPAC, Net Tangible Book Value, Adjusted $ 570,623,252 [2]
De-SPAC, Number of Shares Used [Line Items]  
De-SPAC, Number of Shares Used to Determine Net Tangible Book Value, Adjusted | shares 61,365,247 [2]
No Redemption [Member] | Shareholder Redemptions [Member]  
De-SPAC, Number of Shares Used [Line Items]  
De-SPAC, Number of Shares Used to Determine Net Tangible Book Value, Adjusted | shares 49,359,712 [2]
No Redemption [Member] | SPAC Sponsor Compensation [Member]  
De-SPAC, Number of Shares Used [Line Items]  
De-SPAC, Number of Shares Used to Determine Net Tangible Book Value, Adjusted | shares 6,250,000 [2]
No Redemption [Member] | PIPE Financing [Member]  
De-SPAC, Number of Shares Used [Line Items]  
De-SPAC, Number of Shares Used to Determine Net Tangible Book Value, Adjusted | shares 5,755,535 [2]
Redemption at 100 Percent of Maximum [Member]  
De-SPAC, Net Tangible Book Value [Line Items]  
De-SPAC, Net Tangible Book Value, Adjusted $ 21,781,426 [3]
De-SPAC, Number of Shares Used [Line Items]  
De-SPAC, Number of Shares Used to Determine Net Tangible Book Value, Adjusted | shares 12,005,535 [3]
Redemption at 100 Percent of Maximum [Member] | Shareholder Redemptions [Member]  
De-SPAC, Number of Shares Used [Line Items]  
De-SPAC, Number of Shares Used to Determine Net Tangible Book Value, Adjusted | shares 0 [3]
Redemption at 100 Percent of Maximum [Member] | SPAC Sponsor Compensation [Member]  
De-SPAC, Number of Shares Used [Line Items]  
De-SPAC, Number of Shares Used to Determine Net Tangible Book Value, Adjusted | shares 6,250,000 [3]
Redemption at 100 Percent of Maximum [Member] | PIPE Financing [Member]  
De-SPAC, Number of Shares Used [Line Items]  
De-SPAC, Number of Shares Used to Determine Net Tangible Book Value, Adjusted | shares 5,755,535 [3]
AACTs Net Tangible Book Value [Member]  
De-SPAC, Net Tangible Book Value [Line Items]  
De-SPAC, Net Tangible Book Value, Adjusted $ 533,977,167 [1]
AACTs Net Tangible Book Value [Member] | No Redemption [Member]  
De-SPAC, Net Tangible Book Value [Line Items]  
De-SPAC, Net Tangible Book Value, Adjusted 533,977,167 [2]
AACTs Net Tangible Book Value [Member] | Redemption at 100 Percent of Maximum [Member]  
De-SPAC, Net Tangible Book Value [Line Items]  
De-SPAC, Net Tangible Book Value, Adjusted 533,977,167 [3]
Anticipated Transaction Expenses To Be Incurred By AACT [Member]  
De-SPAC, Net Tangible Book Value [Line Items]  
De-SPAC, Net Tangible Book Value, Adjusted (12,988,376) [1],[4]
Anticipated Transaction Expenses To Be Incurred By AACT [Member] | No Redemption [Member]  
De-SPAC, Net Tangible Book Value [Line Items]  
De-SPAC, Net Tangible Book Value, Adjusted (20,392,333) [2],[4]
Anticipated Transaction Expenses To Be Incurred By AACT [Member] | Redemption at 100 Percent of Maximum [Member]  
De-SPAC, Net Tangible Book Value [Line Items]  
De-SPAC, Net Tangible Book Value, Adjusted (11,084,419) [3],[4]
Anticipated PIPE Investment Proceeds [Member]  
De-SPAC, Net Tangible Book Value [Line Items]  
De-SPAC, Net Tangible Book Value, Adjusted 60,000,000 [1],[5]
Anticipated PIPE Investment Proceeds [Member] | No Redemption [Member]  
De-SPAC, Net Tangible Book Value [Line Items]  
De-SPAC, Net Tangible Book Value, Adjusted 60,000,000 [2],[5]
Anticipated PIPE Investment Proceeds [Member] | Redemption at 100 Percent of Maximum [Member]  
De-SPAC, Net Tangible Book Value [Line Items]  
De-SPAC, Net Tangible Book Value, Adjusted 60,000,000 [3],[5]
Reduction in Trust Account Ddue to April 2025 Redemptions [Member]  
De-SPAC, Net Tangible Book Value [Line Items]  
De-SPAC, Net Tangible Book Value, Adjusted 987,194 [1]
Reduction in Trust Account Ddue to April 2025 Redemptions [Member] | No Redemption [Member]  
De-SPAC, Net Tangible Book Value [Line Items]  
De-SPAC, Net Tangible Book Value, Adjusted 987,194 [2]
Reduction in Trust Account Ddue to April 2025 Redemptions [Member] | Redemption at 100 Percent of Maximum [Member]  
De-SPAC, Net Tangible Book Value [Line Items]  
De-SPAC, Net Tangible Book Value, Adjusted 987,194 [3]
Contributions to AACT Trust Account [Member]  
De-SPAC, Net Tangible Book Value [Line Items]  
De-SPAC, Net Tangible Book Value, Adjusted (3,948,777) [1]
Contributions to AACT Trust Account [Member] | No Redemption [Member]  
De-SPAC, Net Tangible Book Value [Line Items]  
De-SPAC, Net Tangible Book Value, Adjusted (3,948,777) [2]
Contributions to AACT Trust Account [Member] | Redemption at 100 Percent of Maximum [Member]  
De-SPAC, Net Tangible Book Value [Line Items]  
De-SPAC, Net Tangible Book Value, Adjusted (3,948,777) [3]
Redemptions From Trust Account [Member]  
De-SPAC, Net Tangible Book Value [Line Items]  
De-SPAC, Net Tangible Book Value, Adjusted (279,074,870) [1]
Redemptions From Trust Account [Member] | No Redemption [Member]  
De-SPAC, Net Tangible Book Value [Line Items]  
De-SPAC, Net Tangible Book Value, Adjusted 0 [2]
Redemptions From Trust Account [Member] | Redemption at 100 Percent of Maximum [Member]  
De-SPAC, Net Tangible Book Value [Line Items]  
De-SPAC, Net Tangible Book Value, Adjusted $ (558,149,739) [3]
[1] Includes 24,679,856 shares of AACT Class A Ordinary Shares and assumes Public Shareholders exercise redemption rights with respect to 50% of AACT Class A Ordinary Shares for an aggregate of approximately $281.2 million (based on a Redemption Price of $11.39, which was the approximate Redemption Price as of August 18, 2025) from the Trust Account. Numbers may not tie due to rounding.
[2] Includes 49,359,712 shares of AACT Class A Ordinary Shares and assumes that no additional Public Shareholders exercise redemption rights with respect to such AACT Class A Ordinary Shares. Numbers may not tie due to rounding.
[3] Assumes Public Shareholders exercise redemption rights with respect to all AACT Class A Ordinary Shares for an aggregate of approximately $562.3 million (based on a Redemption Price of $11.39, which was the approximate Redemption Price as of August 18, 2025) from the Trust Account.
[4] AACT’s anticipated transaction expenses are expected to decrease as the level of redemptions in connection with the Business Combination increases, as the fees payable to the PIPE Placement Agents are based in part upon the amount remaining in the Trust Account following redemptions in connection with the consummation of the Business Combination.
[5] Assumes (i) completion of a $60.0 million PIPE Investment; and (ii) that $10.0 million of the PIPE Investment prices at the Redemption Price and $50.0 million of the PIPE Investment prices at 90% of the Redemption Price. As of August 18, 2025, the most recent practicable date prior to the date of this proxy statement/prospectus, PIPE Investors have subscribed for $60.0 million of PIPE Stock. AACT and Legacy Kodiak anticipate that the PIPE Investment may increase to $100.0 million by the Closing, although no assurances can be given that AACT will be successful in raising any or all of such incremental PIPE proceeds.