XML 15 R1.htm IDEA: XBRL DOCUMENT v3.25.3
Document and Entity Information - USD ($)
$ in Millions
 10 Months Ended
Sep. 30, 2025
Dec. 19, 2025
Dec. 18, 2025
Mar. 31, 2025
Document Information [Line Items]        
Document Type 10-K      
Document Annual Report true      
Document Period End Date Sep. 30, 2025      
Document Transition Report false      
Entity File Number 001-42537      
Entity Registrant Name Rithm Acquisition Corp.      
Entity Incorporation, State or Country Code E9      
Entity Tax Identification Number 98-1832772      
Entity Address, Address Line One 799 Broadway      
Entity Address, Adress Line Two 8th Floor      
Entity Address, City or Town New York      
Entity Address State Or Province NY      
Entity Address, Postal Zip Code 10003      
Country Region +1      
City Area Code 212      
Local Phone Number 850-7770      
Entity Well-known Seasoned Issuer No      
Entity Voluntary Filers No      
Entity Current Reporting Status Yes      
Entity Interactive Data Current Yes      
Entity Filer Category Non-accelerated Filer      
Entity Small Business true      
Entity Emerging Growth Company true      
Entity Ex Transition Period false      
ICFR Auditor Attestation Flag true      
Document Financial Statement Error Correction [Flag] false      
Entity Shell Company true      
Entity Public Float       $ 236.6
Entity Central Index Key 0002047497      
Current Fiscal Year End Date --09-30      
Document Fiscal Year Focus 2025      
Document Fiscal Period Focus FY      
Amendment Flag false      
Transition Report true      
Inception Date Sep. 30, 2025      
Auditor Name WithumSmith+Brown, PC      
Auditor Location New York      
Auditor Firm ID 100      
Class A ordinary shares        
Document Information [Line Items]        
Title of 12(b) Security Class A ordinary shares, par value $0.0001 per share      
Trading Symbol RAC      
Security Exchange Name NYSE      
Entity Common Stock, Shares Outstanding   23,660,000    
Redeemable warrants, each whole warrant exercisable for one Class A ordinary share at an exercise price of $11.50        
Document Information [Line Items]        
Title of 12(b) Security Redeemable warrants, each whole warrant exercisable for oneClass A ordinary share at an exercise price of $11.50      
Trading Symbol RAC.WS      
Security Exchange Name NYSE      
Units, each consisting of one Class A ordinary share, $0.0001 par value, and one-third of one redeemable warrant        
Document Information [Line Items]        
Title of 12(b) Security units, each consisting of one Class A ordinary share, $0.0001 par value, and one-third of one redeemable warrant      
Trading Symbol RAC.U      
Security Exchange Name NYSE      
Class B ordinary shares        
Document Information [Line Items]        
Entity Common Stock, Shares Outstanding     5,750,000