v3.25.2
Document and Entity Information - shares
 7 Months Ended
Jun. 30, 2025
Aug. 11, 2025
Document Information [Line Items]    
Document Type 10-Q  
Document Quarterly Report true  
Document Period End Date Jun. 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  
Country Region +1  
City Area Code 212  
Local Phone Number 850-7770  
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  
Entity Shell Company true  
Entity Central Index Key 0002047497  
Current Fiscal Year End Date --09-30  
Document Fiscal Year Focus 2025  
Document Fiscal Period Focus Q3  
Amendment Flag false  
Transition Report true  
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  
Redeemable warrants    
Document Information [Line Items]    
Title of 12(b) Security Redeemable warrants included as part of the units, each whole warrant exercisable for one Class A ordinary share at an exercise price of $11.50  
Trading Symbol RAC.WS  
Security Exchange Name NYSE  
Class A ordinary shares    
Document Information [Line Items]    
Title of 12(b) Security Class A ordinary shares included as part of the units  
Trading Symbol RAC  
Security Exchange Name NYSE  
Entity Common Stock, Shares Outstanding   23,660,000
Class B ordinary shares    
Document Information [Line Items]    
Entity Common Stock, Shares Outstanding   5,750,000