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Cover
Feb. 26, 2025
Document Information [Line Items]  
Document Type 8-K
Amendment Flag false
Document Period End Date Feb. 26, 2025
Current Fiscal Year End Date --09-30
Entity File Number 001-42537
Entity Registrant Name Rithm Acquisition Corp.
Entity Central Index Key 0002047497
Entity Tax Identification Number 98-1832772
Entity Incorporation, State or Country Code E9
Entity Address, Address Line One 799 Broadway
Entity Address, Address Line Two 8th Floor
Entity Address, City or Town New York
Entity Address, State or Province NY
Entity Address, Postal Zip Code 10003
City Area Code 212
Local Phone Number 850-7770
Written Communications false
Soliciting Material false
Pre-commencement Tender Offer false
Pre-commencement Issuer Tender Offer false
Entity Emerging Growth Company true
Elected Not To Use the Extended Transition Period false
Units Each Consisting Of One Classa Ordinary Share 0. 0001 Par Value And Onethird Of One Redeemable Warrant [Member]  
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
Classa Ordinary Shares Included As Part Of Units [Member]  
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
Redeemable Warrants Included As Part Of Units Each Whole Warrant Exercisable For One Classa Ordinary Share At Exercise Price Of 11. 50 [Member]  
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