v3.26.1
Cover - shares
6 Months Ended
Jun. 30, 2026
Aug. 12, 2026
Document Information [Line Items]    
Document Type 10-Q  
Document Quarterly Report true  
Document Transition Report false  
Entity Registrant Name ARCHIMEDES TECH SPAC PARTNERS III CO.  
Document Period End Date Jun. 30, 2026  
Document Fiscal Year Focus 2026  
Document Fiscal Period Focus Q2  
Current Fiscal Year End Date --12-31  
Entity Central Index Key 0002083910  
Entity File Number 001-43071  
Amendment Flag false  
Entity Incorporation, State or Country Code E9  
Entity Tax Identification Number 00-0000000  
Entity Address, Address Line One 2093 Philadelphia Pike #1968  
Entity Address, City or Town Claymont  
Entity Address, State or Province DE  
Entity Address, Postal Zip Code 19703  
City Area Code (725)  
Local Phone Number 312-2430  
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 Common Stock, Shares Outstanding   35,262,000
Units, each consisting of one ordinary share, par value $0.0001 per share, and one-fourth of one redeemable warrant    
Document Information [Line Items]    
Title of 12(b) Security Units, each consisting of one ordinary share, par value $0.0001 per share, and one-fourth of one redeemable warrant  
Trading Symbol ARCIU  
Security Exchange Name NASDAQ  
Ordinary Shares    
Document Information [Line Items]    
Title of 12(b) Security Ordinary Shares  
Trading Symbol ARCI  
Security Exchange Name NASDAQ  
Warrants    
Document Information [Line Items]    
Title of 12(b) Security Warrants  
Trading Symbol ARCIW  
Security Exchange Name NASDAQ