PSI Proves Aaronson-Ambainis Conjecture With Anthropic AI Model
Physical Superintelligence said on November 6, 2026 that its AI research system, built around a private Anthropic model, produced a complete proof of the Aaronson-Ambainis conjecture, open since Scott Aaronson and Andris Ambainis proposed it in 2008.
1 source 9m ago
Reporting from 1 source: GIGAZINE.
Why it matters
The claim matters less for the conjecture itself than for the verification trail: a Lean 4 formalization with no unfinished parts or added axioms, checked by two independent programs and published as source code, is the standard an AI proof now has to clear in public.
Key Facts
- Physical Superintelligence announced on November 6, 2026 that it had proven the Aaronson-Ambainis conjecture, open since 2008.
- The PSI research system incorporates a private AI model developed by Anthropic.
- PSI says the system discovered a complete proof on the third day after it began running, then refined it twice.
- The proof was formalized in Lean 4 without unfinished parts or added axioms and confirmed by two independent verification programs.
- The paper, Lean source code, and verification records are published on GitHub.
The startup says the system found the proof on its third day of running, then refined it twice. PSI checked the result in Lean 4 and published the paper and Lean source code on GitHub.
PSI researchers set the problem themselves and ran the system in their own computing environment, per the company. The system found a complete proof on the third day of running, then refined it twice while the team worked on related mathematical problems, and produced a final version.
Lean 4 was used because plausible-looking AI proofs can contain errors in the logic even when the conclusion reads correctly. PSI says the Lean proof was completed without unfinished parts or added axioms and was confirmed by two independent verification programs. Quantum computing researcher Henry Yuen described the result as the resolution of a beautiful problem, and mathematician Partha Ivanishevili said that if the proof is correct it would be a major achievement.
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