PSI's Lean 4 Proof of the Aaronson–Ambainis Conjecture, 6 November 2026: What Lean Checked, What Stanford Is Still Reading, and Why RSA Timelines Hold

What PSI announced on 6 November 2026

Physical Superintelligence (PSI) says a research system it built in-house, running instances of a non-public Anthropic model, found a complete proof of the Aaronson–Ambainis conjecture on the third day of a run, and that the Lean 4 proof assistant accepted it. The conjecture, open since 2008, says every bounded low-degree polynomial on the Boolean cube has an influential variable. Aaronson and Ambainis showed that if it holds, any quantum algorithm making T queries can be approximately imitated on most random inputs by a classical algorithm whose number of queries is polynomial in T. The proof, paper and Lean files are public on GitHub, and four Stanford researchers who proved a special case in August are now reading it.

What the proof assistant checked, and what a person still has to confirm

The repository reports a clean Lean 4 formalization: no placeholders, no added axioms, and replays through two independent kernels plus a third type checker. It also says plainly that confirming the formal statement says what the conjecture says "is for a reader to confirm," and that the paper itself is not machine-checked. For post-quantum cryptography, the result changes nothing in the migration schedules: Shor's algorithm exploits structure, and the theorem concerns inputs that have none.