The short version
● What — the Aaronson-Ambainis conjecture, open since 2008
● Who — PSI, using non-public Anthropic model instances
● How long — a complete proof by day three of the run
● Checked by — Lean, plus an internal audit. No peer review yet.
PSI published a proof of the Aaronson-Ambainis conjecture on 6 November. Scott Aaronson and Andris Ambainis proposed it in 2008, and it asks whether quantum computers can be exponentially faster than ordinary ones on random inputs. They had shown that if the conjecture holds, quantum computers are at most polynomially faster on random inputs, which is why it sits near the centre of how quantum speedups are understood.
The work was done by an internal research system running non-public Anthropic model instances on PSI infrastructure. By PSI's account the system produced a complete proof on the third day of the run, and the Lean proof assistant accepted it. The system then moved on to related open problems, improved the result twice, and Lean accepted the final version. The stated bound is that a bounded polynomial of degree d with a nonconstant value has some bit with influence at least c times v to the power 5/2 over d to the sixth, with c around 0.0025. It builds on earlier work by Lovett and Zhang and by Reimer, replacing a conjectured inequality in the Lovett-Zhang plan with a new one proved in the manuscript.
The human roles are named and worth noting. David Turturean developed the system, scoped the problem, ran it, prompted the model to draft the paper, reviewed the draft, and is stated as responsible for its correctness. Jim Halverson audited the proof and Phiala Shanahan commented on the Lean formalisation; both are PSI advisors, so the audit is internal. There is no peer review or journal publication, and the verification rests on the Lean formalisation plus that internal audit. Separately, in August 2026 Blanc, Docter, Strassle and Tan at Stanford proved the conjecture's prediction for a special case; they have since read the full proof and sent comments, which is informal correspondence rather than review.
More from 7 November
Full dated index: every AI release in November 2026.
Sources