An Unreleased Anthropic Model Proved a 2008 Quantum Computing Conjecture in Three Days

A research system at the startup Physical Superintelligence (PSI), running instances of a non-public Anthropic model, has produced a proof of the Aaronson-Ambainis conjecture — a question about the limits of quantum speedups that had been open since 2008. The system had a complete proof on the third day of its run, and the Lean proof assistant accepted it. The open question now is how fast humans can check and understand it. PSI announced the result on November 6, 2026. The conjecture, posed by Scott Aaronson and Andris Ambainis, is a statement about bounded low-degree polynomials: it says some input bit must have meaningful influence on the polynomial's value. Aaronson and Ambainis showed that if it holds, quantum computers can be at most polynomially — not exponentially — faster than ordinary computers at answering yes-or-no questions about random inputs that lack special structure. PSI's proof follows a plan by Shachar Lovett and Jiapeng Zhang, replacing the one inequality they had left as a conjecture with a new inequality proved via a determinant-based pairing that strengthens David Reimer's Butterfly Lemma. After the first proof, PSI set the system on related problems and it improved the result twice; Lean accepted the final version. The paper and a Lean 4 formalization are public. The repository says the main theorems have no placeholders or added axioms and were re-checked by two independent implementations of the Lean kernel, and that the proof, paper and formalization were produced by AI models. Machine checks have limits: a human still has to confirm the formal statement matches the printed conjecture, and the human-readable paper is not itself machine-checked. Stanford researchers Guy Blanc, Jordan Docter, Carmen Strassle and Li-Yang Tan, who settled a special case in August, called it "a huge result" and are writing a shorter exposition for experts. PSI's David Turturean, who built the system, reviewed the draft and is responsible for the paper's correctness. Business Insider reports it is not clear which unreleased Anthropic model PSI used, and Anthropic did not respond to a request for comment. Visit ainewspaper.org for today’s stories and free email alerts.