AI proof of the Aaronson-Ambainis conjecture

Physical Superintelligence announced on November 6, 2026 that an internal research system running a non-public Anthropic model found a complete proof of the Aaronson-Ambainis conjecture, an open problem in quantum complexity theory since 2008. The conjecture states that every bounded low-degree polynomial has a highly influential variable; proving it implies every T-query quantum algorithm can be classically simulated on most inputs by a classical algorithm making polynomially many queries. The Lean proof assistant confirmed every step. After completing the initial proof during its third day of operation, the system continued on related open problems and improved the result twice. David Turturean, a PSI staff member, is listed as the paper's author and is responsible for correctness. A prior claimed proof by Nathan Keller and Ohad Klein in 2019 was later found to contain an error. In August 2026, four Stanford researchers, Blanc, Docter, Strassle, and Tan, submitted a paper settling a partial case, showing no exponential quantum speedup for algorithms querying input in a fixed number of parallel rounds. Those four researchers have reviewed PSI's full proof and are preparing an exposition for domain experts. The specific Anthropic model used has not been named publicly by PSI or Anthropic.