PSI claims AI system produced a Lean-verified proof of the Aaronson-Ambainis conjecture
inductionheads · x · 2026-11-06
Physical Superintelligence (PSI) announces its internal research system, using instances of a non-public Anthropic model, found a complete proof of the Aaronson-Ambainis conjecture — open since 2008 and central to quantum complexity theory.
- The conjecture implies quantum computers gain at most polynomial speedups on unstructured random inputs, unlike structured cases such as Shor's algorithm
- The system produced a full proof on day three of a run on PSI's own infrastructure; the Lean proof assistant verified every step
- The system then improved the result twice, with Lean accepting the final version, and was set on related open problems
- The proof builds on work by Shachar Lovett, Jiapeng Zhang, David Reimer and others
- If it holds up, this is a landmark case of AI settling a foundational open problem in machine-checkable form; details remain to be independently confirmed
Related event: PSI Says AI System Proves Long-Open Aaronson-Ambainis Conjecture(3 posts)→
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