Physical Superintelligence says AI proved the Aaronson-Ambainis conjecture
Company research page and public Lean 4 repo: an internal system using a non-public Anthropic model found a proof open since 2008; Lean accepted it on day three; peer review still pending.
Why it matters
The Aaronson-Ambainis conjecture asks when quantum algorithms can beat classical ones by an exponential margin on unstructured inputs. PSI says its research system produced a Lean-checked proof on day three of a run, then improved it twice. The formalization is public with no placeholders, but the company notes readers must still confirm the Lean statement matches the printed conjecture, and independent peer review has not finished. Stanford researchers who proved a special case in August are quoted on PSI’s page praising the result. Watch for assessments from Aaronson, Ambainis and outside formal-methods groups.
Key facts
- Open since 2008 (Aaronson–Ambainis)
- Lean accepted proof on day three of run
- Non-public Anthropic model used (claimed)
- Public paper + Lean 4 repo
- Peer review still pending