{"rewrite":{"id":"r_8ce6ad1ed46c9d59ac2ff7cd","clusterId":"c_d9d2363d82b206aa7bb53b64","slug":"psi-proves-aaronson-ambainis-conjecture-with-anthropic-ai-model","model":"deepseek-v4-1-flash","headline":"PSI Proves Aaronson-Ambainis Conjecture With Anthropic AI Model","summary":"Physical Superintelligence said on November 6, 2026 that its AI research system, built around a private Anthropic model, produced a complete proof of the Aaronson-Ambainis conjecture, open since Scott Aaronson and Andris Ambainis proposed it in 2008. The startup says the system found the proof on its third day of running, then refined it twice. PSI checked the result in Lean 4 and published the paper and Lean source code on GitHub.","whyItMatters":"The claim matters less for the conjecture itself than for the verification trail: a Lean 4 formalization with no unfinished parts or added axioms, checked by two independent programs and published as source code, is the standard an AI proof now has to clear in public.","webCardHtml":"\u003cp\u003ePSI researchers set the problem themselves and ran the system in their own computing environment, per the company. The system found a complete proof on the third day of running, then refined it twice while the team worked on related mathematical problems, and produced a final version.\u003c/p\u003e\u003cp\u003eLean 4 was used because plausible-looking AI proofs can contain errors in the logic even when the conclusion reads correctly. PSI says the Lean proof was completed without unfinished parts or added axioms and was confirmed by two independent verification programs. Quantum computing researcher Henry Yuen described the result as the resolution of a beautiful problem, and mathematician Partha Ivanishevili said that if the proof is correct it would be a major achievement.\u003c/p\u003e","blueskyPost":"PSI's Lean 4 check is the part worth reading: it verifies the proof, not the model that found it. The claim rests on a formal artifact anyone can inspect, not on Anthropic's private system.","twitterPost":"PSI published the Lean source. That check verifies the proof, not the private Anthropic model that found it.","threadsPost":"PSI's claim about the Aaronson-Ambainis conjecture leans on Lean 4, not the AI. The published source code lets anyone check the proof is valid. It cannot confirm a private Anthropic model reached it in three days.","newsletterBlurb":"Physical Superintelligence announced on November 6 that its AI research system, built around a private Anthropic model, produced a proof of the Aaronson-Ambainis conjecture, open since 2008. PSI says the system found the proof on its third day and refined it twice. The proof was formalized in Lean 4 with no unfinished parts or added axioms, and the source code is public on GitHub.","attributionJson":"[{\"source\":\"GIGAZINE\",\"url\":\"https://gigazine.net/news/20261109-anthropic-psi-aaronson-ambainis/\",\"title\":\"18-year-old unsolved quantum computing problem proven using Anthropic's private AI model\"}]","lintFlagsJson":null,"lintHits":0,"costUsd":0,"inputTokens":5451,"outputTokens":763,"status":"published","repairAttempts":0,"nextRepairAt":null,"factsAttemptedAt":1794203382,"createdAt":"2026-11-09T05:44:30.000Z","publishedAt":"2026-11-09T05:47:28.000Z","updatedAt":"2026-11-09T05:47:28.000Z"},"cluster":{"id":"c_d9d2363d82b206aa7bb53b64","canonicalTitle":"Anthropicの非公開AIモデルを使って18年間未解決だった量子コンピューターの難問が証明される","representativeArticleId":"a_7cf963343446b2e64dc42dac","sourceCount":1,"writtenSourceCount":1,"writeAttempts":0,"isSolo":true,"entitiesJson":"{\"anime_titles\":[],\"manga_titles\":[],\"work_titles\":[],\"studios\":[],\"people\":[],\"type\":\"news\",\"domain\":\"other\",\"is_roundup\":false}","contentType":"news","status":"published","firstSeenAt":"2026-11-09T05:10:00.000Z","lastSeenAt":"2026-11-09T05:10:00.000Z","updatedAt":"2026-11-09T05:47:26.000Z"},"attribution":[{"source":"GIGAZINE","url":"https://gigazine.net/news/20261109-anthropic-psi-aaronson-ambainis/","title":"Anthropicの非公開AIモデルを使って18年間未解決だった量子コンピューターの難問が証明される"}],"entities":{"anime_titles":[],"manga_titles":[],"work_titles":[],"studios":[],"people":[],"type":"news","domain":"other","is_roundup":false},"keyFacts":["Physical Superintelligence announced on November 6, 2026 that it had proven the Aaronson-Ambainis conjecture, open since 2008.","The PSI research system incorporates a private AI model developed by Anthropic.","PSI says the system discovered a complete proof on the third day after it began running, then refined it twice.","The proof was formalized in Lean 4 without unfinished parts or added axioms and confirmed by two independent verification programs.","The paper, Lean source code, and verification records are published on GitHub."],"pageLinks":{"healthSlugs":[],"storySlugs":[],"entities":[],"stories":[],"entitiesOk":true,"storiesOk":true}}