{"schema":"sanctity-signal/0.2","record_type":"signal","id":"psi-aaronson-ambainis-e078","domain":"science","drop_id":"signal-e078","occurred_at":"2026-11-06","how_to_use":"This is a structured record of one real-world action and its competing interpretations, from Sanctity Signal. To build content from it (a reel script, a blog, a thread): open on the hook, ground the viewer with plain and observed, walk the dated trail, present the interpretations as live tension between named readings, and close on the before/after shift and what_to_watch. Hard rules: items under established are fact; items under unknown are never presented as fact; the evidence status (verified or reported) is stated, not dropped; sources are cited.","actor":"Physical Superintelligence","action_type":"publication of a claimed proof of the Aaronson-Ambainis conjecture, with a Lean formalization, produced by an internal research system running instances of a non-public Anthropic model","observed":"Physical Superintelligence, which goes by PSI, published A proof of the Aaronson-Ambainis conjecture at psi.inc on November 6, 2026, and we read it there. The claim: a research system PSI built internally, running instances of a non-public Anthropic model it does not name, found a proof of the conjecture. It says the system had a complete proof during the third day of the run, was then set to work on related open problems, improved the result twice, and that Lean, a proof assistant in which a computer checks every step, accepted the final version, with a complete formalization in Lean. The conjecture was proposed by Scott Aaronson and Andris Ambainis and the page says it has been open since 2008. It concerns whether quantum computers can be exponentially faster than ordinary computers on random inputs. Aaronson and Ambainis showed that if a statement about certain polynomials is true, quantum computers are at most polynomially faster on random inputs, and the page says the proof establishes that statement, stating a bound on the influence of some bit in terms of the variance and the degree. The page opens by saying the Aaronson-Ambainis conjecture is now a theorem. On who checked it: Lean accepted the proof and its revision; PSI adviser Jim Halverson audited the proof; PSI adviser Phiala Shanahan commented on the Lean formalization; David Turturean, a PSI member of technical staff, led the work and is named responsible for the paper's correctness; and Guy Blanc, Jordan Docter, Carmen Strassle and Li-Yang Tan at Stanford read the proof and sent comments, having proved a special case in August 2026. The page quotes the Stanford comment as calling it a huge result. It does not say they endorse the full proof. The page is PSI's own announcement, so its claims are self-reported. The paper and code are linked on GitHub. Not established: which Anthropic model, whether Anthropic knew or agreed, the length of the run, whether the Lean code has had independent review, and whether mathematicians accept the result.","corrections":[],"evidence":{"status":"verified","note":"Verified as an action: we read the announcement and the claim at psi.inc, which carries the authorship, the Lean formalization claim, the named advisers and the Stanford readers. The page shows November 6, 2026 and no time of day. The mathematics itself is not something we verify; the paper and code are linked on GitHub for anyone who will.","sources":[{"role":"primary","label":"Physical Superintelligence: A proof of the Aaronson-Ambainis conjecture, Nov 6, 2026, read at psi.inc","url":"https://psi.inc/research/aaronson-ambainis/"},{"role":"corrob","label":"Runtimewire: Physical Superintelligence says its AI system proved the Aaronson-Ambainis conjecture, Nov 2026","url":"https://runtimewire.com/article/physical-superintelligence-aaronson-ambainis-proof"},{"role":"corrob","label":"Shiftdelete: Aaronson-Ambainis Conjecture Proved by PSI AI System, Nov 2026","url":"https://shiftdelete.net/en/aaronson-ambainis"},{"role":"corrob","label":"Inshorts: AI system proves 18-year-old Aaronson-Ambainis conjecture, Nov 7, 2026, 03:31 UTC","url":"https://inshorts.com/en/news/ai-system-proves-18-yr-old-aaronson-ambainis-conjecture-in-72-hrs-1794022281041"}]},"strength":{"cost":"Medium","commitment":"High","reversibility":"Low","persistence":"Structural","rationale":"Cost is medium: a multi-day run of a frontier model across many instances is expensive, and the formalization behind a complete Lean proof cannot be shortcut. Commitment is high because PSI put its name on a specific mathematical claim, named the staff member responsible for correctness, and published the paper and the code, which is the opposite of a press release. Reversibility is low in the sense that matters: a published Lean file either checks or it does not. Persistence is structural, because a theorem does not expire and the method outlasts this result."},"shift":{"prior":"AI writes proof sketches, and people spend months deciding whether they hold.","action":"Physical Superintelligence, which goes by PSI, published A proof of the Aaronson-Ambainis conjecture at psi.inc on November 6, 2026, and we read it there. The claim: a research system PSI built internally, running instances of a non-public Anthropic model it does not name, found a proof of the conjecture. It says the system had a complete proof during the third day of the run, was then set to work on related open problems, improved the result twice, and that Lean, a proof assistant in which a computer checks every step, accepted the final version, with a complete formalization in Lean. The conjecture was proposed by Scott Aaronson and Andris Ambainis and the page says it has been open since 2008. It concerns whether quantum computers can be exponentially faster than ordinary computers on random inputs. Aaronson and Ambainis showed that if a statement about certain polynomials is true, quantum computers are at most polynomially faster on random inputs, and the page says the proof establishes that statement, stating a bound on the influence of some bit in terms of the variance and the degree. The page opens by saying the Aaronson-Ambainis conjecture is now a theorem. On who checked it: Lean accepted the proof and its revision; PSI adviser Jim Halverson audited the proof; PSI adviser Phiala Shanahan commented on the Lean formalization; David Turturean, a PSI member of technical staff, led the work and is named responsible for the paper's correctness; and Guy Blanc, Jordan Docter, Carmen Strassle and Li-Yang Tan at Stanford read the proof and sent comments, having proved a special case in August 2026. The page quotes the Stanford comment as calling it a huge result. It does not say they endorse the full proof. The page is PSI's own announcement, so its claims are self-reported. The paper and code are linked on GitHub. Not established: which Anthropic model, whether Anthropic knew or agreed, the length of the run, whether the Lean code has had independent review, and whether mathematicians accept the result.","update":"A machine can produce a proof that another machine verifies line by line."},"inference":{"established":["PSI published a proof of the Aaronson-Ambainis conjecture with a Lean formalization.","PSI says Lean accepted the proof and its final revision.","The system ran instances of an Anthropic model that is not public."],"unknown":["That the mathematics community accepts it. Stanford readers sent comments, not endorsement.","Which Anthropic model. PSI does not name it, and Anthropic has said nothing.","That the Lean code is sound. No independent review is reported."]},"narrative":{"hook":"A startup says its system proved an 18-year-old conjecture, and a computer checked the proof.","plain":"Physical Superintelligence ran instances of a non-public Anthropic model and published the proof with a Lean formalization. Caveat: outside mathematicians have read it and sent comments, not endorsement.","story":["The bottleneck in AI mathematics has been validation: a model produces a candidate and people spend months judging it. Lean removes that step for anything formalizable. PSI says the system had the proof on day 3, then improved the result twice on its own. The referee is now software, and software does not get tired."],"trail":[{"d":"2008","t":"Scott Aaronson and Andris Ambainis propose the conjecture, on PSI's account. It concerns whether quantum computers can be exponentially faster than ordinary ones on random inputs."},{"d":"SEP 8","t":"OpenAI publishes a proof of one of mathematics' 7 great open problems and says a model it has not released wrote it. Edition 016's science card."},{"d":"SEP 11","t":"25 Fields Medal winners sign a single page saying the AI companies racing to solve famous problems are damaging mathematics. Edition 019."},{"d":"AUG 2026","t":"Guy Blanc, Jordan Docter, Carmen Strassle and Li-Yang Tan at Stanford prove a special case of the conjecture. They are among the readers PSI names."},{"d":"NOV 6","t":"PSI publishes the proof and a Lean formalization, says Lean accepted it and its revision, and names 2 advisers and 4 Stanford readers. The model is a non-public Anthropic model it does not name."},{"d":"Reacts","r":true,"t":"Scott Aaronson and Andris Ambainis, whose conjecture it is; the Stanford group that proved the special case 3 months ago; Anthropic, whose unreleased model is credited by a third party rather than by itself; the quantum complexity community, which has to read a machine-written proof; and the journals with no process for a Lean file as the primary artefact."}],"glossary":[{"term":"Lean","def":"Software in which every step of a mathematical argument is written formally and checked by computer. It cannot be persuaded, only satisfied."},{"term":"Conjecture","def":"A statement mathematicians believe but have not proved. Proving one makes it a theorem, which is what PSI claims happened here."},{"term":"Exponential speedup","def":"A quantum computer being unreachably faster, not merely somewhat faster. The conjecture rules that out on random inputs."},{"term":"Formalization","def":"Rewriting a proof in a language a computer can check. Slow, unglamorous work, and it turns a claim into something verifiable."}]},"judgment":{"prompt":"Which explanation do you believe?","interpretations":[{"id":"a","label":"Formal proof broke the validation wall","text":"Lean checks the work, so a model closes a problem without waiting for people.","abstain":false},{"id":"b","label":"One ripe problem fell","text":"A special case was proved in August. The remaining gap was small.","abstain":false},{"id":"c","label":"A new lab needed a result","text":"A named conjecture and a startup's announcement are a convenient pairing.","abstain":false},{"id":"d","label":"The ordinary pace of assisted mathematics","text":"Computers have helped prove theorems for decades. This is the next increment.","abstain":false},{"id":"e","label":"Too early to call.","text":"The evidence cannot yet separate these.","abstain":true}],"distribution":{"status":"held back until you have made your call","calls":null}},"story_thread":null,"what_to_watch":[{"linked_interpretation":"a","direction":"strengthens","observable_event":"A second open conjecture is closed by a machine-produced proof accepted by a proof assistant, from any laboratory, by June 30, 2027.","window_end":"2027-06-30","state":"unresolved"},{"linked_interpretation":"a","direction":"weakens","observable_event":"A named mathematician or the Stanford group publishes an error in the proof or the Lean formalization, or PSI withdraws or materially revises the claim, by March 31, 2027.","window_end":"2027-03-31","state":"unresolved"},{"linked_interpretation":"b","direction":"strengthens","observable_event":"Scott Aaronson, Andris Ambainis or a referee describes the remaining gap after the August special case as small, by March 31, 2027.","window_end":"2027-03-31","state":"unresolved"}]}