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PSI says its research system, running a non-public Anthropic model, proved the Aaronson-Ambainis conjecture; the Lean-checked paper is not yet peer reviewed
PSI says a system with a non-public Anthropic model proved the Aaronson-Ambainis conjecture, checked in Lean. The claim is PSI's; no peer review yet.
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This is PSI's claim, backed by a public paper and a Lean formalization, and it has not been peer reviewed. On November 6, 2026, Physical Superintelligence (PSI) announced that an internal research system running a non-public Anthropic model found a proof of the Aaronson-Ambainis conjecture, a problem in quantum complexity theory open since 2008. PSI says a complete proof existed on the third day of a run and that the Lean proof assistant accepted it. Anthropic has not commented in the sources we found, and the model is not named.
The essentials
- What is claimed: the conjecture, which says every bounded low-degree polynomial has an influential variable, is now a theorem. PSI says its system found the proof and Lean checked it.
- What it implies: reports say quantum query algorithms can be approximated on most random inputs by classical algorithms with polynomially many queries. That does not mean efficient classical simulation in running time.
- How it was checked: PSI published the manuscript and Lean files. Its own advisers audited the proof, and four Stanford researchers say they have read it and are writing a shorter exposition.
- What is missing: no peer review, no public assessment by Aaronson or Ambainis that we found, and no Anthropic statement.
What does the Lean check cover?
Lean verifies each logical step of a formal proof. Unite.AI notes that experts still have to confirm that the formal statement matches the original conjecture and assess the parts of the paper outside Lean. PSI says the system later improved the result twice and that Lean accepted the final version.
What role did the model and the people play?
PSI says David Turturean built and ran the research system, scoped the problem, had the model package a first draft, reviewed it, and is responsible for the paper's correctness. The proof follows a plan by Shachar Lovett and Jiapeng Zhang and replaces one of their conjectured inequalities with a new one. The model is described only as non-public and from Anthropic; the terms of PSI's access are not stated.
What is not established
- Whether the proof is correct for the original conjecture: independent review and peer review are still pending.
- Which Anthropic model was used, and on what terms: PSI does not say; Anthropic has not commented in what we found.
- How much of the discovery was the model's and how much the system's or the people's: PSI's account is the only one.
- Whether Aaronson and Ambainis endorse it: PSI's page does not mention their review.
Summary table
| Point | What is stated as of November 7, 2026 | Source |
|---|---|---|
| Announcement | PSI, November 6, 2026, paper and Lean repository | PSI |
| Claim | Aaronson-Ambainis conjecture proved, open since 2008 | PSI |
| Model | Non-public Anthropic model, unnamed | PSI |
| Verification | Lean accepted; advisers and Stanford readers | PSI, Unite.AI |
| Peer review | None reported | FourWeekMBA |
FAQ
Is the conjecture proved?
PSI says so and its Lean check was accepted, but the paper is not peer reviewed and experts are still reviewing it.
Which Anthropic model was used?
PSI only says a non-public Anthropic model. No name has been given.
Does this break quantum computing advantages?
Reports say it implies that exponential quantum advantages in query count need structure on random inputs; it does not show quantum computers are not useful.
Method and limits
Sources checked on November 7, 2026. We read PSI's announcement page and press coverage but not the full paper or the Lean files, and we could not verify the mathematics. Disclosure: Anthropic makes Claude, which helps draft articles on this site.
Sources
- Physical Superintelligence (PSI): A proof of the Aaronson-Ambainis conjecture (verified 2026-11-07)
- The Quantum Insider: AI-Assisted Proof Settles Longstanding Question About Quantum Speedups (verified 2026-11-07)
- Unite.AI: PSI Reports Machine-Checked Proof of Aaronson-Ambainis Conjecture (verified 2026-11-07)
- FourWeekMBA: PSI Says Anthropic Model Proved 18-Year Quantum Conjecture (verified 2026-11-07)
- Axis of Ordinary: Links for 2026-11-06 (verified 2026-11-07)
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