An undisclosed Anthropic model, three days, and a complete proof of a 2008 conjecture

On November 6 the research organization Physical Superintelligence (PSI) announced on its research page that its AI research system had produced a complete proof of an open problem from 2008 — the Aaronson–Ambainis conjecture — with the Lean proof assistant accepting the system's formalization. The companion repository went up the same day (our November 8 API check: created 2026-11-06T03:19Z, a single push, Apache-2.0, paper PDF inside). The announcement also names what ran: “Instances of a non-public Anthropic model were used in the run” — an undisclosed Anthropic model, with no name, version or size. Anthropic itself has published no confirmation.

The timeline is concrete in the announcement: on the third day of the run the system “had a complete proof,” followed by two more improvements, with Lean accepting the final version. The roles are spelled out too: David Turturean led the work and answers for the proof's correctness; Jim Halverson audited the proof; Phiala Shanahan commented on the Lean formalization. On November 7, Business Insider's report and IT Home's retelling carried “an undisclosed Anthropic model” to a wider audience — and the retelling's line that “which model PSI used is still unknown” is exactly the footnote this story deserves.

This is not Anthropic models' first touch of Lean mathematics. Our September 9 article recorded Anthropic formalizing Fermat's Last Theorem — a theorem with a human proof — into Lean in about 11 days, using an internal research model around Fable 5.1 plus multiple agents. The difference between September and November is worth keeping: September moved an existing proof into a checker; November, if expert validation holds, is a new proof of an open problem. The difficulty and the verification burden differ, and this site verified no proof and ran no model — the two kinds of information are kept separate.

• Read PSI's announcement ↗
• Compare: our Fermat formalization article →

Posed in 2008, the Aaronson–Ambainis conjecture is an influence lower bound for low-degree polynomials: for a bounded degree-d polynomial f with values in [0,1] and variance v, some variable's influence must be at least a fixed power of v/d. PSI's announcement puts constants to it: Infi(f) ≥ c·v^(5/2)/d⁶ ≥ (v/d)⁷, where c = 815/(125π⁴) ≈ 0.0025 (the announcement's own statement). Why it matters: the 2011 Aaronson–Ambainis paper “The Need for Structure in Quantum Speedups” reduced a chain of questions about when quantum computing truly speeds things up to this conjecture — if it holds, quantum computers gain at most polynomial speedups on random inputs with no promised structure, and exponential speedups like Shor's need structure in the problem itself.

The conjecture is not untouched ground. Aaronson's 2019 retrospective records a decade of attacks: O'Donnell, Kindler, even Terence Tao. In November 2019, Nathan Keller and Ohad Klein posted a preprint claiming a proof; Aaronson initially called it “great.” The two authors then retracted it — a then-apparently-fatal flaw in Lemma 5.3, found by Paata Ivanishvili. The retraction explains this field's default posture toward any new claim: ask first where the formalization lives and who can re-verify it, then talk conclusions.

The step closest to this announcement came in August 2026: Stanford's Blanc, Docter, Strassle and Tan proved a special case of the conjecture. PSI's announcement states that this group is reading the full proof and writing a shorter expert exposition — in progress, unpublished. In other words, the researchers closest to this problem have not yet given their reading, and that is the single most worth-waiting-for signal in weighing this announcement.

• Read Aaronson's history of the conjecture ↗

The credibility of this announcement does not live in the sentence “AI proved a hard problem in three days”; it lives in what each layer of the verification chain checks. Machine layer: the Lean proof assistant checks step by step under formal rules, and Lean's acceptance means every step derives from the axioms with no gaps — a layer done by machine, re-verifiable by anyone against the public repo, where the cost of verification drops from “read hundreds of pages” to “run the checker.” Human layer: Turturean answers for correctness, Halverson audited, Shanahan reviewed the formalization — a layer checking what the machine layer cannot: whether the proof's direction is meaningful and whether the formal statement matches the original conjecture.

A key detail from the Fermat formalization applies here too: Lean guarantees only internal consistency of the formalization, and whether the formal statement matches the original problem needs its own check — axiom checks and Mathlib statement comparison carry part of that. The same holds now: Lean's acceptance is not an endpoint, and PSI's page claims no independent peer review has happened; the auditors it names are all PSI's own employees. The other gap is the model: with name, version and size undisclosed, the split between AI and human contribution cannot be independently assessed — how much of “a proof in three days” is model capability versus harness and human design is currently unreadable.

One more boundary deserves its own paragraph: this site verified no proof, ran no Lean and read no repository line by line — every fact here rests on the announcement page, repository metadata and Aaronson's retrospective. Readers likewise need not understand the proof themselves to follow along: wait for two signals — the Stanford group's expert exposition, and word from Aaronson and Ambainis themselves. Until those arrive, the correct reading of “Lean accepted” is “the formalization is internally consistent and publicly checkable,” not “mathematics has confirmed it.”

• See the public Lean repository ↗
• What formalization checks: our earlier piece →

Keep the capability story and the verification story apart — that is the right posture. Capability story: an undisclosed frontier model, inside a research harness, reached a complete proof of an open problem in three days. Verification story: Lean's machine acceptance plus PSI's internal audit plus the Stanford group's in-progress reading, with independent review not yet happening. Both stories are true today, but only the first travels well; the second decides where this eventually sits in the history of mathematics — the 2019 proof once called “great” ended in retraction, proof that the second story can overturn the first.

In the larger picture, this is the third shape of the “AI solving open problems” line. Tencent's Hyra 1.0 used open models plus self-built tools on an additive-combinatorics open problem (recorded in our Hy4 article); the Fermat formalization was “existing human proof + AI formalization”; PSI's run is “open problem + new AI proof + Lean as the closer.” Verification requirements rise across the three, and PSI's chain is the most complete public record of the three — the machine-checkable layer is done, while the human layer still lacks independent review. Our October 31 piece “Aligned to whom?” covered AI's pull on expert judgment; this announcement moves “models as research participants” one notch further, and how the human layer of the verification chain gets filled is what to watch in the coming months.

Three actionable readings: first, to check, the Lean repo is public (Apache-2.0) — machine-checkable does not mean everyone understands it, but “has anyone re-verified this” now has a definite place to look; second, to follow, wait for the Stanford group's exposition and the two namers' verdicts — either is worth rereading this article for; third, to parse such announcements, remember this one's structure — undisclosed model, internal audit, machine layer closed: capability ceiling and verification progress are two independent lines, and neither should speak for the other.

• Compare: Aligned to whom? (AI's pull on expert judgment) →
• Compare: Hyra 1.0 and open problems (our Hy4 article) →