The headline: a frontier model enters theoretical computer science
Physical Superintelligence, or PSI, says its internal research system has found a proof of the Aaronson–Ambainis conjecture, a quantum-computing problem open since 2008, while running instances of a non-public Anthropic model . PSI’s account is unusually specific: the system produced a complete proof during the third day of the run, Lean accepted the proof, and the system later improved the result twice before Lean accepted the final version . Business Insider reported the claim on November 7, noting that the particular Anthropic model was not identified and that Anthropic did not respond to a request for comment .
That combination is why this story matters beyond quantum computing. The claim is not just that an AI model drafted text, wrote support code, or suggested lemmas. PSI says the mathematical statements, the first draft of the paper, and the Lean formalization were produced by AI models inside a research harness developed by PSI’s David Turturean, who reviewed the paper and took responsibility for its correctness . If the result survives expert scrutiny, it will stand as a case study in frontier AI acting as a collaborator in formal research rather than merely as a productivity layer.
What was the conjecture about?
The Aaronson–Ambainis conjecture asks, in effect, when quantum computers can be exponentially faster than ordinary computers. PSI frames the issue through the contrast between structured and unstructured inputs: Shor’s famous factoring algorithm exploits hidden structure, while the open question was whether quantum computers could also gain exponential speedups on random inputs that lack such patterns . PSI’s explanation says Aaronson and Ambainis translated that question into a statement about bounded low-degree polynomials: if the conjecture were true, ordinary computers could simulate certain quantum algorithms on most inputs with only polynomial overhead rather than exponential overhead .
The proof, as summarized in the public repository, establishes that a bounded low-degree polynomial on the discrete cube must have at least one influential variable when its variance is large enough . More formally, for a real polynomial of degree at most d, valued between 0 and 1 on Boolean inputs, variance at least ε implies that some input coordinate has influence at least a fixed expression proportional to ε^(5/2)/d^6, and in particular at least (ε/d)^7 . That is the mathematical bridge back to quantum query algorithms: if a quantum algorithm’s acceptance probability can be represented by such a polynomial, then the proof constrains how much advantage it can obtain on unstructured inputs .
Why “three days” is the industry signal
The speed is startling, but the stronger signal is workflow. PSI says the system had the proof by day three, then kept working on related open problems and improved the result twice . That makes the episode look less like a chatbot answering a hard question and more like a semi-autonomous research loop: identify a formal target, search for a proof, generate statements, formalize them, and push the result through a proof checker.
The repository describes a concrete verification stack rather than a vague “AI solved math” claim. It contains a paper and a Lean 4 formalization, with public declarations for the main theorems, including aaronson_ambainis and explicit-bound variants . It also provides build and replay instructions, including make check, make replay, and make replay-fresh, alongside a trust-boundary section explaining what the checks do and do not establish . For an AI-research industry hungry for credible demonstrations of reasoning, this is the important part: the output is not just a narrative; it is an artifact other researchers can inspect.
Three days is practically a speedrun by theoretical-computer-science standards. But the speed only counts if the target is the right target, the formalization matches the printed conjecture, and independent experts agree that the Lean theorem is the intended mathematical statement.
What Lean verifies, and what it does not
Lean acceptance is a powerful check, but it is not magic. The repository says the Lean development is complete for four theorems, with no placeholders and no added axioms, and that the results were rechecked by two independent implementations of the Lean kernel . It also states that the sources contain no sorry, no new axiom, and no bypasses such as unsafe or extern declarations in the library being checked . A separate comparator setup replayed final theorem proofs through additional checking machinery, according to the repository’s trust-boundary notes .
The limitations are equally important. The repository explicitly says that readers must still confirm that the formal definition called PrintedConjecture matches the Aaronson–Ambainis conjecture as printed, and that the human-readable paper itself is not machine-checked . Unite.AI’s report made the same point: formal proof checking narrows the trust problem, but it does not remove the need for domain experts to verify that the encoded statement is the right one and that the informal exposition accurately reflects the formal artifact .
That is the sensible way to read the claim today. The Lean artifact, if reproducible, is a major credibility upgrade over a plain preprint. It is not the same thing as broad peer review.
Human researchers are still in the loop
PSI attributes the system to David Turturean, a member of its technical staff, who developed the research harness, scoped the problem, prompted the model to prepare an initial draft, reviewed the paper, and accepted responsibility for correctness . Business Insider also identified Turturean as the person who developed the system using the unreleased Anthropic model . AREX reported that the repository’s disclosure says the mathematical statements, paper draft, and Lean formalization were produced by AI models inside Turturean’s harness, with Turturean reviewing the paper .
There is also early expert engagement, though not yet the same as full independent validation. PSI says Guy Blanc, Jordan Docter, Carmen Strassle, and Li-Yang Tan of Stanford, who had proved a special case in August 2026, have been reading the proof, sending comments, and preparing a shorter exposition for experts . PSI quotes them calling the result “a huge result” and saying that the proof brings together lines of work in Boolean function analysis and probabilistic combinatorics in a “magical” way . Business Insider also reported that researchers who had worked on the problem characterized the proof as a major result .
That reaction matters because this is a specialized corner of quantum complexity theory. A proof can pass a formal checker and still need community interpretation: Does it resolve exactly the conjecture experts care about? Does the constant or exponent matter for downstream consequences? Which parts are new, and which are inherited from Lovett, Zhang, Reimer, and earlier work? PSI says the proof builds on those lines of research .
Why quantum computing companies should care
This proof does not make quantum computers obsolete. Quite the opposite: it clarifies where their dramatic advantages are likely to come from. PSI’s summary says the result supports the idea that exponential quantum speedups require special structure in the input . In practical terms, that reinforces a long-running theme in quantum algorithms: the hard part is not simply building qubits, but finding problems whose structure lets quantum machines exploit superposition and interference in a way classical machines cannot efficiently imitate.
For the AI industry, the implication is different. If frontier models can help compress months or years of theoretical work into days, research roadmaps may change. AI systems could become search engines over proof space, generators of formal lemmas, and tireless assistants for converting informal mathematical ideas into machine-checkable artifacts. The PSI case is especially striking because the system reportedly moved across the whole chain: proposition, paper draft, formalization, and verification .
The caution is that this is still a claim centered on PSI’s own announcement and repository, supported by early reporting and partial external reaction. The model is unreleased, the exact architecture is undisclosed, and Anthropic has not publicly confirmed details of the system used . The proof has not yet gone through the slow social process by which theoretical computer science absorbs a major theorem: seminars, alternative expositions, independent reruns, and eventually citations by experts who have rebuilt the argument for themselves.
The bottom line
As of the latest reports, the story is this: PSI says a research system using a non-public Anthropic model proved the 18-year-old Aaronson–Ambainis conjecture in three days; the proof has a public Lean formalization; the repository describes multiple machine-checking safeguards; and outside experts are beginning to review and explain the result . The strongest version of the claim is not “AI replaces mathematicians.” It is that AI may now be capable of participating in the deepest layer of mathematical work: generating candidate proofs that humans can inspect, formal systems can verify, and research communities can challenge.
If that holds, the real breakthrough is not only a new theorem about quantum speedups. It is a new research tempo.
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