On November 6, 2026, Physical Superintelligence (PSI) published a claimed proof of the Aaronson–Ambainis conjecture. The company says its internal research system used a non-public Anthropic model and reached a proof on the third day of the run. It reports acceptance by Lean and supplies public materials. SIExpo confirmed that those materials are accessible, but has not rerun the formal checks or reproduced the proof.
What kind of result is claimed
The conjecture links properties of bounded polynomials to when quantum algorithms can have a large advantage in queries to an input. The claimed consequence concerns most Boolean inputs under specified conditions. It does not mean quantum computers have no useful applications or that all tasks can now be performed equally quickly on classical hardware.
The public repository describes four final theorems, recorded checks and a trust boundary. It explicitly separates a stronger variant requiring an additional hypothesis not formalized there. The authors say that matching the formal statement to the original conjecture requires human reading. David Turturean reviewed the paper and takes responsibility for its correctness. These are project declarations and artifacts, not independent certification by SIExpo.
Editorial assessment: three different checks
A written mathematical argument, a formalized statement and the machinery checking its steps are different objects. Strong evidence about the second and third does not automatically establish that the formalized problem is exactly the intended one. A missing condition or changed definition, for example, could alter what was proved even if subsequent steps were internally consistent.
Accessible code and the non-public model are also separate aspects of reproducibility. Other specialists may be able to check a published result without repeating the process that discovered it. Such an artifact does not automatically show that the same system can solve arbitrary open mathematical questions, or that another team can reproduce its discovery timeline.
A careful next review would compare definitions with the original problem, inspect assumptions attached to each final theorem and repeat the documented checks against fixed file versions. The mathematical exposition should then be understandable to specialists outside the project. These are our criteria for evaluating a public AI-assisted research result, not an audit already performed by the newsroom.
The announcement matters because it supplies a specific result that can be examined. Responsible coverage preserves the strength of the claim, the accessible artifacts and the limits of our own verification together. This is not a demonstration of faster quantum hardware and does not measure a universal capability of the unreleased model.
Editorial verification: 2026-11-09T07:12:30.497786+00:00.
