Physical Superintelligence says its AI system, running a non-public Anthropic model, proved the Aaronson-Ambainis quantum conjecture, with the proof accepted by Lean

Physical Superintelligence (PSI), an AI science startup, says its research system, running a non-public Anthropic model, found a proof of the Aaronson-Ambainis conjecture, a quantum computing question open since 2008. The company says the proof was complete by day three of the run and was accepted by the Lean proof assistant. It also says the system then improved the result twice on related open problems, with Lean accepting the final version. We only have the claim as relayed by the Import AI newsletter, which links to PSI's own blog. The extraction found no primary links, and the proof has not been confirmed by an outside mathematician.

If the proof holds, it would be a notable example of an AI system settling a named open problem in theoretical computer science. Lean acceptance is a strong check on whether the proof is logically valid, so this is not a vague claim. The people most affected are mathematicians and theoretical computer scientists, plus AI labs competing on research capability. There is no product or deployment here, so the near-term practical impact is limited. The bigger open questions are how much human steering went into the run and whether the result can be repeated.

The "taste of the singularity" line and the claim that this settles "one of the most fundamental questions in quantum computing" are framing from the newsletter author and the startup, not findings. A Lean-checked proof shows the argument is valid for the statement as formalised. It does not show the formal statement matches the conjecture as the field understands it, and it says nothing about how autonomous the process was. The Meta tactile glove paper and the 2016 NASA paper in the same issue are unrelated to this event.

1. 01Comments from Scott Aaronson, Andris Ambainis or other quantum complexity researchers on whether the Lean formalisation matches the actual conjecture.
2. 02Release of the Lean files and a written paper (for example on arXiv) so others can check the proof and see how much human guidance was involved.
3. 03Whether PSI or others reproduce the approach on other open problems within the next few months, and whether Anthropic comments on the non-public model involved.