What happened
PSI’s November 6, 2026 research announcement says the Aaronson–Ambainis conjecture is now a theorem. Scott Aaronson and Andris Ambainis posed the conjecture in a question about quantum computers: when can they achieve an exponential advantage over ordinary computers? The issue is whether such an advantage can occur on random inputs, which generally lack the rare repeating structure used by examples such as Shor’s factoring algorithm. The conjecture concerns bounded low-degree polynomials and the influence of individual input bits.
PSI says it found the proof using a research system developed internally and run on the company’s own infrastructure. Instances of a non-public Anthropic model were used. The system had a complete proof during the third day of the run. PSI says Lean, a proof assistant that checks each step, accepted it. The company then set the system to work on related open problems; along the way, it improved the result twice, and Lean accepted the final version.
The announcement describes the mathematical consequence in terms of query complexity. For yes-or-no questions about random strings, a classical computer can predict a quantum computer’s probability of answering yes, up to a small error, while making a number of queries that grows at most as a fixed power of the quantum computer’s query count. The bound applies for any fixed error and fraction of strings. It rules out an exponential saving in the number of input queries on such random inputs; exponential quantum speedups require special structure. PSI gives a specific influence bound for a nonconstant polynomial of degree d and variance v: some bit has influence at least c v^(5/2)/d^6, and also states this is at least (v/d)^7, with c about 0.0025.
PSI says the proof builds on work by Shachar Lovett and Jiapeng Zhang, David Reimer and others. Its account says Lovett and Zhang’s plan left an inequality conjectural; the new proof replaces it with an inequality established in the manuscript. A determinant-based pairing of input settings is part of that argument. PSI also notes that Stanford researchers Guy Blanc, Jordan Docter, Carmen Strassle and Li-Yang Tan had proved a special case in August 2026. They have since read the full proof, sent comments and are writing a shorter exposition for experts.
David Turturean, a PSI member of technical staff, led the work: he developed the system, scoped the problem, ran it, prompted it to package results into a first paper draft and reviewed that draft. PSI says Turturean is responsible for the paper’s correctness. Advisor Jim Halverson audited the proof, and advisor Phiala Shanahan commented on the Lean formalization. The announcement links to a paper and proofs and code. It does not identify the Anthropic model by name.
What the archive adds
New Runtime’s earlier coverage described a separate machine-checked proof claim whose expert verification remained an open question (earlier note). The current announcement is a new event, not a restatement: PSI reports a Lean-accepted proof of a different conjecture and says Stanford researchers are examining it.
Trend signal
This supports scientific agents need artifact evidence: PSI’s account foregrounds a proof artifact accepted by Lean, rather than a model’s unsupported assertion. The evidence is still incomplete as a measure of autonomous research capability: the announcement also assigns scoping, review and responsibility to a human researcher, and external expert review is ongoing.
Why now
PSI dates the announcement November 6, 2026 and ties it to ongoing expert reading of the proof. The stated timing therefore marks both a claimed result and the start of scrutiny by researchers familiar with the conjecture’s special case.
Connections to other events
New Runtime’s earlier coverage of Anthropic’s research-scaling policy discussed the contested use of estimates of AI-attributable research speedup (earlier note). PSI’s announcement adds a concrete claimed result and a described proof workflow, but it does not quantify research speedup or establish how broadly the approach generalizes.
Why it matters
The useful lesson for AI builders is architectural, not that a model can be treated as a mathematician whose answers need no review. PSI describes a system that searched for a proof, used Lean to check formal steps, and involved people in framing, reviewing and taking responsibility for the work. That is a more inspectable claim than a successful-looking natural-language derivation: a proof assistant can reject invalid steps within its formal system.
The announcement also shows what remains hard to evaluate from a headline result. It does not report the compute budget, model identity, total human labor or comparison with prior approaches. Nor does Lean acceptance by itself settle whether the formalization captures the intended mathematical claim or whether the result will withstand expert scrutiny. Teams building research agents should distinguish generation, formal verification and independent validation as separate stages, and record who is accountable for each. The claim becomes more useful if other researchers can inspect the artifact and reproduce the checks.
Limits and uncertainty
PSI does not name the non-public Anthropic model or disclose the run’s compute cost, infrastructure details, total human time or baseline used to assess the system’s contribution. The announcement says Lean accepted the proof, but external expert review of the full argument is still underway: Stanford researchers have sent comments and are preparing an exposition. The announcement does not establish that the workflow generalizes to other open problems, or independently quantify how much of the proof was produced by the model versus shaped by human direction. Turturean’s stated responsibility for correctness remains central to interpreting the claim.
Reader takeaway
PSI’s claim is significant because it combines a reported mathematical proof with a formal checker and an explicit human owner. The result is not yet the same as independently established, repeatable autonomous research. For builders, watch whether experts validate the argument and whether the proof artifact makes the model-assisted process inspectable.
Open question
Will independent experts validate the full proof, and will PSI publish enough detail about the system and run for others to assess or reproduce its contribution?