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PSI says its AI research system proved a quantum conjecture open since 2008
On November 6, 2026, PSI said its research system, using a non public Anthropic model, found a proof of the Aaronson–Ambainis conjecture by its third day; Lean accepted the formalization. The conjecture concerns how many input bits quantum algorithms need to read on most random inputs—not a blanket limit on quantum...
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Key takeaways
- On November 6, 2026, PSI said its research system, using a non public Anthropic model, found a proof of the Aaronson–Ambainis conjecture by its third day; Lean accepted the formalization.
- The conjecture concerns how many input bits quantum algorithms need to read on most random inputs—not a blanket limit on quantum computing’s practical advantages.
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openai.comCreate a landscape editorial hero image for this Studio Global article: What did physics-focused AI startup Physical Superintelligence (PSI) announce on November 6 about its research system using an undisclosed,. Article summary: On November 6, 2026, Physical Superintelligence (PSI) announced that its internal research system, using a non-public Anthropic model, had found a proof of the Aaronson–Ambainis conjecture, open since 2008, and released . Topic tags: general, general web, user generated. Style: premium digital editorial illustration, source-backed research mood, clean composition, high detail, modern web publication hero. Use reference image context only for broad subject, composition, and topical grounding; do not copy the exact image. Avoid: logos, brand marks, copyrighted characters, real person likenesses, fake screenshots, UI text, readable text, watermarks, charts with fak
Physical Superintelligence (PSI) announced on November 6, 2026, that an internal research system using a non-public Anthropic model had found a proof of the Aaronson–Ambainis conjecture, an open problem dating to 2008. PSI released a paper and Lean 4 formalization; the company says Lean accepted the proof. The result has not yet been peer-reviewed by a journal. 6
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What PSI says the system did
PSI reports that the system produced a complete proof during its third day of operation on the company’s infrastructure. It then worked on related problems and improved the result twice, according to reports of the announcement. The available accounts do not specify the successive bounds or provide enough detail to reconstruct the system’s reasoning step by step. 5
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David Turturean, a member of PSI’s technical staff, led the work and developed the research system. Reporting says he scoped the problem, directed the system to prepare a draft, reviewed it, and is named as responsible for the paper’s correctness. 1
7 PSI adviser Jim Halverson reportedly audited the proof, while adviser Phiala Shanahan discussed the role of its Lean formalization.
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The model itself remains unnamed. PSI’s announcement identifies it only as a non-public Anthropic model; the available sources do not establish how Anthropic was involved or whether the company has independently endorsed the result. 6
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What the conjecture says
In the formulation posted with the proof, a real polynomial of degree at most d, bounded between zero and one on the Boolean cube, must have a variable with meaningful influence if the polynomial has variance of at least ε. PSI’s repository gives a lower bound of at least (ε/d)^7 for that influence, alongside a stronger stated bound. 41
In plain language, the result rules out a bounded, low-degree polynomial that varies substantially while depending only imperceptibly on every individual input variable. The conjecture’s quantum-computing significance is about query complexity: how many times an algorithm needs to access its input. The reported consequence is that, for yes-or-no computations on most uniformly random inputs, a classical algorithm can approximate a quantum algorithm’s acceptance probability without needing exponentially more input accesses. 4
That is not the same as saying classical computers can always simulate quantum computers efficiently in total running time. A bound on input queries does not, by itself, settle how much computation an algorithm performs between queries. Nor does the result amount to a blanket claim that quantum computers offer no useful advantages. 4
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What Lean acceptance establishes—and what it doesn’t
PSI has published a mathematical paper and a Lean 4 formalization of the proof. Lean is a proof assistant: it checks whether a formal argument follows from the definitions and assumptions encoded in the formalization. The repository also records checks associated with preparing the release. 10
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That is meaningful evidence that the formalized proof is internally valid, but it does not eliminate the need to examine whether the formal statement faithfully captures the original conjecture. Formal verification, expert interpretation of the mathematics, and journal peer review address related but distinct questions. The result is therefore best described as a substantial proof claim backed by a public formalization—not as a claim that every aspect has already received independent scholarly review. 15
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The public summaries establish the claimed timeline, published formalization, and Lean acceptance, but do not give enough detail to verify a specific account of how the proof extends earlier work or uses a determinant-based pairing of input settings. That technical route should not be inferred from the announcement alone.
What remains open
The proof announcement does not settle what the model was, how much Anthropic contributed, or whether outside researchers have completed a detailed audit. The central near-term test is whether independent mathematicians and computer scientists can scrutinize both the formal proof and its correspondence to the conjecture as originally stated. 6
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For now, the careful takeaway is two-part: PSI has made a notable claim and released a machine-checkable formalization, while independent evaluation remains important before treating the result as fully settled.
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On November 6, 2026, PSI said its research system, using a non public Anthropic model, found a proof of the Aaronson–Ambainis conjecture by its third day; Lean accepted the formalization.
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On November 6, 2026, PSI said its research system, using a non public Anthropic model, found a proof of the Aaronson–Ambainis conjecture by its third day; Lean accepted the formalization. The conjecture concerns how many input bits quantum algorithms need to read on most random inputs—not a blanket limit on quantum computing’s practical advantages.