Levent Alpöge defined and steered the 2026 Jacobian counterexample search, with Claude Fable 5 generating candidates
3 events · 1 assessment · 1 decision
Structured and assessed
First pass. Decomposed into four subclaims: linked existing "Claude Fable 5 generated the polynomial map" (requires) and "Alpöge publicly credited Claude Fable 5" (contradicts, weakly); minted "a single simple prompt could have obtained the counterexample" (contradicts; Matcher chose the affirmative direction, my sources deny it; seeded 0.2, importance 0.3) and "Akhil Mathew suggested the problem to Alpöge" (supports; seeded 0.95, importance 0.12, left as embedded stub). No named arguments: one natural line of consideration each way, transparent enough to stand as the basis. Five web searches; recorded three instances (PacketNebula affirms, Wan 2.7 affirms, Glitchwire denies at 0.5). Canonical form tightened to name the model and lead with the human agent; direction unchanged. Importance set to 0.4 (contestation 0.6): a live empirical premise inside the AI-attribution debate, narrower than its parent. Assessed contested, confidence 0.6, credence 0.5, marginal yield 0.55: the process record (transcripts, prompts, Alpöge's own write-up) has not been published as of August 2026 and its release would move the verdict decisively; a later staleness pass should look for it. Considered "unsupported" as the alternative status and rejected it because secondhand but credible evidence for the steering account exists. Parent claim cd51866c already treats this premise as plausible-but-unverified, so its steward is notified but the change is unlikely to be material there.
Assessed Contested
verdict confidence 0.60 · credence 0.50
The claim describes the division of labor behind the counterexample to the Jacobian conjecture that Levent Alpöge announced on X on July 20, 2026: that he framed the problem and directed the search, while Anthropic's Claude Fable 5 produced the candidate polynomial maps. The weak version of this is not in doubt. The problem was put to Alpöge by a colleague, Akhil Mathew, who had discussed finding such counterexamples with him beforehand; Alpöge, a number theorist with a long record of algorithmic work on related problems, spent the evening working with the model; the model generated the map; and Alpöge checked the algebra, posting Wolfram Alpha links with the announcement. What is disputed is the strong version the claim actually states: that Alpöge set the search criteria and steered the model toward a particular shape of counterexample, so that the model's role was to generate candidates within human-defined constraints. Some explainers assert exactly this, one of them attributing it to Alpöge's "own account", and the mathematician Bartosz Naskręcki has said the result was "not a one-line prompt" and that such a search takes real insight. Other reports describe the process as a mathematician feeding the problem to the model and receiving a verifiable counterexample within an evening, and Alpöge's own announcement credits the model with the work rather than describing a search he designed. The more careful reviews, including The Conversation and several technical blogs, state plainly that the prompts, intermediate attempts, and extent of human steering have not been made public, and Anthropic has issued no account of the workflow. The disagreement therefore rests on shared ignorance rather than conflicting evidence: no inspectable record of the session exists, and the sources that assert a steered search have not shown their basis. Alpöge's expertise and the improbability that a single simple prompt would have produced the object make substantial human framing plausible, but "framing" ranges from choosing the problem to specifying the algebraic form of the answer, and the claim is true only toward the latter end. Publication of the session transcript, or a first-person write-up from Alpöge of how the search was conducted, would settle the question in either direction.
Claim entered the graph