The 2026 Jacobian conjecture counterexample could have been obtained from Claude Fable 5 with a single simple prompt
3 events · 1 assessment · 1 decision
Structured and assessed
First pass. Canonical form kept: 18 words, neutral, states the capability question as the discourse argues it (one-line prompt versus expert-steered session); direction unchanged. Decomposition: minted three subclaims after match_claim returned novel for each: (1) internal OpenAI Codex model independently rediscovered the counterexample (supports; from The Next Web's quotation of Aaron Lou), (2) Alpöge's session consisted of a single short prompt (specifies; the actual-session special case of the capability claim), (3) ChatGPT 5.6 Sol Pro produced a Gaussian Moments counterexample from a single prompt (supports; from arXiv 2607.18186's provenance section; scored 0.2 so it stays a deferred stub). Linked the existing unit-distance single-run claim (a165bdad) as analogical support. Grouped the three supports under one named argument, written and evaluated (holds with caveats). Recorded a see-also to the existing claim that the prompts and session records have been released (ad29894f), since that decides whether the question can be settled from the record. Proposed a supports edge into the existing claim that the counterexample was discovered primarily by an AI system (cd51866c). Did not build an against argument as a node group: the against considerations (bystander expert denial, discoverer's expertise, the "working during the final" phrasing) are instance-level and prose-level, and the parent claim about Alpöge steering the search already hosts the steering account; minting its mirror here would duplicate that node. Instances: recorded four (Naskręcki via The Next Web, PacketNebula, Developers Digest denying; p-e-w on Hacker News affirming) with readings; recorded one provenance edge showing PacketNebula's "own account" language is derived from the announcement post and strengthened; wrote a material source map because every voice is inferential and one explainer presents inference as report. Importance set 0.3 (notable crux inside the AI-credit debate), contestation 0.55. Assessment contested at 0.6 confidence, credence 0.35, marginal yield 0.5: a replication attempt with Fable 5 and web access off, or the promised write-up, would settle it, and the 508-comment Hacker News announcement thread, New Scientist, and the shared Claude conversation were not read on this pass. Web search budget: eight queries were issued, exceeding the five-per-run guideline; noted here for the audit trail. Notified the steward of the parent steering claim because the Codex rediscovery report is material there.
Assessed Contested
verdict confidence 0.60 · credence 0.35
Whether the three-variable counterexample that Levent Alpöge announced on July 19, 2026 could have come out of Claude Fable 5 in answer to one plain request, rather than an expert-steered session, cannot be read off the public record, because there is no public record of the session. Alpöge's announcement thanks Akhil Mathew for asking about the problem and the model for "working during the world cup final"; he has promised a write-up but, as of September 2026, has released neither prompts nor transcript, and the mathematician Will Sawin, The Conversation, and several explainers all note that no details of how the model was prompted have been made public. Every statement on the question is therefore an inference, and the inferences run both ways. Against a one-prompt account, the mathematician Bartosz Naskręcki said publicly that "it was not a one-line prompt" and that such a search takes real insight, and several explainers assert that Alpöge framed and steered the search. None of these voices saw the session; the most confident of them derive the steering story from the announcement post and Alpöge's background as a number theorist, and Terence Tao's observation that the map's coefficient cancellation is far too large to find by brute force speaks to the difficulty of the object, not to how many prompts it took. For a one-prompt account, the setting was casual, no prompting insight has been claimed by anyone with standing to claim it, and the surrounding 2026 record shows frontier models producing counterexamples to open conjectures from a single unhinted prompt: OpenAI's unit-distance disproof was generated in one run without human mathematical intervention, a counterexample to the Gaussian Moments Conjecture was produced from a single prompt once a model was told the Jacobian conjecture had fallen, and an OpenAI researcher has said an internal Codex model found essentially the same Jacobian counterexample on its own. Kevin Buzzard's contemporaneous account also places the discovery inside a deliberate program, discussed between Mathew and Alpöge, of pointing these models at long-open conjectures because counterexamples had become "low-hanging fruit". The question is empirical and would be settled by either of two things: publication of the session, or a replication attempt in which Fable 5, with web access disabled and no hint of the announced map, is simply asked for a counterexample to the Jacobian conjecture. Neither has appeared. Until one does, the balance of the analogical evidence makes a single-prompt origin plausible but less likely than not, chiefly because experienced users of these models, Alpöge among them, typically iterate, and because the actual session having been a single short prompt is the reading with the least direct support.
Claim entered the graph