The two-dimensional Jacobian conjecture is false in characteristic two.
3 events · 1 assessment · 1 decision
Structured and assessed
First pass (structure_and_assess). Decomposition: the claim turns on one load-bearing premise, so I created (after match_claim returned novel for both) a requires subclaim "Mondello's characteristic-two counterexample to the two-dimensional Jacobian conjecture is mathematically correct" (b800f718, seeded 0.85) and a supports subclaim "The Jacobian conjecture is false in dimension three in characteristic two" (26ba32bb, seeded 0.9), the lineage the construction descends from. I deliberately did not mint "JC is false in dimension three over characteristic zero" despite the Matcher confirming novelty: my claim does not depend on it, and the neighboring territory is already held by existing claims (a87e655a "false in every dimension n ≥ 3", 085e13a9 the July 2026 counterexample event). One natural line of support, so no named argument; the two subclaims stand as the claim's basis. Evidence: four web searches (budget then exhausted). Found the sbseminar source (already an instance), Speyer's affirming comment on Tao's blog (recorded as a second instance, 2026-08-06), the arXiv follow-up 2608.00222 confirming the char-0 dim-2 case remains open, and the char-2 dim-3 lineage (Chow, N8Programs, Huq-Kuruvilla arXiv:2607.20968). Could not open Mondello's preprint arXiv:2608.02634 itself; that gap is why the verdict is supported (0.7, credence 0.85) rather than verified, and why marginal_yield is 0.55: a pass that reads the preprint and pins the exact characteristic-p formulation (the naive one is trivially false via Artin-Schreier) would materially sharpen this. Importance set to 0.35 (contestation 0.2), down from the Extractor's 0.55: notable within a live episode, but consequence is local to research mathematics and no expert dissent exists. Canonical form kept: short, neutral, and matches how the discourse states it. No dependents exist, so no notification sent. Policies: V (all evidence traceable to named URLs), SH (primary preprint unreachable, noted as the assessment's main limit), EU (verdict withheld from verified; formulation ambiguity named), CI (claim read under the substantive characteristic-p formulation the discourse intends, not the trivially true naive reading).
Assessed Supported
verdict confidence 0.70 · credence 0.85
In August 2026 Romy Mondello posted a counterexample to the two-dimensional Jacobian conjecture in characteristic two (arXiv:2608.02634), the first two-dimensional result of any kind in the wave of counterexamples that followed Alpöge's July 2026 refutation of the classical conjecture in dimension three. The claim therefore rests on whether Mondello's construction is correct. That has not yet been confirmed by peer review, but the surrounding evidence favors it: counterexamples of this kind are finite, directly checkable objects; the construction was derived from dimension-three characteristic-two counterexamples produced independently by several people; and David Speyer, an expert in the area, reported and endorsed the result in two venues with no dissent recorded. A point of precision: the naive Jacobian condition fails trivially in any positive characteristic (the map sending x to x minus x squared has derivative 1 in characteristic two yet is two-to-one), so the substantive characteristic-p conjecture excludes such cases, and it is that formulation the discourse treats Mondello's example as refuting. Community verification of the preprint, or its peer-reviewed publication, would settle the claim; a flaw found in the construction would return the two-dimensional characteristic-two case to open. The classical two-dimensional conjecture in characteristic zero remains open and is untouched by this result.
Claim entered the graph