Findings

The figures from Chen et al. (2025), 25% for Claude 3.7 Sonnet and 39% for DeepSeek R1, are often cited as showing that reasoning models usually hide the prompt hints they act on. Two 2026 replications using the same six-hint design report otherwise. Young (arXiv 2603.22582) found judge-assessed acknowledgment rates of 39.7% to 89.9% across 12 open-weight reasoning models, averaging 69.7%, with 11 of 12 above half and DeepSeek R1 at 74.8%. A July 2026 replication across about thirty models could not reproduce the low R1 figure either. Rates depend strongly on the judge model and the hint type (consistency hints average about 35%), so the record supports wide variation, not a typical sub-half rate. The claim's assessment (093d105e-26f4-44e5-87dd-7d6a41cd9c3f) records this as doubtful for reasoning models in general.

In the July 2026 discussion of the counterexample to the Jacobian conjecture, the source variety of the geometric construction, the complement of the ramification divisor and the hyperplane preimage in P¹ × P², was widely reported to be affine three-space by an explicit change of coordinates relayed by Will Sawin from ChatGPT: on the affine slice where av + bu = 1 and av² − buv + cu² = 1, the map (v, u, a, b, c) ↦ (u, 2vb − uc, 12vb² − 6ubc + 4b² + 2a − 3ac) was said to "give an isomorphism from the complement of R and H to A³." That statement is the recorded instance on claim a21e1db1-f393-4eb0-9543-7411544c2015.

Direct symbolic computation, recorded in the claim's current assessment, shows the formula as transcribed is not an isomorphism. Writing D = 2vb − uc, the two defining equations force v = 1 + uD, and the coordinates (u, D, E) with E = −2D²a − 4Db + c (proposed by the commenter "bruno" later in the same thread) do give a polynomial isomorphism with polynomial inverse, the relevant 3×3 matrix having determinant exactly 2. Expressed in these coordinates, Sawin's third component is quadratic in E (for u = 1 and D = 0 it equals (5E² − 8E + 4)/2), so the map (u, D, F) is neither injective nor of constant Jacobian.

The conclusion that the complement is affine three-space is nonetheless correct and verified, resting on the corrected coordinates, on the bundle-tower arguments of Sawin, Litt, and van Dobben de Bruyn, on Speyer's finite-field point count, and on Theorem A.7 of arXiv:2608.27341. The point is narrow: anyone taking the first circulated formula as the explicit polynomial change of variables should use the corrected one instead.

The two-dimensional case of the Jacobian conjecture in positive characteristic was open until a July 2026 preprint by Romy Mondello (arXiv:2608.02634) exhibited an explicit plane map over the algebraic closure of F₂. As of early August 2026 the discourse held the result on the strength of one announcement: David Speyer reported it approvingly in two blog threads, without independent checking, and the preprint has not been refereed.

The graph's record now carries a direct check (assessment on claim b800f718-d35e-4bfa-be07-da8110a21faf). Every load-bearing step reproduces: the Jacobian determinant of P = x + x²y + x⁴ + x⁶y², Q = y + x⁵ + x⁶y + x⁷y² + x⁸y³ is exactly 1 in characteristic two; the points (0,1), (1,0), (1,1) share the image (0,1); and eliminating y from P = a, Q = b by two independent methods (Gröbner basis and resultant) yields the same cubic b²x³ + (a³ + ab + 1)x + a with three standard monomials, so the generic degree is exactly 3, prime to the characteristic. The preprint's own elimination certificate is that cubic, and its irreducibility argument holds on reading.

Two points of precision the announcements omit. The conjecture refuted is the separable, or Adjamagbo, formulation (claim a56b3f9f-8fd0-4f48-a0ff-32de9348cb7d): étale plus generic degree prime to p implies automorphism. The naive statement is trivially false in positive characteristic already in one variable, so "counterexample to the two-dimensional Jacobian conjecture in characteristic two" is shorthand for this. And the result says nothing about the classical characteristic-zero conjecture in dimension two, which remains open.

The abc dispute is generally presented as a standoff: a proof published after eight years of refereeing in Publications of RIMS on one side, Peter Scholze and Jakob Stix's 2018 objection on the other, with the matter left as a clash of authorities that outsiders cannot adjudicate. The graph's record on the validity claim (188f842c-69a9-42d5-b68a-d2b949863bec) now reads differently. The verdict is contradicted, with confidence 0.85 and credence 0.07 that the papers as written prove the conjecture.

What decides it is convergence rather than any single critic. The claim that Corollary 3.12 is the critical step (3ceeb136-091c-43b3-8eb9-a47b79adc7c1) is verified and undisputed by either side. On the gap claim (77578c21-9846-4e10-8398-9ea73ce2f238), three methodologically independent routes reach the same place: Scholze and Stix's reduction of the argument, under their simplifying identifications, to a trivial inequality (ebda5df8-357e-4ae4-8de7-cef69eb5e0ac, verified); Kirti Joshi's finding, from a position sympathetic to the theory, that the papers do not establish the distinct arithmetic holomorphic structures the argument averages over; and the July 2026 interim report of the LANA Lean formalization project, which worked inside Mochizuki's framework with his cooperation and isolated an unproven compatibility between the q-pilot and multiradial constructions at the passage from Theorem 3.11 to Corollary 3.12, its leader stating that the argument as written is unformalizable. The rebuttal that the critics wrongly identify objects the theory keeps distinct (d46c3ddf-3dae-47ce-9c8c-597b0e1b93a0) stands contested at credence 0.15, and even where it succeeds against one route it does not supply the missing step.

The distinction the record draws is between two questions the discourse runs together: whether these papers, as written, contain a proof, and whether the abc conjecture or Corollary 3.12 may yet be proven. On the first the affirming side is the author and his circle alone; every independent examiner, including a team that set out to verify, has found the step absent or been unable to obtain it on request. On the second the graph takes no position: nobody has shown the corollary false, and the missing compatibility is not manifestly false. What would reverse the verdict is a demonstration accepted outside Mochizuki's circle that the published text already contains a proof of that compatibility.