Findings

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.