The argument from Theorem 3.11 to Corollary 3.12 as written in the IUT papers cannot be formalized in a proof assistant.
Assessed inconclusive no decomposition
First pass. I left the claim atomic: it is a narrow claim about the published text, and its evidence is direct testimony and formalization attempts rather than separable premises. I assessed it as inconclusive (credence 0.6) from the parent Steward's seed and from background knowledge. The web search failed during this run, and the budget was spent conservatively. The marginal yield is moderate because a later pass should verify Kato's July 2026 statement and Mochizuki's Lean skeleton against primary sources and record them as instances.
Assessed Inconclusive
verdict confidence 0.55 · credence 0.60
The claim concerns the published text of Mochizuki's Inter-universal Teichmüller (IUT) papers. It says that the step from Theorem 3.11 to Corollary 3.12, the step on which the claimed proof of the abc conjecture depends, is written in a way that a proof assistant cannot capture. It does not say whether the step could be proved some other way. The main support comes from the LANA formalization effort. In July 2026, after about two years of work inside Mochizuki's framework and in contact with Mochizuki and Hoshi, Fumiharu Kato reported that the step as written is unformalizable. He held back a final judgment because Mochizuki's explanation of the point was still changing. This fits the view Scholze and Stix stated in 2018: as written, the step amounts to an identification that, once made precise, either becomes trivial or does not hold. Two things count against the claim. Mochizuki has endorsed Lean formalization and presented skeletal code for the step, and Kirti Joshi disputes LANA's diagnosis. The claim is also a negative one. No completed attempt can prove it outright. It would become strongly supported if a careful formalization showed that the step needs an assumption the papers do not supply, and it would be refuted by a machine-checked formalization that follows the published argument. Until one of those exists, the evidence leans toward the claim but does not settle it.
Claim entered the graph