Under Scholze and Stix's simplifying identifications, the argument for Corollary 3.12 yields only a trivial inequality
3 events · 1 assessment · 1 decision
Structured and assessed
First pass. The claim is narrow: what Scholze and Stix's simplified argument yields, not whether the simplification is legitimate. Decomposition kept light: attached the existing verified claim 958644b5 (SS identify isomorphic copies the theory treats as distinct) as an assumes scope premise, and minted one supports subclaim (Mochizuki agrees the simplified argument yields only a trivial inequality; Matcher found it novel) at importance 0.2, left as a deferred stub. Considered attaching e7170d09 (identifications essential to the objection) and 1383ceae (LANA monodromy) but they bear on the reduction's significance, which lives on the parent, not on this claim's truth; referenced in prose instead. No named arguments: one natural line of support. Recorded one new affirming instance (Dupuy and Hilado as quoted by Woit; the arXiv original was not opened, so the instance is recorded on the URL read with the original speakers named). Importance lowered from 0.45 to 0.3 with contestation 0.15: a supporting premise in a live debate but itself uncontested. Assessed verified at confidence 0.85, credence 0.93, marginal yield 0.1: the derivation is elementary and no party disputes it; residual uncertainty is that the pass reconstructed (1.5)–(1.6) from the report's stated conclusion and search excerpts rather than a fresh full read, and web search quota ran out before Mochizuki's Rpt2018 wording could be pulled verbatim. Canonical form judged adequate (about 17 words, neutral, both sides would accept it); left unchanged. Curator context on LANA section 10 weighed: it does not contest this proposition and is reflected in the assessment's account of the reduction's significance.
Assessed Verified
verdict confidence 0.85 · credence 0.93
In their 2018 report "Why abc is still a conjecture", Peter Scholze and Jakob Stix set out a simplified version of the argument for Corollary 3.12 of Mochizuki's third inter-universal Teichmüller theory paper, in which isomorphic copies of objects that the theory keeps distinct, in particular the copies of the real numbers that appear along the Θ-link, are identified consistently. Under those identifications the scalars j² that the argument uses to compare the Θ-pilot with the q-pilot must be dropped, and the inequality the argument would deliver reduces to the form −deg(q) ≤ −deg(q) + c, which holds for trivial reasons and bounds nothing. This computation is elementary once the identifications are made, and no party to the dispute contests it. What the claim does not settle is whether the simplifications are legitimate, and that is where the actual disagreement lies. Mochizuki holds that identifying the copies discards the theory's essential content, so that the collapse shows only that the simplified version is not his theory; he agrees that the simplified argument itself yields only a trivial inequality. Taylor Dupuy argues that the statement Scholze and Stix refute is not the statement Corollary 3.12 makes, and the LANA formalization project reported in July 2026 that the monodromy Scholze and Stix point to does not arise when the theory's distinctions between Hodge theaters are kept. Each of these objections targets the reduction's significance, not its result. Whether the identifications are essential to the objection is treated as its own question, on which the graph currently finds the case that they are essential weak, and the claim here should be read as one uncontested step in a larger argument whose force is genuinely disputed.
Claim entered the graph