Scholze and Stix's analysis of IUT identifies isomorphic copies of mathematical objects that Mochizuki's theory treats as distinct.
3 events · 1 assessment · 1 decision
Structured and assessed first pass
First pass (structure_and_assess). Decomposition: left atomic. The claim is a directly verifiable documentary fact about the content of the Scholze–Stix report and Mochizuki's formalism; the only genuinely disputed proposition nearby (whether the identifications are essential to the objection) already exists as sibling claim e7170d09-3a68-4f8d-94b7-d7e6281d2723 under the shared parent, and any further breakdown would be derivation steps or source-specific facts failing the §2 claim bar. Assessment: VERIFIED, confidence 0.92, credence 0.97, marginal_yield 0.05. Verified against the Scholze–Stix report itself (which states the identifications were made), Mochizuki's rebuttals (which presuppose them, e.g. his "Redundant Copies School" label), and independent commentary (Roberts in Inference 2019; Aberdein's "Deep Disagreement in Mathematics" 2022). Three affirming instances recorded, none denying; this matches the seed credence 0.85 from the parent's steward and the parent's own assessment prose. Importance set to 0.25 with contestation 0.05: load-bearing for the parent but uncontested by both sides, so near the minor/settled anchor, slightly elevated for sitting inside a heavily consulted controversy. Canonical form kept: 19 words, neutral, acceptable to both sides as a statement of the fact. Notification skipped: the sole dependent is the parent (d46c3ddf), whose current contested assessment already states this fact is not in serious dispute; a verified verdict consistent with the seed and with the parent's existing reasoning is not material to it.
Assessed Verified
verdict confidence 0.92 · credence 0.97
In their 2018 report "Why abc is still a conjecture", Peter Scholze and Jakob Stix analyzed the proof of Corollary 3.12 in Shinichi Mochizuki's inter-universal Teichmüller theory (IUT) papers by making a series of simplifications, explicitly including the identification of isomorphic copies of objects, such as copies identified along the identity, that Mochizuki's formalism keeps as distinct, separately labeled objects. This is not in dispute between the parties: Scholze and Stix state in their report that they made these identifications, presenting them as harmless, and Mochizuki's rebuttals are built entirely on the premise that they were made, to the point of referring to his critics' approach as the "redundant copies" reading of IUT. Independent commentators on the controversy describe the exchange the same way. What remains contested is the significance of the identifications, not their existence: whether the simplifying identifications are essential to Scholze and Stix's objection, as Mochizuki maintains, or are removable bookkeeping that leaves the objection intact, as Scholze and Stix maintain. That question is a separate claim; this one records only the documentary fact on which both sides agree.
Claim entered the graph