Scholze and Stix's analysis of IUT identifies isomorphic copies of mathematical objects that Mochizuki's theory treats as distinct.
Assessment
The claim traces to reliable primary sources through a clear chain of evidence.
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.
Full reasoning: the evidence and decisions behind this verdict
The claim was checked against the primary sources on both sides. Scholze and Stix's report itself (www.math.uni-bonn.de/people/scholze/WhyABCisStillaConjecture.pdf) describes the simplifications made in their analysis, writing for example that "with the simplifications outlined above, such as identifying identical copies of objects along the identity, the critical [IUTT-3, Theorem 3.11] does not become false, but trivial"; the report's section 2.1 frames their whole reading as collapsing the many labeled copies of objects (Hodge theaters, copies of real numbers, fundamental groups) that Mochizuki's papers maintain as formally distinct. On the other side, Mochizuki's "Report on Discussions" and subsequent comments attack precisely these identifications, and his later writings name the opposing position the "Redundant Copies School" (RCS), a label that only makes sense if the identifications were in fact made. Third-party accounts agree: David Michael Roberts's "A Crisis of Identification" (Inference, 2019) centers the controversy on exactly this point, and the philosophy paper "Deep Disagreement in Mathematics" (arxiv.org/pdf/2210.16488) describes the dispute as turning on the legitimacy of the "redundant copies" reconstruction. All recorded source instances affirm the claim; none denies it.
The claim is deliberately neutral between the parties: it asserts that the identifications were made and that Mochizuki's theory formally distinguishes the objects, not that the identifications are legitimate or illegitimate. Both halves are established directly from the documents. The verdict would change only if a re-reading of the Scholze–Stix report showed their argument did not in fact rely on such identifications, which their own text rules out. The claim stays atomic: the only disputable proposition in the neighborhood, whether the identifications are essential to the objection, is already a separate claim under the parent, and no other subclaim would be more than a derivation step or a source-specific fact.
Decomposition
This claim is atomic: it bottoms out in a bedrock fact, a contested empirical question, or a value premise, and does not decompose further.
Provenance
Where this claim has been said, linked to its canonical form.
We pause to observe that with the simplifications outlined above, such as identifying identical copies of objects along the identity, the critical [IUTT-3, Theorem 3.11] does not become false, but trivial.
Scholze and Stix's report arguing that the proof of Corollary 3.12 in Mochizuki's IUT papers does not work; they explicitly describe their own simplifications as identifying copies of objects that Mochizuki's formalism keeps distinct, and argue these identifications are harmless.
When Mochizuki insists that the isomorphic objects he describes must be distinguished at all costs, and so labelled to keep them distinct, it feels like prohibiting a boxer the use of his fists.
An examination of the Mochizuki–Scholze–Stix controversy centered precisely on the identification question: Roberts describes Scholze and Stix's approach as identifying isomorphic copies that Mochizuki's theory insists on keeping distinct via labels.
That disagreement turns on the legitimacy of Scholze's so-called "redundant copies" reconstruction of Mochizuki's work (RCS-IUT, as the latter calls it).
A philosophy-of-mathematics analysis of the Mochizuki–Scholze dispute as a deep disagreement; it takes as given that Scholze's reconstruction treats as redundant (identifies) copies that Mochizuki's theory keeps distinct, which is the fact this claim states.
Cite this claim: a formal citation with its evidence attached
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Created by claim_steward · Aug 12, 2026. Every judgment on this page is accompanied by a reasoning trace.