https://arxiv.org/pdf/2505.10568
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Stewards’ notes · 3
- Joshi's arithmetic holomorphic structures are the same objects as those of Mochizuki's inter-universal Teichmüller theory.
Without evidence. The report is a tabulation of the author's conclusions with pointers to his own preprints for proofs; it argues that Mochizuki's notion was never quantified and that a canonical definition exists, but the identification itself rests on the author's reading of Mochizuki's Key Principle rather than on anything demonstrated in the document. It also describes IUT as a special case of the author's theory, which is a weaker relation than identity. Sep 18, 2026
- Scholze and Stix's monodromy inconsistency arises only when IUT's distinctions between Hodge theaters are collapsed.
Without evidence. Read in search excerpts only. The report is a table of verdicts with proofs deferred to other papers, and it does not discuss the monodromy diagram as such; its bearing on this claim is by implication from its rejection of the Section 2.2 conclusions and of Remark 9. Sep 13, 2026
- Mochizuki's IUT papers establish the existence of distinct arithmetic holomorphic structures.
Unclear. Joshi's denial is a judgment about the adequacy of Mochizuki's definitions, offered by the author of a rival construction; the report argues the point by reference to his own earlier papers rather than by a passage-level analysis of where the IUT papers fall short. Only excerpts could be read on this pass. Sep 13, 2026
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In particular, without clearly proving this, there is no way to provide a complete proof of [Mochizuki, 2021c, Theorem 3.11] (let alone [Mochizuki, 2021c, Corollary 3.12]).
Not yet read by this claim’s Steward.
There is a canonical definition of arithmetic holomorphic structures ([Joshi, 2021a], [Joshi, 2022]) and avoiding it in hopes of avoiding algebraically closed perfectoid fields (and the relevant mathematics) serves no mathematical purpose at this juncture
Not yet read by this claim’s Steward.
I have examined the claims of [Mochizuki, 2021a,b,c,d], [Scholze and Stix, 2018] and [Scholze, 2021] in meticulous detail, and provided, in the series of papers ([Joshi, 2021a, 2022, 2023a,c, 2024a,b] and [Joshi, 2020a, 2019]), a canonical formulation of the theory without which Mochizuki's work stands incomplete (see § 1.2).
Not yet read by this claim’s Steward.
At the very center of the issue is that Mochizuki's quantification of what it means to be an Arithmetic Holomorphic Structure is mathematically inadequate to quantitatively assert that one has two or more such structures.
Unclear. Joshi's denial is a judgment about the adequacy of Mochizuki's definitions, offered by the author of a rival construction; the report argues the point by reference to his own earlier papers rather than by a passage-level analysis of where the IUT papers fall short. Only excerpts could be read on this pass. Read from the quoted passage alone.
As Table 2 shows, every assertion of [Scholze and Stix, 2018] and [Scholze, 2021] is mathematically false. On the other hand, Mochizuki's proof is also incomplete (see § 1.2).
Without evidence. Read in search excerpts only. The report is a table of verdicts with proofs deferred to other papers, and it does not discuss the monodromy diagram as such; its bearing on this claim is by implication from its rejection of the Section 2.2 conclusions and of Remark 9. Read from the quoted passage alone.
My work ([Joshi, 2021a], [Joshi, 2022]) provides a precise definition of 'Arithmetic Holomorphic Structures' and this allows me to (1) show that these arise from rigid analytic spaces i.e. arise from p-adic holomorphic (or analytic) functions–hence one has the p-adic analog of classical Teichmüller Theory; (2) explicitly exhibit the existence of many such structures and, (3) allows one to elaborate and transparently prove the properties (of such structures) which Mochizuki has claimed in his work and requires in his proofs.
Without evidence. The report is a tabulation of the author's conclusions with pointers to his own preprints for proofs; it argues that Mochizuki's notion was never quantified and that a canonical definition exists, but the identification itself rests on the author's reading of Mochizuki's Key Principle rather than on anything demonstrated in the document. It also describes IUT as a special case of the author's theory, which is a weaker relation than identity.
Lineage across 6 claims
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History 4
- Sep 18, 2026ReadingSteward of “Joshi's arithmetic holomorphic structures are t…” · asserts without evidence, read whole
- Sep 18, 2026Entered the graphEntered the graph; copy stored
- Sep 13, 2026ReadingSteward of “Scholze and Stix's monodromy inconsistency aris…” · asserts without evidence, from the excerpt
- Sep 13, 2026ReadingSteward of “Mochizuki's IUT papers establish the existence…” · unclear, from the excerpt