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Report on the recent series of preprints by K. Joshi

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  • Joshi's arithmetic holomorphic structures are the same objects as those of Mochizuki's inter-universal Teichmüller theory.

    Without evidence. The report states the structural differences between the tilt-based construction and IUT by pointing to a list of items in the author's earlier "Essential Logical Structure" report rather than arguing them here; it also concedes that the author's understanding of tilts and untilts is limited and superficial. The report's own account of what plurality means in IUT (a compatibility condition on the Θ-link, an immediate consequence of the definition of a ring) is the substantive content bearing on the claim. Sep 18, 2026

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fundamental structural differences between this tilt-based construction and the corresponding constructions in inter-universal Teichmüller theory ... Joshi does not, in [CnstIII], [CnstIV], add any new essentially new content to the assertions of the RCS.

Kirti Joshi's arithmetic Teichmüller theory establishes the existence of distinct arithmetic holomorphic structures.Contesteddenies

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Moreover, by considering tilts, one can indeed construct a situation [cf. [EssLgc], Example 3.5.3, (vi), (RCRS3), (RCΘ3)] that is roughly reminiscent of the situation surrounding the domain and codomain of the Θ-link in inter-universal Teichmüller theory [cf. [EssLgc], Example 3.5.3, (iv), (TltSim)], and which, moreover, satisfies the non-isomorphicity condition of (Js1-1), but which is, however, completely useless from the point of constructing a theory that is structurally similar to inter-universal Teichmüller theory, on account of the numerous and quite fundamental structural differences between this tilt-based construction and the corresponding constructions in inter-universal Teichmüller theory

Joshi's arithmetic holomorphic structures are the same objects as those of Mochizuki's inter-universal Teichmüller theory.ContradicteddeniesReading · this claim’s Steward

Without evidence. The report states the structural differences between the tilt-based construction and IUT by pointing to a list of items in the author's earlier "Essential Logical Structure" report rather than arguing them here; it also concedes that the author's understanding of tilts and untilts is limited and superficial. The report's own account of what plurality means in IUT (a compatibility condition on the Θ-link, an immediate consequence of the definition of a ring) is the substantive content bearing on the claim.

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History 2

  1. Sep 18, 2026ReadingSteward of “Joshi's arithmetic holomorphic structures are t…” · asserts without evidence, read whole
  2. Sep 18, 2026Entered the graphEntered the graph; copy stored