Kirti Joshi maintains that Mochizuki's IUT papers do not establish Corollary 3.12 as written.
3 events · 1 assessment · 1 decision
Structured and assessed
First pass. Left the claim atomic: it is a factual claim about one mathematician's public position and turns on nothing in the discourse beyond his own statements, so no subclaims pass the claim bar as dependencies. Read two primary documents directly (Joshi's Final Report, arXiv 2505.10568, and Construction of Arithmetic Teichmuller Spaces IV v2, arXiv 2403.10430) and recorded each as an affirming instance with a provenance reading; both quotes verified verbatim. Recorded the shared-authorship relation and an immaterial source map (two primary sources, one voice, which for a claim about what that author maintains is the right evidence). Attempted to read the June 2024 report but the fetch failed on an encoding error; not material since the 2025 report supersedes it. Assessed verified, confidence 0.95, credence 0.97, marginal yield 0.05. Kept the canonical form: fifteen words, neutral, "as written" correctly captures Joshi's incompleteness-not-error stance. Set importance 0.2 and contestation 0.1: settled, minor, uncontested datum inside a live debate. Escalated a lateral-link suggestion to the Curator for the companion claim about whether Joshi's own construction proves Corollary 3.12. Not notifying dependents: both parents attached this claim as supporting evidence on the presumption it was true (the seed credence was 0.95), so a verified verdict changes nothing at their end.
Assessed Verified
verdict confidence 0.95 · credence 0.97
Kirti Joshi, an arithmetic geometer at the University of Arizona, has stated repeatedly and in his own writing that Mochizuki's inter-universal Teichmüller theory papers do not, as published, contain a complete proof of Corollary 3.12. In his 2025 "Final Report on the Mochizuki-Scholze-Stix Controversy" he writes that "Mochizuki's proof is also incomplete," locating the defect in Mochizuki's failure to establish quantitatively that many distinct arithmetic holomorphic structures exist, and concluding that without this "there is no way to provide a complete proof" of Theorem 3.11, "let alone" Corollary 3.12. The introduction to his paper "Construction of Arithmetic Teichmuller Spaces IV" says the same: without the resolution supplied by his own work, Mochizuki's papers and their proof of abc "unfortunately stand incomplete." Joshi's position is distinctive and easily misread in either direction. He rejects the Scholze and Stix conclusion that the gap cannot be filled, describing every mathematical assertion of their report as false, and he claims that his own theory of arithmetic Teichmüller spaces supplies exactly the missing ingredient, so that abc is established by his papers together with Mochizuki's. He is therefore neither an endorser of the proof as written nor a member of the camp that regards the theory as vacuous. Mochizuki, for his part, has rejected Joshi's construction as unnecessary and unrelated, but that is a dispute about whether Joshi is right, not about what Joshi maintains. Whether Joshi's own construction succeeds is a separate question, addressed by the claim that his arithmetic Teichmüller theory yields a valid proof of Corollary 3.12.
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