trailJoshi's arithmetic holomorphic structures are the same objects as those of Mochizuki's inter-universal Teichmüller theory.
Kirti Joshi's arithmetic Teichmüller theory establishes the existence of distinct arithmetic holomorphic structures.
Joshi's precisification argument· for
Mochizuki's IUT papers give no definition of arithmetic holomorphic structure precise enough to prove that two such structures differ.
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Mochizuki's Key Principle of Inter-Universality requires arbitrary geometric base-points for tempered fundamental groups, which only algebraically closed perfectoid fields supply.
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Joshi's arithmetic Teichmüller theory yields a valid proof of Mochizuki's Corollary 3.12.
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Different notions under one name· against
In IUT, "distinct arithmetic holomorphic structures" means ring structures related by a non-ring-theoretic link, not non-isomorphic structures.
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The untilt data that defines Joshi's arithmetic holomorphic structures plays no role in the constructions of Mochizuki's IUT papers.
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claim · empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →claim page ↗︎
Joshi's arithmetic holomorphic structures are the same objects as those of Mochizuki's inter-universal Teichmüller theory.
✕ContradictedThe evidence, examined directly, weighs against the claim.constitution →credence 0.15Credence, from 0 to 1: the Steward's probability that the claim, as stated, is true. Stated only where a single number is an honest summary; normative and evaluative claims usually carry none.constitution →
1depended on by
this rests on ↓
claimA box is a claim: a single proposition the graph assesses, with its own page and map. Click any claim to centre the map on it.constitution →quantityA box with a rule beneath its text is a quantity: a value the graph estimates rather than a proposition it affirms or denies. Its estimate stands where a claim's status would.constitution →questionA rounded box is a question: answered rather than affirmed or denied, with its candidate answers, subquestions and presuppositions beneath it. Its mark says how well answered it is.constitution →argumentA pill is an argument: one line of reasoning stating how the claims beneath it combine to bear on the claim above it, for or against. Click one to see its reasoning and open its page.constitution →✓verifiedThe evidence, examined directly, establishes the claim.constitution →↑supportedThe evidence favors the claim, but the examination is incomplete or the evidence is indirect.constitution →⇄inconclusiveThe evidence and argument have been examined and do not come down on either side.constitution →↓doubtfulThe evidence weighs against the claim, but the examination is incomplete or the evidence is indirect.constitution →✕contradictedThe evidence, examined directly, weighs against the claim.constitution →?unknownInsufficient information to assess.constitution →◌unassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →verified factunsettledvalue premisetheoremprizeA double ring marks a claim with a live prize: an amount in owls offered for a machine-checked proof or disproof of its published formal statement. The amount is in the preview and on the claim page; a prize changes nothing about how the claim is assessed or how important it is judged to be.prize rules →⊢machine-checked⊢ marks a claim whose published formal statement has a machine-checked proof or disproof. The checker confirms the proof; the verdict beside it is still the steward's judgment of the claim as worded.prize rules →supportsthis provides evidence for the parentsteward instructions →contradictsthis argues against the parentsteward instructions →assumesbackground the parent's framing takes as givensteward instructions →requiresa load-bearing premise: the parent is false without itsteward instructions →answersa candidate answer to the questionconstitution →Fig. Detail falls off with distance; every claim is an address.