trailThe distinctions IUT draws between isomorphic copies of objects carry essential mathematical content.
The simplifying identifications in Scholze and Stix's analysis are essential to their objection to Corollary 3.12.
Distinct arithmetic holomorphic structures are real· for
Mochizuki's IUT papers establish the existence of distinct arithmetic holomorphic structures.
The Θ-link of inter-universal Teichmüller theory is not compatible with the ring structures of the Hodge theaters it relates.
In IUT, "distinct arithmetic holomorphic structures" means ring structures related by a non-ring-theoretic link, not non-isomorphic structures.
The Hodge theaters on the two sides of IUT's Θ-link are isomorphic as abstract mathematical objects.
Mochizuki's IUT papers give no definition of arithmetic holomorphic structure precise enough to prove that two such structures differ.
Kirti Joshi's arithmetic Teichmüller theory establishes the existence of distinct arithmetic holomorphic structures.
A perfectoid field of characteristic p has infinitely many distinct untilts to characteristic zero, parametrized by the Fargues–Fontaine curve.
Joshi's arithmetic holomorphic structures are the same objects as those of Mochizuki's inter-universal Teichmüller theory.
◌
◌
◌
Scholze and Stix's monodromy inconsistency arises only when IUT's distinctions between Hodge theaters are collapsed.
Mochizuki's intended derivation of Corollary 3.12 compares degrees of arithmetic line bundles within one arithmetic holomorphic structure rather than pilot-object volumes across the Θ-link.
The monodromy diagram Scholze and Stix exhibit does not arise in the LANA project's formulation of the derivation of Corollary 3.12.
The compatibility the LANA project isolated at the final stage of IUT is the same obstruction Scholze and Stix identified in 2018.
The passage from Theorem 3.11 to Corollary 3.12 in IUT depends on an unproven compatibility between the q-pilot's native construction and its multiradial reconstruction.
◌
Identifications along isomorphisms are harmless bookkeeping· against
Mochizuki has not identified a specific step in Scholze and Stix's argument that fails without their simplifications.
atomic
Mochizuki's rebuttals to Scholze and Stix have not persuaded arithmetic geometers outside his circle.
claim · empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →claim page ↗︎
The distinctions IUT draws between isomorphic copies of objects carry essential mathematical content.
⇄ContestedCredible evidence or argument exists on multiple sides.constitution →credence 0.35Credence, 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 →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. Arguments are not destinations; click their claims to explore.constitution →✓verifiedThe claim traces to reliable primary sources through a clear chain of evidence.constitution →↑supportedEvidence favors the claim, but the chain is incomplete or the sources are secondary.constitution →⇄contestedCredible evidence or argument exists on multiple sides.constitution →○unsupportedNo credible evidence found, though the claim is not contradicted.constitution →✕contradictedAvailable evidence 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 factopen questionvalue 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 →Fig. Detail falls off with distance; every claim is an address.