Browse
Claims
Search the graph by meaning. Each result carries its current verdict; open one to see its decomposition, provenance, and the reasoning behind the assessment.
ShowingImportancePrizesTopicArithmetic holomorphic structures
The mathematical object called an "arithmetic holomorphic structure" in Mochizuki's inter-universal Teichmüller theory and in Kirti Joshi's related construction of p-adic Teichmüller theory and a claimed abc proof. Claims defining, constructing, or comparing these objects (e.g. whether Joshi's structures coincide with Mochizuki's) belong here.
Mochizuki's IUT papers establish the existence of distinct arithmetic holomorphic structures.
ContradictedAvailable evidence weighs against the claim.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Inter-universal Teichmüller theoryNumber theoryimportance · minorImportance 0.40, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
Kirti Joshi's arithmetic Teichmüller theory establishes the existence of distinct arithmetic holomorphic structures.
ContestedCredible evidence or argument exists on multiple sides.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Number theoryimportance · minorImportance 0.35, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
Joshi's arithmetic holomorphic structures are the same objects as those of Mochizuki's inter-universal Teichmüller theory.
ContradictedAvailable evidence weighs against the claim.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Number theoryInter-universal Teichmüller theoryimportance · minorImportance 0.35, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
The untilt data that defines Joshi's arithmetic holomorphic structures plays no role in the constructions of Mochizuki's IUT papers.
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 →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Inter-universal Teichmüller theoryNumber theoryimportance · minorImportance 0.30, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
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.
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 →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Inter-universal Teichmüller theoryIUT Corollary 3.12 gapimportance · minorImportance 0.40, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
Mochizuki's IUT papers give no definition of arithmetic holomorphic structure precise enough to prove that two such structures differ.
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 →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Inter-universal Teichmüller theoryNumber theoryimportance · minorImportance 0.35, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
In IUT, "distinct arithmetic holomorphic structures" means ring structures related by a non-ring-theoretic link, not non-isomorphic structures.
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 →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Inter-universal Teichmüller theoryIUT Corollary 3.12 gapimportance · minorImportance 0.30, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
Contribute
If a claim here is wrong, or missing evidence, open it: every claim page carries its own entry for challenges, evidence, and corrections. If the graph is missing a claim entirely, propose it below. A proposal is reviewed on its merits; accepted claims are matched against the graph and enter it with their reasoning on record.