trailMochizuki's inter-universal Teichmüller theory papers constitute a valid proof of the abc conjecture.
Formal publication· for
Mochizuki's IUT papers were peer-reviewed and published in Publications of RIMS
atomic
Mochizuki's rebuttal· for
Scholze and Stix's objection to Mochizuki's IUT proof rests on wrongly identifying objects the theory treats as distinct.
shared · shown elsewhere
If Mochizuki's Corollary 3.12 holds, the abc conjecture follows from his remaining arguments.
atomic
The gap at Corollary 3.12· against
The proof of Corollary 3.12 in Mochizuki's IUT papers contains a fundamental gap
Under Scholze and Stix's simplifying identifications, the argument for Corollary 3.12 yields only a trivial inequality
◌
✓
Taylor Dupuy argues that Scholze and Stix's simplified argument does not refute Corollary 3.12.
Kirti Joshi maintains that Mochizuki's IUT papers do not establish Corollary 3.12 as written.
Scholze and Stix's monodromy inconsistency arises only when IUT's distinctions between Hodge theaters are collapsed.
◌
◌
◌
+1
Absence of independent acceptance· against
The mathematical community broadly does not accept Mochizuki's IUT proof of the abc conjecture.
shared · shown elsewhere
assumed
Corollary 3.12 is the critical step in Mochizuki's claimed IUT proof of the abc conjecture.
claim · empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →claim page ↗︎
Mochizuki's inter-universal Teichmüller theory papers constitute a valid proof of the abc conjecture.
✕ContradictedAvailable evidence weighs against the claim.constitution →credence 0.07Credence, 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 →
Nothing in the graph builds on this claim yet.
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.