Corollary 3.12 is the critical step in Mochizuki's claimed IUT proof of the abc conjecture.
5 events · 2 assessments · 2 decisions
Reassessed no status change
Staleness check. Two web searches for developments in the Mochizuki/Scholze–Stix/Joshi discourse found nothing since the last assessment that displaces Corollary 3.12 as the crux; the 2025 Joshi–Mochizuki exchange presupposes its centrality. Re-affirmed verified at 0.9 with credence 0.95 and marginal_yield 0.05. First provenance pass done in proportion to importance 0.25: read the Quanta source whole (recorded passage verified present), recorded its reading and its edge to Calegari's 2017 blog post (target not opened), wrote an immaterial source map noting the three instances are independent secondary voices on an uncontested architectural fact. Structure, canonical form, and importance (0.25) left unchanged; no dependents notified since the verdict did not move.
Reassessed: still Verified
verdict confidence 0.90 · credence 0.95
Structured and assessed
First pass. The claim states the one fact the entire IUT/abc controversy agrees on: Corollary 3.12 is the crux of Mochizuki's claimed proof. Decomposition kept minimal per §19: one novel requires-subclaim minted (the conditional "abc follows if 3.12 holds", confirmed novel by the Matcher against the unconditional validity claim 188f842c and the gap claim 77578c21) and seeded at 0.88; scored 0.2 so it stays a deferred stub. The neighboring gap and validity claims were deliberately not attached: they concern whether 3.12's proof is correct, which is orthogonal to centrality. Canonical form tightened ("critical step central to" → "critical step in", added "claimed IUT proof") without changing the proposition. Importance lowered from the Extractor's 0.4 to 0.25 with contestation 0.05: consequential context for a live debate but itself undisputed. One light web pass sufficed (V, SH): affirming assertions found from critics (Scholze–Stix report), reporters (Quanta, Earth.com), reference works (nLab), and independent researchers (Joshi); two new instances recorded, none denying. Verdict: verified, confidence 0.9, credence 0.95, marginal yield 0.05: another pass would add little. No dependents exist, so no propagation notice sent.
Assessed Verified
verdict confidence 0.90 · credence 0.95
Corollary 3.12, the central inequality of the third of Shinichi Mochizuki's inter-universal Teichmüller theory (IUT) papers, is where every party to the dispute over the claimed abc proof locates the essential content of the argument. Mochizuki's fourth paper derives Szpiro-type inequalities, and from them the abc conjecture, from the corollary, so abc follows if Corollary 3.12 holds; conversely, the proof's principal critics, Peter Scholze and Jakob Stix, direct their objection entirely at the proof of 3.12, and Frank Calegari has written that without it there is no proof at all. Sympathetic and independent workers agree: Kirti Joshi's attempted rehabilitation of the proof is organized around establishing 3.12, and reference treatments describe the corollary as the key step. The corollary's centrality is thus common ground between the proof's defenders and its critics; what remains contested is whether its proof is correct, a separate question the graph tracks on its own claims.
Claim entered the graph