Scholze and Stix's analysis of IUT identifies isomorphic copies of mathematical objects that Mochizuki's theory treats as distinct.
6 events · 2 assessments · 3 decisions
Reassessed (re-affirmed verified); provenance recorded; instance corrected; instance added; importance lowered
Staleness check. The claim concerns the fixed method of the 2018 Scholze–Stix note, so the evidence landscape cannot have moved materially; one web search confirmed no new source denies it and surfaced Kirti Joshi's papers, which affirm it from the anti-identification side (recorded as a new affirming instance from arXiv 2210.11635). Read Roberts's Inference essay in full through the provenance reader: the recorded passage is verbatim, but a later sentence states the claim directly, so the instance's verbatim text was replaced with that sentence, its confidence raised, and its date refined to 2019-03; recorded a reading (supports, read) and an edge to the Scholze–Stix note (derives_from, faithful, target not read). Could not open the Scholze–Stix PDF: provenance_read_source fails on PDFs with NUL bytes, a known triaged issue (4fb8e166) which this run joined as a sighting; the reasoning trace discloses the gap. Source map written and marked immaterial: four affirming sources, one primary, three secondary that rest on the primary and characterise it faithfully. Verdict re-affirmed as verified at confidence 0.93, credence 0.98, marginal yield 0.05. Importance lowered from 0.25 to 0.2 with contestation 0.05: load-bearing for three parents but undisputed by anyone. Canonical form judged adequate: neutral, affirmative, accepted by both sides, about twenty words; no change. No status change, so dependents were not notified. No structure changes: the claim remains atomic and no missing dependency surfaced.
Reassessed: still Verified
verdict confidence 0.92 → 0.93 · credence 0.98
Updated claim instance
Instance 8d8c2687-9d35-4f3f-aba8-2761f45d0a7c (https://inference-review.com/article/a-crisis-of-identification): was stance=affirms, confidence=0.8, speaker=David Michael Roberts; set confidence=0.95, verbatimText="They have allowed themselves to identify isomorphic objects for the purpose of simplifying an argument. In places where Mochizuki supplies two distinct but isomorphic mathematical objects, Scholze and Stix see only one on the grounds that they are isomorphic.", sourceDate="2019-03". Read the full article. The previously recorded "boxer" sentence is present and expresses Roberts' attitude, but the passage two paragraphs later states the claim itself directly and without metaphor: Scholze and Stix identified isomorphic objects that Mochizuki supplies as distinct. This is the statement that carries the stance, so it replaces the earlier one; confidence raised since it is an unambiguous assertion of exactly this proposition. Date refined to March 2019 from the article's masthead (Vol. 4, No. 3, March 2019).
Structured and assessed first pass
First pass (structure_and_assess). Decomposition: left atomic. The claim is a directly verifiable documentary fact about the content of the Scholze–Stix report and Mochizuki's formalism; the only genuinely disputed proposition nearby (whether the identifications are essential to the objection) already exists as sibling claim e7170d09-3a68-4f8d-94b7-d7e6281d2723 under the shared parent, and any further breakdown would be derivation steps or source-specific facts failing the §2 claim bar. Assessment: VERIFIED, confidence 0.92, credence 0.97, marginal_yield 0.05. Verified against the Scholze–Stix report itself (which states the identifications were made), Mochizuki's rebuttals (which presuppose them, e.g. his "Redundant Copies School" label), and independent commentary (Roberts in Inference 2019; Aberdein's "Deep Disagreement in Mathematics" 2022). Three affirming instances recorded, none denying; this matches the seed credence 0.85 from the parent's steward and the parent's own assessment prose. Importance set to 0.25 with contestation 0.05: load-bearing for the parent but uncontested by both sides, so near the minor/settled anchor, slightly elevated for sitting inside a heavily consulted controversy. Canonical form kept: 19 words, neutral, acceptable to both sides as a statement of the fact. Notification skipped: the sole dependent is the parent (d46c3ddf), whose current contested assessment already states this fact is not in serious dispute; a verified verdict consistent with the seed and with the parent's existing reasoning is not material to it.
Assessed Verified
verdict confidence 0.92 · credence 0.97
In their 2018 report "Why abc is still a conjecture", Peter Scholze and Jakob Stix analyzed the proof of Corollary 3.12 in Shinichi Mochizuki's inter-universal Teichmüller theory (IUT) papers by making a series of simplifications, explicitly including the identification of isomorphic copies of objects, such as copies identified along the identity, that Mochizuki's formalism keeps as distinct, separately labeled objects. This is not in dispute between the parties: Scholze and Stix state in their report that they made these identifications, presenting them as harmless, and Mochizuki's rebuttals are built entirely on the premise that they were made, to the point of referring to his critics' approach as the "redundant copies" reading of IUT. Independent commentators on the controversy describe the exchange the same way. What remains contested is the significance of the identifications, not their existence: whether the simplifying identifications are essential to Scholze and Stix's objection, as Mochizuki maintains, or are removable bookkeeping that leaves the objection intact, as Scholze and Stix maintain. That question is a separate claim; this one records only the documentary fact on which both sides agree.
Claim entered the graph