Not evaluated
Anticanonical nonvanishing under smooth semipositivity (family 068)
The gist
On October 6, 2026, OpenAI published seven manuscripts, from an unreleased internal model, on anticanonical nonvanishing under smooth semipositivity.
DiscoverIA status on October 12, 2026: not evaluated, meaning no third-party evaluation found.
AI draft, not reviewedWhat has not been reviewed?
Text written by an AI (DiscoverIA pipeline), on . The status and its sources come from the registry; only the explanatory text has not been reviewed. A reported error is corrected, then the text is reviewed.
Cite this entry
A single status snapshot since Oct 12, 2026: a citation always points to a dated snapshot.
Cite snapshot 1, Oct 12, 2026
APA citation with the dated link
BibTeX @misc, key discoveria-oai-fam-068-anticanonical-nonvanishing-under-smooth-r1
@misc{discoveria-oai-fam-068-anticanonical-nonvanishing-under-smooth-r1,
author = {{DiscoverIA}},
title = {Anticanonical nonvanishing under smooth semipositivity (family 068)},
howpublished = {DiscoverIA registry, entry oai-fam-068-anticanonical-nonvanishing-under-smooth},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-068-anticanonical-nonvanishing-under-smooth#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
The subject is the anticanonical object of an algebraic variety (something attached to its overall curvature): under a smooth semipositivity hypothesis, are certain objects associated with it really non-zero? If the manuscripts were correct, they would provide, going by their titles, elements of an answer, using metrics (ways of measuring distances) and invariant sections.
What remains unclear
No Lean (a language in which a computer checks every step of a proof) is supplied and no independent assessment is recorded. The sources read say neither what each manuscript claims exactly nor where the question stood before the announcement.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · README.md
Step 1 of 4 on the scale: not evaluated. Next step: under review.
- Announced
- Recordednot evaluated
- nextTo follow
What this status means
Source reading : Source read word for word (level 3 of 3)
The result is declared neither right nor wrong.
To move to “Under review”: a public review under way. To “Peer reviewed”: a journal publication or a review by named experts.
Sources
- Main sourcegithub.com · CONTENTS.mdlink only, reading not recorded
- Repositorygithub.com · Anticanonical…link only, reading not recorded
- Repositorygithub.com · Invariant-anticanonical…link only, reading not recorded
- Repositorygithub.com · Bounded-anticanonical…link only, reading not recorded
- Repositorygithub.com · Cohomological-transfer…link only, reading not recorded
- Repositorygithub.com · Metric-descent-and-rank…link only, reading not recorded
- Repositorygithub.com · Integrable-metrics-and…link only, reading not recorded
- Repositorygithub.com · Exact-orders-and…link only, reading not recorded
Method
The manuscripts are all dated September 26, 2026 and include “Anticanonical nonvanishing from smooth semipositivity”, “Bounded anticanonical metrics on klt pairs and torus quotients” and “Exact orders and invariant anticanonical linear systems”. They are filed under the “Algebraic and complex geometry” section of the openai/math repository; there is no lean/docs/068.md file, and history.md reports no revision. DiscoverIA status: not evaluated, meaning that no third-party evaluation has been found in the sources read. Set on October 12, 2026 from github.com (page read, quotation checked word for word: “Not all have accompanying Lean formalizations.”).
Limits
DiscoverIA has not checked this result itself.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (Algebraic and complex geometry)
- In openai/math
- family 068, section “Algebraic and complex geometry”, 7 manuscripts dated Sep 26, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 8 : 8 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with no Lean proof supplied. No third-party evaluation read.
Source: github.comread word for word
An observation is added; none is ever erased.
In the same set
openai/math: 719 manuscripts in 372 families from an unreleased internal model · entry 66 of 372, by family number
- Not evaluated : Virasoro constraints for complete intersections and projective bundles (family 065)
- Not evaluated : Bounded klt complements for Fano contractions (family 066)
- Not evaluated : The Campana–Peternell conjecture in dimension six (family 067)
- Not evaluated : Anticanonical nonvanishing under smooth semipositivity (family 068)
- Not evaluated : Quantum geometric Langlands at irrational level (family 069)
- Not evaluated : Koebe's circle-domain conjecture and circle-domain rigidity (family 071)
- Not evaluated : Brennan's conjecture and a counterexample to Kraetzer's prediction (family 072)
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