Not evaluated
Numerical semiampleness and generalized minimal models (family 036)
The gist
On October 6, 2026, OpenAI claims, with an unreleased internal model, to have obtained algebraic geometry results on minimal models and numerical semiampleness.
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-036-numerical-semiampleness-generalized-minimal-r1
@misc{discoveria-oai-fam-036-numerical-semiampleness-generalized-minimal-r1,
author = {{DiscoverIA}},
title = {Numerical semiampleness and generalized minimal models (family 036)},
howpublished = {DiscoverIA registry, entry oai-fam-036-numerical-semiampleness-generalized-minimal},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-036-numerical-semiampleness-generalized-minimal#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
If the four manuscripts were correct, nef adjoint classes (nef: “numerically effective”) would be numerically semiample, on compact Kähler manifolds as well as for adjoint divisors. They would also establish results on minimal models and Mori fibre spaces for generalised log canonical Q-pairs, and on minimal models in numerical dimension one.
What remains unclear
No Lean (a language in which a computer checks every step of a proof) is supplied for this family, and no third-party assessment is recorded. The sources read do not say 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 · Numerical-semiampleness…link only, reading not recorded
- Repositorygithub.com · Numerical-Semiampleness…link only, reading not recorded
- Repositorygithub.com · Minimal-models-and-Mori…link only, reading not recorded
- Repositorygithub.com · Minimal-models-in…link only, reading not recorded
Method
The family comprises four manuscripts in the openai/math repository, dated September 24, 2026, October 3, 2026 and October 6, 2026, and has no lean/docs/036.md file. The file history.md reports, on October 7, 2026, a revision of “Numerical semiampleness of nef adjoint classes on compact Kähler manifolds”: this version states explicitly the Iitaka, model and contraction inputs used in the divisorial-decomposition argument. 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 036, section “Algebraic and complex geometry”, 4 manuscripts dated Sep 24, 2026
- Lean proof
- none supplied
- Checked by
- no verifier identified
- Sources
- 5 : 5 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 36 of 372, by family number
- Not evaluated : Campana's orbifold Iitaka conjecture and logarithmic subadditivity (family 033)
- Not evaluated : Log abundance and effective Iitaka fibrations (family 034)
- Not evaluated : Threefold log abundance in numerical dimension one in characteristic p>3 (family 035)
- Not evaluated : Numerical semiampleness and generalized minimal models (family 036)
- Not evaluated : The sharp ordinary-double-point volume gap (family 037)
- Not evaluated : Fujita's freeness conjecture (family 038)
- Not evaluated : Nagata's conjecture and maximal Seshadri constants (family 039)
Report an error or suggest a source
Thank you, your message was sent.
Sending failed. Try again, or write to contact@discoveria.ai.
Is your result listed?What each status requires, correcting this entry, replying to it.