Not evaluated
Nagata's conjecture and maximal Seshadri constants (family 039)
The gist
In its release of October 6, 2026, OpenAI presents four manuscripts on Nagata's conjecture for plane curves and on maximal Seshadri constants.
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-039-nagatas-conjecture-maximal-seshadri-r1
@misc{discoveria-oai-fam-039-nagatas-conjecture-maximal-seshadri-r1,
author = {{DiscoverIA}},
title = {Nagata's conjecture and maximal Seshadri constants (family 039)},
howpublished = {DiscoverIA registry, entry oai-fam-039-nagatas-conjecture-maximal-seshadri},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-039-nagatas-conjecture-maximal-seshadri#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
If the manuscripts were correct, they would address Nagata's conjecture, which concerns the minimal degree of a plane curve passing through points in general position with a prescribed multiplicity. They would also address maximal Seshadri constants, numbers that measure the local positivity of a surface or a variety: on arbitrary polarized surfaces, in higher dimensions and in positive characteristic (an arithmetic setting where calculations “wrap around”, as on a clock face).
What remains unclear
The Lean formalisation (Lean is a language in which a computer checks every step of a proof) is supplied by OpenAI itself; no third-party check 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 · 039.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 · Nagatas-Conjecture-for…link only, reading not recorded
- Repositorygithub.com · Maximal-Seshadri…link only, reading not recorded
- Repositorygithub.com · Maximal-Multipoint…link only, reading not recorded
- Repositorygithub.com · Maximal-multipoint…link only, reading not recorded
- Lean proofgithub.com · 039.mdpage read word for word
- Lean proofgithub.com · MaximalSeshadriConstants.l…link only, reading not recorded
- Lean proofgithub.com · Nagata.leanlink only, reading not recorded
Method
According to OpenAI, an unreleased internal model produced it. In the openai/math repository, family 039 comprises four manuscripts: “Nagata's conjecture for plane curves” and “Maximal Seshadri constants on arbitrary polarized surfaces” (September 23, 2026), “Maximal Multipoint Seshadri Constants in Higher Dimensions” and “Maximal multipoint Seshadri constants in positive characteristic” (October 5, 2026). lean/docs/039.md provides 2 Comparator statements (MaximalSeshadriConstants.lean and Nagata.lean); formalization.yaml carries “review: status: unchecked” and lists this family among its sources, 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: “describes the scope of the Lean formalization”).
Limits
No named third party: the recorded checks come from the claimant or from a platform tool. The claimant supplies a Lean proof; as of this date, DiscoverIA has found no independent verification of this proof or of the result.
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 039, section “Algebraic and complex geometry”, 4 manuscripts dated Sep 23, 2026
- Lean proof
- supplied by the claimant, marked “unchecked” (not reviewed) in its repository
- Revisions
- none reported by the claimant
- Checked by
- claimant (Lean supplied, not checked by a third party)
- Sources
- 8 : 1 read word for word, 7 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with a Lean proof supplied by the claimant. No third-party check read; the source marks this proof as not reviewed (“unchecked”).
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 39 of 372, by family number
- 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)
- Not evaluated : Bloch's conjecture for complex surfaces (family 040)
- Not evaluated : Hyperkähler SYZ and projective-space bases (family 041)
- Not evaluated : Oka classification for K3 surfaces and other compact complex surfaces (family 042)
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