Not evaluated
A characteristic-zero counterexample to Lipman–Zariski (family 048)
The gist
In its release of October 6, 2026, OpenAI claims, using an unreleased internal model, to have exhibited a counterexample in characteristic zero to the Lipman–Zariski conjecture.
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-048-characteristic-zero-counterexample-r1
@misc{discoveria-oai-fam-048-characteristic-zero-counterexample-r1,
author = {{DiscoverIA}},
title = {A characteristic-zero counterexample to Lipman–Zariski (family 048)},
howpublished = {DiscoverIA registry, entry oai-fam-048-characteristic-zero-counterexample},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-048-characteristic-zero-counterexample#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
The Lipman–Zariski conjecture states that a variety whose tangent sheaf is locally free is smooth (it has no singular point). If the manuscript were correct, it would be false in characteristic zero (the usual setting of rational, real or complex numbers): it describes a singular normal affine surface whose tangent sheaf is free.
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 · A-singular-normal-affine…link only, reading not recorded
Method
The openai/math repository contains the manuscript “A singular normal affine surface with free tangent sheaf”, dated September 23, 2026, with no lean/docs/048.md file; the README states that not all manuscripts have a Lean formalisation, 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 048, section “Algebraic and complex geometry”, 1 manuscript dated Sep 23, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 2 : 2 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 47 of 372, by family number
- Not evaluated : The equivariant cohomological Hikita conjecture for quivers (family 044)
- Not evaluated : Counterexamples to Shafarevich holomorphic convexity (family 046)
- Not evaluated : Complex counterexamples to cancellation and affine fibrations (family 047)
- Not evaluated : A characteristic-zero counterexample to Lipman–Zariski (family 048)
- Not evaluated : A stable-coordinate counterexample in four variables (family 049)
- Not evaluated : A counterexample to Griffiths' positivity conjecture (family 050)
- Not evaluated : Kobayashi's canonical-ampleness conjecture (family 051)
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