Not evaluated
Yau's nodal conjecture: surfaces and counterexamples (family 350)
The gist
On October 6, 2026, OpenAI announced three manuscripts on Yau's nodal 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-350-yaus-nodal-conjecture-surfaces-r1
@misc{discoveria-oai-fam-350-yaus-nodal-conjecture-surfaces-r1,
author = {{DiscoverIA}},
title = {Yau's nodal conjecture: surfaces and counterexamples (family 350)},
howpublished = {DiscoverIA registry, entry oai-fam-350-yaus-nodal-conjecture-surfaces},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-350-yaus-nodal-conjecture-surfaces#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 nodal set of a function is the set of points where it vanishes. If the manuscripts were correct, Yau's nodal upper bound would fail in dimensions three and four through smooth counterexamples, and through power-law violations in another manuscript. A third manuscript, “Sharp nodal length on smooth surfaces”, concerns nodal length on smooth surfaces.
What remains unclear
The Lean code (Lean is a language in which a computer checks every step of a proof) was supplied by OpenAI itself for the three manuscripts, and no third-party verification is recorded; formalization.yaml carries the entry “review: status: unchecked”. The sources read do not specify what each of the three Comparator statements covers.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 350.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 · Sharp-nodal-length-on…link only, reading not recorded
- Repositorygithub.com · Smooth-counterexamples-to…link only, reading not recorded
- Repositorygithub.com · Power-law-violations-of…link only, reading not recorded
- Lean proofgithub.com · 350.mdpage read word for word
- Lean proofgithub.com · NodalLength.leanlink only, reading not recorded
- Lean proofgithub.com · SmoothYau.leanlink only, reading not recorded
- Lean proofgithub.com · YauCounterexample.leanlink only, reading not recorded
Method
The openai/math repository contains three manuscripts dated September 23, 2026 (family 350, section “Differential geometry” of overview.tex): “Sharp nodal length on smooth surfaces”, “Smooth counterexamples to Yau's nodal upper bound in dimensions three and four” and “Power-law violations of Yau's nodal upper bound”. The file lean/docs/350.md, which “describes the scope of the Lean formalization”, comes with 3 Comparator statements: lean/ComparatorChallenges/NodalLength.lean, lean/ComparatorChallenges/SmoothYau.lean and lean/ComparatorChallenges/YauCounterexample.lean. The recorded note is: family present in the `sources` of formalization.yaml; history.md reports no revision; commit fd4aeeb of October 7, 2026. 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).
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 (Differential geometry)
- In openai/math
- family 350, section “Differential geometry”, 3 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 344 of 372, by family number
- Not evaluated : Counterexamples to strong forms of Arnold's fixed-point conjecture (family 347)
- Not evaluated : Nonnegatively curved Einstein four-manifolds and a topological gap (family 348)
- Not evaluated : The Solomon–Yau least-volume conjecture (family 349)
- Not evaluated : Yau's nodal conjecture: surfaces and counterexamples (family 350)
- Not evaluated : Scalar curvature detects four-dimensional Ricci-flow singularities (family 351)
- Not evaluated : Finite-time singularity of Calabi flow (family 352)
- Not evaluated : The sharp dimension threshold for affine Bernstein rigidity (family 353)
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