Not evaluated
Spectral scalar curvature and codimension-two width (family 336)
The gist
On October 6, 2026, OpenAI published three manuscripts on scalar curvature and notions of width, from an unreleased internal model.
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-336-spectral-scalar-curvature-codimension-two-r1
@misc{discoveria-oai-fam-336-spectral-scalar-curvature-codimension-two-r1,
author = {{DiscoverIA}},
title = {Spectral scalar curvature and codimension-two width (family 336)},
howpublished = {DiscoverIA registry, entry oai-fam-336-spectral-scalar-curvature-codimension-two},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-336-spectral-scalar-curvature-codimension-two#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
These manuscripts belong to differential geometry. If their results were correct, they would concern scalar curvature (positive, or “spectral”) and two kinds of width (“Urysohn width”, “codimension-two width”). One of them is set in dimension three.
What remains unclear
The sources read do not state the results of these three manuscripts. No Lean (a language in which a computer checks every step of a proof) is supplied for this family, and the sources read report no third-party assessment.
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 · …uniform-Urysohn-width…link only, reading not recorded
- Repositorygithub.com · …Urysohn-width-in…link only, reading not recorded
- Repositorygithub.com · Positive-scalar-curvature…link only, reading not recorded
Method
Three manuscripts of family 336 are listed in CONTENTS.md of the openai/math repository. One, dated September 23, 2026, is “Positive scalar curvature and uniform codimension-two width”. The other two, dated October 5, 2026, are “Spectral scalar curvature and uniform Urysohn width” and “Spectral scalar curvature and Urysohn width in dimension three”. There is no lean/docs/336.md; the repository README states: “Not all have accompanying Lean formalizations.” 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).
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 (Differential geometry)
- In openai/math
- family 336, section “Differential geometry”, 3 manuscripts dated Sep 23, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 4 : 4 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 330 of 372, by family number
- Not evaluated : Smooth isometric immersions of surfaces into ℝ⁴ (family 333)
- Not evaluated : A smooth surface metric with no local immersion in ℝ³ (family 334)
- Not evaluated : Gromov's integral scalar-curvature inequality (family 335)
- Not evaluated : Spectral scalar curvature and codimension-two width (family 336)
- Not evaluated : Cartan–Hadamard isoperimetry and CAT(0) fillings (family 337)
- Not evaluated : Yau's uniformization conjecture (family 338)
- Not evaluated : Katok's entropy rigidity conjecture (family 339)
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