Not evaluated
Scalar curvature detects four-dimensional Ricci-flow singularities (family 351)
The gist
OpenAI presents on October 6, 2026 three manuscripts filed under differential geometry; one claims a closed Ricci flow with bounded scalar curvature and finite-time curvature blowup.
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-351-scalar-curvature-detects-four-dimensional-r1
@misc{discoveria-oai-fam-351-scalar-curvature-detects-four-dimensional-r1,
author = {{DiscoverIA}},
title = {Scalar curvature detects four-dimensional Ricci-flow singularities (family 351)},
howpublished = {DiscoverIA registry, entry oai-fam-351-scalar-curvature-detects-four-dimensional},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-351-scalar-curvature-detects-four-dimensional#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 first manuscript were correct, bounded scalar curvature would not always rule out curvature blowup in finite time; its title does not give the dimension. The other two manuscripts deal, going by their titles, with the smooth extension of Ricci flow in dimension four and with degenerating Ricci-flat trees.
What remains unclear
No third-party evaluation was read and no Lean file is provided for this family. The sources read give only the titles of the three manuscripts: they do not say how the manuscripts fit together.
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-closed-Ricci-flow-with…link only, reading not recorded
- Repositorygithub.com · Bounded-scalar-curvature…link only, reading not recorded
- Repositorygithub.com · Path-selection-and-an…link only, reading not recorded
Method
The stated origin is an unreleased internal model from OpenAI. The openai/math repository holds three manuscripts dated September 24, 2026, in the “Differential geometry” section. The first is titled “A closed Ricci flow with bounded scalar curvature and finite-time curvature blowup”. The second is titled “Bounded scalar curvature and smooth extension of four-dimensional Ricci flow”. The third is titled “Path selection and an elliptic inequality on degenerating Ricci-flat trees”. There is no lean/docs/351.md; 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 (Differential geometry)
- In openai/math
- family 351, section “Differential geometry”, 3 manuscripts dated Sep 24, 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 345 of 372, by family number
- 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)
- Not evaluated : Isoperimetric regions in the cubic three-torus (family 354)
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