Not evaluated
Nonnegatively curved Einstein four-manifolds and a topological gap (family 348)
The gist
OpenAI presents, on October 6, 2026, three manuscripts on Einstein four-manifolds, dated September 23, October 4 and October 5, 2026.
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-348-nonnegatively-curved-einstein-four-manifolds-r1
@misc{discoveria-oai-fam-348-nonnegatively-curved-einstein-four-manifolds-r1,
author = {{DiscoverIA}},
title = {Nonnegatively curved Einstein four-manifolds and a topological gap (family 348)},
howpublished = {DiscoverIA registry, entry oai-fam-348-nonnegatively-curved-einstein-four-manifolds},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-348-nonnegatively-curved-einstein-four-manifolds#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 three manuscripts held, they would bring results in differential geometry on four-dimensional Einstein manifolds (spaces that, seen up close, resemble ordinary flat space): zero-plane rigidity, a gap for nonnegative curvature, and positive curvature.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI alone, with the mention “review: status: unchecked” in formalization.yaml. No third-party verification has been read.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 348.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 · Zero-Plane-Rigidity-for…link only, reading not recorded
- Repositorygithub.com · An-L2-Einstein-Gap-for…link only, reading not recorded
- Repositorygithub.com · Positively-curved…link only, reading not recorded
- Lean proofgithub.com · 348.mdpage read word for word
- Lean proofgithub.com · EinsteinFour.leanlink only, reading not recorded
Method
Three manuscripts: “Zero-Plane Rigidity for Einstein Four-Manifolds” (October 4, 2026), “An L2 Einstein Gap for Nonnegatively Curved Four-Manifolds” (October 5, 2026) and “Positively curved Einstein four-manifolds” (September 23, 2026). A single Comparator statement accompanies them (lean/ComparatorChallenges/EinsteinFour.lean, described in lean/docs/348.md); the family is absent from the sources of formalization.yaml. 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 (Differential geometry)
- In openai/math
- family 348, 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
- 6 : 1 read word for word, 5 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 342 of 372, by family number
- Not evaluated : Infinitely many closed geodesics on spheres and three-manifolds (family 345)
- Not evaluated : Sharp singular-set bounds for stationary integral varifolds (family 346)
- 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)
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