Not evaluated
Gromov's integral scalar-curvature inequality (family 335)
The gist
On October 6, 2026, OpenAI announced two differential geometry manuscripts on scalar curvature, 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-335-gromovs-integral-scalar-curvature-inequality-r1
@misc{discoveria-oai-fam-335-gromovs-integral-scalar-curvature-inequality-r1,
author = {{DiscoverIA}},
title = {Gromov's integral scalar-curvature inequality (family 335)},
howpublished = {DiscoverIA registry, entry oai-fam-335-gromovs-integral-scalar-curvature-inequality},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-335-gromovs-integral-scalar-curvature-inequality#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 these manuscripts were correct, one would bring an integral scalar curvature bound for real simplicial volume, the other would show that positive scalar curvature forces rational inessentiality. These are two distinct results, filed by the repository under differential geometry.
What remains unclear
No proof in Lean (a language in which a computer checks every step of a proof) is supplied, and no third-party assessment is recorded. The sources read do not specify how these two manuscripts relate to the Gromov inequality that gives the entry its title.
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 · An-integral-scalar…link only, reading not recorded
- Repositorygithub.com · Positive-scalar-curvature…link only, reading not recorded
Method
The openai/math repository contains two manuscripts, in the “Differential geometry” section: “Positive scalar curvature forces rational inessentiality” (September 23, 2026) and “An integral scalar curvature bound for real simplicial volume” (October 5, 2026). No Lean is supplied for this family (no lean/docs/335.md file); OpenAI's README states that not all manuscripts have a Lean formalisation. history.md reports no revision of these manuscripts. 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 335, section “Differential geometry”, 2 manuscripts dated Sep 23, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 3 : 3 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 329 of 372, by family number
- Not evaluated : Metric Markov cotype two for ℓ_1 (family 332)
- 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)
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