Not evaluated
The sharp ordinary-double-point volume gap (family 037)
The gist
On October 6, 2026, OpenAI released two manuscripts from an unreleased internal model on the volume gap of ordinary double points, a type of singularity in geometry.
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-037-sharp-ordinary-double-point-volume-gap-r1
@misc{discoveria-oai-fam-037-sharp-ordinary-double-point-volume-gap-r1,
author = {{DiscoverIA}},
title = {The sharp ordinary-double-point volume gap (family 037)},
howpublished = {DiscoverIA registry, entry oai-fam-037-sharp-ordinary-double-point-volume-gap},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-037-sharp-ordinary-double-point-volume-gap#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
An ordinary double point is one of the simplest singularities: a place where a geometric shape, smooth elsewhere, pinches like the tip of a cone. If the manuscripts held, they would, going by their titles, establish a sharp (optimal) gap for these points, in every dimension and then for the normalised volume in dimension four; the sources read do not give their precise statement.
What remains unclear
No Lean proof (checkable by computer) is supplied for this family, and no third-party assessment is recorded. The sources read do not say where the question stood before the announcement.
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 · The-ordinary-double-point…link only, reading not recorded
- Repositorygithub.com · The-normalized-volume-gap…link only, reading not recorded
Method
In the openai/math repository, family 037 comprises two manuscripts dated September 24, 2026: "The ordinary-double-point gap in every dimension" and "The normalized-volume gap in dimension four". No revision is reported in history.md. The absence of Lean is inferred from the absence of the file lean/docs/037.md; OpenAI's README states that not all manuscripts have a Lean formalisation. 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 (Algebraic and complex geometry)
- In openai/math
- family 037, section “Algebraic and complex geometry”, 2 manuscripts dated Sep 24, 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 37 of 372, by family number
- Not evaluated : Log abundance and effective Iitaka fibrations (family 034)
- Not evaluated : Threefold log abundance in numerical dimension one in characteristic p>3 (family 035)
- Not evaluated : Numerical semiampleness and generalized minimal models (family 036)
- Not evaluated : The sharp ordinary-double-point volume gap (family 037)
- Not evaluated : Fujita's freeness conjecture (family 038)
- Not evaluated : Nagata's conjecture and maximal Seshadri constants (family 039)
- Not evaluated : Bloch's conjecture for complex surfaces (family 040)
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