Not evaluated
The three-dimensional Ball–Evans approximation problem (family 368)
The gist
OpenAI presents, on October 6, 2026, two manuscripts dated September 24, 2026 on strong diffeomorphic approximation in three dimensions, one for 1≤p≤2, the other for p>2.
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-368-three-dimensional-ballevans-approximation-r1
@misc{discoveria-oai-fam-368-three-dimensional-ballevans-approximation-r1,
author = {{DiscoverIA}},
title = {The three-dimensional Ball–Evans approximation problem (family 368)},
howpublished = {DiscoverIA registry, entry oai-fam-368-three-dimensional-ballevans-approximation},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-368-three-dimensional-ballevans-approximation#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 both manuscripts held, they would treat strong approximation by diffeomorphisms (smooth bijections whose inverse is smooth) in three dimensions, separately for 1≤p≤2 and for p>2. The field concerned is partial differential equations.
What remains unclear
No Lean (a language in which a computer checks every step of a proof) is supplied for this family, and no third-party evaluation has been read. The repository says only that not all manuscripts have a Lean formalisation.
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 · …1-le-p-le-2-September-24…link only, reading not recorded
- Repositorygithub.com · …p-gt-2-September-24-2026link only, reading not recorded
Method
Two manuscripts: “Strong diffeomorphic approximation in three dimensions for 1≤p≤2” and “Strong diffeomorphic approximation in three dimensions for p>2”, dated September 24, 2026. There is no lean/docs/368.md for this family. 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 (Partial differential equations)
- In openai/math
- family 368, section “Partial differential equations”, 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 361 of 372, by family number
- Not evaluated : Joint metric and connection recovery from one boundary patch (family 365)
- Not evaluated : The planar Mumford–Shah regularity conjecture (family 366)
- Not evaluated : The critical dimension for the one-phase Bernoulli problem (family 367)
- Not evaluated : The three-dimensional Ball–Evans approximation problem (family 368)
- Not evaluated : The hot spots conjecture for simply connected planar domains (family 369)
- Not evaluated : The subcritical Lane–Emden and Hénon–Lane–Emden conjectures (family 370)
- Not evaluated : Stable blowup for a defocusing Schrödinger equation (family 371)
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