Not evaluated
Counterexamples to disk embedding and Wall's manifold conjecture (family 305)
The gist
On October 6, 2026, OpenAI announced three topology manuscripts, from an unreleased internal model, on four-dimensional disk embedding and on a PD4 group.
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-305-counterexamples-disk-embedding-walls-r1
@misc{discoveria-oai-fam-305-counterexamples-disk-embedding-walls-r1,
author = {{DiscoverIA}},
title = {Counterexamples to disk embedding and Wall's manifold conjecture (family 305)},
howpublished = {DiscoverIA registry, entry oai-fam-305-counterexamples-disk-embedding-walls},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-305-counterexamples-disk-embedding-walls#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, two of them would provide obstructions to embedding a disk in dimension four, one depending only on the boundary, the other on a marked tensor. The third would describe a PD4 group without an aspherical manifold model.
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 title of the entry mentions counterexamples to Wall's manifold conjecture, but no manuscript title mentions them.
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-boundary-only…link only, reading not recorded
- Repositorygithub.com · A-marked-tensor…link only, reading not recorded
- Repositorygithub.com · A-PD4-group-without-an…link only, reading not recorded
Method
The openai/math repository contains three manuscripts dated September 24, 2026: “A boundary-only obstruction to four-dimensional disk embedding”, “A marked tensor obstruction to four-dimensional disk embedding” and “A PD4 group without an aspherical manifold model”, in the “Topology” section. The absence of Lean is inferred from the absence of a lean/docs/305.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 (Topology)
- In openai/math
- family 305, section “Topology”, 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 299 of 372, by family number
- Not evaluated : The Phillips–Toms formula for minimal integer actions (family 302)
- Not evaluated : From ordinary to strong pure infiniteness (family 303)
- Not evaluated : The Hilbert–Smith conjecture in every dimension (family 304)
- Not evaluated : Counterexamples to disk embedding and Wall's manifold conjecture (family 305)
- Not evaluated : The purely cosmetic surgery conjecture for knots in S³ (family 306)
- Not evaluated : Failure of rational injectivity for maximal coarse assembly (family 307)
- Not evaluated : Smith–Toda complexes at every height with varying primes (family 308)
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