Not evaluated
A counterexample to Wall's finite D(2) conjecture (family 321)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, a manuscript claiming a counterexample to Wall's D(2) problem.
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-321-counterexample-walls-finite-d-2-conjecture-r1
@misc{discoveria-oai-fam-321-counterexample-walls-finite-d-2-conjecture-r1,
author = {{DiscoverIA}},
title = {A counterexample to Wall's finite D(2) conjecture (family 321)},
howpublished = {DiscoverIA registry, entry oai-fam-321-counterexample-walls-finite-d-2-conjecture},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-321-counterexample-walls-finite-d-2-conjecture#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 manuscript were correct, Wall's D(2) conjecture, which OpenAI's repository files under topology, would be false.
What remains unclear
No Lean (a language in which a computer checks every step of a proof) is supplied and no third-party assessment is recorded, so it is not known whether anyone else has checked the counterexample. The family title speaks of Wall's “finite D(2)” conjecture and the manuscript of a “D(2) Problem”; the sources read do not say whether the statement is the same.
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-Counterexample-to-Walls…link only, reading not recorded
Method
The openai/math repository holds a single manuscript for family 321, “A Counterexample to Wall's D(2) Problem”, dated October 6, 2026, in the “Topology” section of overview.tex. The absence of Lean is inferred from the absence of a lean/docs/321.md file; OpenAI's README states that not all manuscripts have a Lean formalisation. According to history.md, no revision is reported for this manuscript. 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 321, section “Topology”, 1 manuscript dated Oct 6, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 2 : 2 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 315 of 372, by family number
- Not evaluated : Chromatic splitting: counterexamples and filtrations (family 318)
- Not evaluated : Counterexamples to the Hahn–Wilson conjecture at height two (family 319)
- Not evaluated : A four-dimensional counterexample to Borel rigidity (family 320)
- Not evaluated : A counterexample to Wall's finite D(2) conjecture (family 321)
- Not evaluated : Tingley's sphere-isometry problem (family 322)
- Not evaluated : Relative independence of the separable quotient problem (family 323)
- Not evaluated : Lipschitz equivalence without linear isomorphism (family 324)
Report an error or suggest a source
Thank you, your message was sent.
Sending failed. Try again, or write to contact@discoveria.ai.
Is your result listed?What each status requires, correcting this entry, replying to it.