Not evaluated
The four-dimensional Singer conjecture (family 315)
The gist
On October 6, 2026, OpenAI announced a manuscript on the Singer conjecture in dimension four, 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-315-four-dimensional-singer-conjecture-r1
@misc{discoveria-oai-fam-315-four-dimensional-singer-conjecture-r1,
author = {{DiscoverIA}},
title = {The four-dimensional Singer conjecture (family 315)},
howpublished = {DiscoverIA registry, entry oai-fam-315-four-dimensional-singer-conjecture},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-315-four-dimensional-singer-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, dated September 25, 2026, were correct, it would bring a result on this conjecture, which the repository files under topology.
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 say whether the manuscript addresses the whole conjecture or only part of it.
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-Singer-conjecture-in…link only, reading not recorded
Method
The openai/math repository contains one manuscript, “The Singer conjecture in dimension four”, in the “Topology” section. The absence of Lean is inferred from the absence of a lean/docs/315.md file; OpenAI's README states that not all manuscripts have a Lean formalisation. history.md reports no revision of 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 315, section “Topology”, 1 manuscript dated Sep 25, 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 309 of 372, by family number
- Not evaluated : The Grothendieck homotopy hypothesis (family 312)
- Not evaluated : Finite generation for the K(n)-local sphere (family 313)
- Not evaluated : The chromatic Smith fixed-point problem for finite p-groups (family 314)
- Not evaluated : The four-dimensional Singer conjecture (family 315)
- Not evaluated : Curtis’s conjecture (family 316)
- Not evaluated : Thomason model structures in every strict higher dimension (family 317)
- Not evaluated : Chromatic splitting: counterexamples and filtrations (family 318)
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