Not evaluated
The Kervaire invariant problem at the prime three (family 309)
The gist
On October 6, 2026, OpenAI announced a new result on the Kervaire invariant problem at the prime three, 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-309-kervaire-invariant-problem-prime-three-r1
@misc{discoveria-oai-fam-309-kervaire-invariant-problem-prime-three-r1,
author = {{DiscoverIA}},
title = {The Kervaire invariant problem at the prime three (family 309)},
howpublished = {DiscoverIA registry, entry oai-fam-309-kervaire-invariant-problem-prime-three},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-309-kervaire-invariant-problem-prime-three#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
Topology studies the properties of a shape that do not change when it is deformed without tearing or gluing it. If the manuscript were correct, it would bring a new result on this problem, which the repository files under topology.
What remains unclear
No Lean proof (Lean is a language in which a computer checks every step of a proof) is supplied for this family, and no third-party assessment is recorded. The sources read do not say exactly what the manuscript claims.
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-Kervaire-Invariant…link only, reading not recorded
Method
The openai/math repository contains one manuscript, “The Kervaire invariant problem at the prime three”, dated September 24, 2026 (family 309, section “Topology” of overview.tex). The absence of Lean is inferred from the absence of a lean/docs/309.md file; OpenAI's README states: “Not all have accompanying Lean formalizations.” history.md reports no revision for the manuscripts of 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).
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 309, section “Topology”, 1 manuscript dated Sep 24, 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 303 of 372, by family number
- 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)
- Not evaluated : The Kervaire invariant problem at the prime three (family 309)
- Not evaluated : Quillen's conjecture in rational homology (family 310)
- Not evaluated : Chai's invariant-ideal conjecture (family 311)
- Not evaluated : The Grothendieck homotopy hypothesis (family 312)
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