Not evaluated
Integral counterexamples to Gersten’s conjecture (family 209)
The gist
In its release of October 6, 2026, OpenAI announces two manuscripts, each presenting an “integral” counterexample to Gersten's conjecture.
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-209-integral-counterexamples-gerstens-conjecture-r1
@misc{discoveria-oai-fam-209-integral-counterexamples-gerstens-conjecture-r1,
author = {{DiscoverIA}},
title = {Integral counterexamples to Gersten’s conjecture (family 209)},
howpublished = {DiscoverIA registry, entry oai-fam-209-integral-counterexamples-gerstens-conjecture},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-209-integral-counterexamples-gerstens-conjecture#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 10 s reading time, estimated
What it changes
If either manuscript held, Gersten's conjecture would not be true in the setting it treats. The two manuscripts concern the same conjecture.
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 assessment is recorded.
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 · An-Integral…link only, reading not recorded
- Repositorygithub.com · An-Integral-Degree-Three…link only, reading not recorded
Method
The openai/math repository contains “An integral counterexample to Gersten's conjecture”, dated September 25, 2026. It also contains “An integral degree-three Gersten counterexample”, dated September 26, 2026. It contains no file lean/docs/209.md, and 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 (Algebra)
- In openai/math
- family 209, section “Algebra”, 2 manuscripts dated Sep 25, 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 203 of 372, by family number
- Not evaluated : Finite lattice representation: counterexamples and undecidability (family 206)
- Not evaluated : The ℓ¹-Bass and complex Bass trace conjectures (family 207)
- Not evaluated : The finite Benson–Etingof–Ostrik conjecture (family 208)
- Not evaluated : Integral counterexamples to Gersten’s conjecture (family 209)
- Not evaluated : Foulkes’ conjecture for sixth powers and quadratic stabilization (family 210)
- Not evaluated : Geometry, diffusion, and spectra of random planar maps (family 211)
- Not evaluated : No bigeodesics and smooth limit shapes in planar first-passage percolation (family 212)
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