Not evaluated
Gersten's conjecture for one-relator groups (family 258)
The gist
On October 6, 2026, OpenAI announced 2 manuscripts on one-relator groups, filed under the title “Gersten's conjecture for one-relator groups”.
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-258-gerstens-conjecture-one-relator-groups-r1
@misc{discoveria-oai-fam-258-gerstens-conjecture-one-relator-groups-r1,
author = {{DiscoverIA}},
title = {Gersten's conjecture for one-relator groups (family 258)},
howpublished = {DiscoverIA registry, entry oai-fam-258-gerstens-conjecture-one-relator-groups},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-258-gerstens-conjecture-one-relator-groups#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
A one-relator group is defined by generators and a single relation between them. If the manuscripts held, the first would conclude that those which are “Baumslag-Solitar-free” are hyperbolic, and the second would concern the “virtual compact specialness” of the hyperbolic ones.
What remains unclear
No Lean (a language in which a computer checks every step of a proof) is supplied, and no third-party evaluation is read in the sources. They do not specify the link between these 2 manuscripts and Gersten's conjecture.
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 · Baumslag-Solitar-free-one…link only, reading not recorded
- Repositorygithub.com · Virtual-compact…link only, reading not recorded
Method
2 manuscripts dated September 25, 2026: “Baumslag-Solitar-free one-relator groups are hyperbolic” and “Virtual compact specialness of hyperbolic one-relator groups”. The family is filed under the section “Group theory” (overview.tex), with no lean/docs/258.md. 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 (Group theory)
- In openai/math
- family 258, section “Group theory”, 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 252 of 372, by family number
- Not evaluated : Quasi-isometric rigidity of virtually polycyclic groups (family 255)
- Not evaluated : Howie's conjecture on equations over groups (family 256)
- Not evaluated : A hyperbolic group with no geometric CAT(0) action (family 257)
- Not evaluated : Gersten's conjecture for one-relator groups (family 258)
- Not evaluated : A group without fixed price (family 259)
- Not evaluated : Spacetime Penrose inequalities and rigidity (family 260)
- Not evaluated : Localization and delocalization in the Anderson model (family 261)
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