Not evaluated
A non-residually-finite torsion-free hyperbolic group (family 252)
The gist
In its release of October 6, 2026, OpenAI claims a torsion-free hyperbolic group that is not residually finite (manuscript dated September 23, 2026).
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-252-non-residually-finite-torsion-free-r1
@misc{discoveria-oai-fam-252-non-residually-finite-torsion-free-r1,
author = {{DiscoverIA}},
title = {A non-residually-finite torsion-free hyperbolic group (family 252)},
howpublished = {DiscoverIA registry, entry oai-fam-252-non-residually-finite-torsion-free},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-252-non-residually-finite-torsion-free#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
If the manuscript held, it would describe a torsion-free group: no element other than the identity returns to the identity after being multiplied by itself a certain number of times. This group would not be residually finite: for at least one non-identity element, every finite quotient (a reduced, finite version of the group) sends it to the identity. The subject belongs to group theory.
What remains unclear
No third party is recorded as a checker, and the Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI itself, marked “unchecked”. The sources read do not say how the group is constructed.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 252.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-torsion-free-hyperbolic…link only, reading not recorded
- Lean proofgithub.com · 252.mdpage read word for word
- Lean proofgithub.com · TorsionFreeHyperbolic.leanlink only, reading not recorded
Method
OpenAI publishes in its openai/math repository the manuscript “A torsion-free hyperbolic group that is not residually finite”, dated September 23, 2026, the only one of family 252. Lean supplied: lean/docs/252.md and lean/ComparatorChallenges/TorsionFreeHyperbolic.lean (1 Comparator statement). The family is present in the `sources` of formalization.yaml; history.md reports no revision. 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: “describes the scope of the Lean formalization”).
Limits
No named third party: the recorded checks come from the claimant or from a platform tool. The claimant supplies a Lean proof; as of this date, DiscoverIA has found no independent verification of this proof or of the result.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (Group theory)
- In openai/math
- family 252, section “Group theory”, 1 manuscript dated Sep 23, 2026
- Lean proof
- supplied by the claimant, marked “unchecked” (not reviewed) in its repository
- Revisions
- none reported by the claimant
- Checked by
- claimant (Lean supplied, not checked by a third party)
- Sources
- 4 : 1 read word for word, 3 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with a Lean proof supplied by the claimant. No third-party check read; the source marks this proof as not reviewed (“unchecked”).
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 246 of 372, by family number
- Not evaluated : A finitely generated counterexample to Eilenberg–Ganea (family 249)
- Not evaluated : The Boone–Higman conjecture and higher finiteness (family 250)
- Not evaluated : Amenability, unitarizability, and Ulam stability (family 251)
- Not evaluated : A non-residually-finite torsion-free hyperbolic group (family 252)
- Not evaluated : An infinite finitely presented simple amenable group (family 253)
- Not evaluated : Artin's K(π,1) conjecture and CAT(0) obstructions (family 254)
- Not evaluated : Quasi-isometric rigidity of virtually polycyclic groups (family 255)
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