Not evaluated
Quasi-isometric rigidity of virtually polycyclic groups (family 255)
The gist
On October 6, 2026, OpenAI announced a manuscript on quasi-isometric recognition of virtually polycyclic groups, 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-255-quasi-isometric-rigidity-virtually-r1
@misc{discoveria-oai-fam-255-quasi-isometric-rigidity-virtually-r1,
author = {{DiscoverIA}},
title = {Quasi-isometric rigidity of virtually polycyclic groups (family 255)},
howpublished = {DiscoverIA registry, entry oai-fam-255-quasi-isometric-rigidity-virtually},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-255-quasi-isometric-rigidity-virtually#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
Two groups are quasi-isometric when they have the same large-scale geometry. A group is virtually polycyclic when it contains a polycyclic subgroup (built by a sequence of cyclic steps) of finite index. If the manuscript were correct, it would specify what this geometry determines for this family of groups.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI: the repository marks its review “unchecked”, and no third-party verification has been found. The sources read do not give the exact statement of the recognition result.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 255.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 · quasi-isometric…link only, reading not recorded
- Lean proofgithub.com · 255.mdpage read word for word
- Lean proofgithub.com · PolycyclicRecognition.leanlink only, reading not recorded
Method
The manuscript “Quasi-isometric recognition of virtually polycyclic groups” is dated September 24, 2026; family 255 has only this one, filed under the section “Group theory” of overview.tex. The repository contains lean/docs/255.md and one Comparator statement (PolycyclicRecognition.lean, in lean/ComparatorChallenges). The family is absent from the sources of formalization.yaml, and 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 255, section “Group theory”, 1 manuscript dated Sep 24, 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 249 of 372, by family number
- 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)
- 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)
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