Not evaluated
Toms–Winter and equivariant Jiang–Su stability (family 291)
The gist
On October 6, 2026, OpenAI announced four operator algebra manuscripts around Jiang–Su stability.
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-291-tomswinter-equivariant-jiangsu-stability-r1
@misc{discoveria-oai-fam-291-tomswinter-equivariant-jiangsu-stability-r1,
author = {{DiscoverIA}},
title = {Toms–Winter and equivariant Jiang–Su stability (family 291)},
howpublished = {DiscoverIA registry, entry oai-fam-291-tomswinter-equivariant-jiangsu-stability},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-291-tomswinter-equivariant-jiangsu-stability#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
If these manuscripts held up, they would bring new results on equivariant Jiang–Su stability, Cuntz comparison, nuclear dimension and uniform property Gamma. The titles do not state the exact statements.
What remains unclear
OpenAI itself supplies the Lean (a language in which a computer checks every step of a proof), and its review is marked “unchecked”. No third-party check or evaluation has been read.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 291.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 · Equivariant-Jiang-Su…link only, reading not recorded
- Repositorygithub.com · Cuntz-comparison-and…link only, reading not recorded
- Repositorygithub.com · Nuclear-dimension-and…link only, reading not recorded
- Repositorygithub.com · Tracial-projection…link only, reading not recorded
- Lean proofgithub.com · 291.mdpage read word for word
- Lean proofgithub.com · UniformGamma.leanlink only, reading not recorded
Method
Four manuscripts are published: “Equivariant Jiang–Su Stability for Amenable Actions in the Unital Stably Finite Case” (October 5, 2026), then “Cuntz comparison and Jiang–Su absorption”, “Nuclear dimension and Jiang–Su stability without elementary subquotients” and “Tracial projection methods and uniform property Gamma” (September 23, 2026). OpenAI supplies lean/docs/291.md and 1 Comparator statement, lean/ComparatorChallenges/UniformGamma.lean. 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 (Operator algebras)
- In openai/math
- family 291, section “Operator algebras”, 4 manuscripts 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
- 7 : 1 read word for word, 6 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 285 of 372, by family number
- Not evaluated : Kadison's similarity conjecture (family 288)
- Not evaluated : The strong Kadison–Kastler conjecture (family 289)
- Not evaluated : Connes' bicentralizer conjecture and relative bicentralizers (family 290)
- Not evaluated : Toms–Winter and equivariant Jiang–Su stability (family 291)
- Not evaluated : A counterexample to Kirchberg's norm-ultrapower embedding problem (family 292)
- Not evaluated : A counterexample to the hyperinvariant-subspace problem (family 293)
- Not evaluated : A counterexample to Kaplansky's quasitrace conjecture (family 294)
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