Not evaluated
A counterexample to Kirchberg's norm-ultrapower embedding problem (family 292)
The gist
In its release of October 6, 2026, OpenAI claims an explicit obstruction to nuclear norm-ultrapower embeddings (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-292-counterexample-kirchbergs-norm-ultrapower-r1
@misc{discoveria-oai-fam-292-counterexample-kirchbergs-norm-ultrapower-r1,
author = {{DiscoverIA}},
title = {A counterexample to Kirchberg's norm-ultrapower embedding problem (family 292)},
howpublished = {DiscoverIA registry, entry oai-fam-292-counterexample-kirchbergs-norm-ultrapower},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-292-counterexample-kirchbergs-norm-ultrapower#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 the manuscript held, it would add a new result on these embeddings, in the field of operator algebras. The family is titled “A counterexample to Kirchberg's norm-ultrapower embedding problem”.
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 obstruction relates to Kirchberg's problem named in the family title.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 292.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-explicit-obstruction…link only, reading not recorded
- Lean proofgithub.com · 292.mdpage read word for word
- Lean proofgithub.com · NuclearUltrapower.leanlink only, reading not recorded
Method
OpenAI publishes in its openai/math repository the manuscript “An explicit obstruction to nuclear norm-ultrapower embeddings”, dated September 23, 2026, the only one of family 292. Lean supplied: lean/docs/292.md and lean/ComparatorChallenges/NuclearUltrapower.lean (1 Comparator statement). The family is absent from 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 (Operator algebras)
- In openai/math
- family 292, section “Operator algebras”, 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 286 of 372, by family number
- 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)
- Not evaluated : The Kadison–Ringrose cohomology conjecture (family 295)
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