Not evaluated
A counterexample to Kaplansky's quasitrace conjecture (family 294)
The gist
On October 6, 2026, OpenAI claimed a counterexample to Kaplansky's quasitrace conjecture and a failure of tensor-product stable finiteness.
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-294-counterexample-kaplanskys-quasitrace-r1
@misc{discoveria-oai-fam-294-counterexample-kaplanskys-quasitrace-r1,
author = {{DiscoverIA}},
title = {A counterexample to Kaplansky's quasitrace conjecture (family 294)},
howpublished = {DiscoverIA registry, entry oai-fam-294-counterexample-kaplanskys-quasitrace},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-294-counterexample-kaplanskys-quasitrace#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 up, an example would contradict this conjecture, and stable finiteness might not be preserved by tensor products. The titles do not say in which class of algebras this counterexample lies.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is provided by OpenAI alone, and its review is marked “unchecked”; it is not known whether a third party has checked it.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 294.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-counterexample-to…link only, reading not recorded
- Lean proofgithub.com · 294.mdpage read word for word
- Lean proofgithub.com · KaplanskyQuasitrace.leanlink only, reading not recorded
- Lean proofgithub.com · KaplanskyStableFiniteness.…link only, reading not recorded
Method
A single manuscript, “A counterexample to Kaplansky's quasitrace conjecture and failure of tensor-product stable finiteness”, dated September 23, 2026. The repository provides lean/docs/294.md and two Comparator files, KaplanskyQuasitrace.lean and KaplanskyStableFiniteness.lean; the family is noted as “présente des `sources` de formalization.yaml”. No revision is recorded in history.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: “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 294, 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
- 5 : 1 read word for word, 4 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 288 of 372, by family number
- 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)
- Not evaluated : The generator problem for finite factors (family 296)
- Not evaluated : A ZFC counterexample to Naimark's problem (family 297)
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