Not evaluated
The generator problem for finite factors (family 296)
The gist
On October 6, 2026, OpenAI published a manuscript on relative generation and the generator problem for finite factors, 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-296-generator-problem-finite-factors-r1
@misc{discoveria-oai-fam-296-generator-problem-finite-factors-r1,
author = {{DiscoverIA}},
title = {The generator problem for finite factors (family 296)},
howpublished = {DiscoverIA registry, entry oai-fam-296-generator-problem-finite-factors},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-296-generator-problem-finite-factors#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
This manuscript belongs to operator algebras (section “Operator algebras” of overview.tex). If the manuscript were correct, it would provide a result on this problem for finite factors.
What remains unclear
The sources read do not state the manuscript's result. The Lean (a language in which a computer checks every step of a proof) was supplied by OpenAI and has not been verified by a third party: the repository records it as “review: status: unchecked”. The sources read report no third-party assessment of the manuscript.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 296.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 · Relative-generation-and…link only, reading not recorded
- Lean proofgithub.com · 296.mdpage read word for word
- Lean proofgithub.com · FactorGeneration.leanlink only, reading not recorded
- Lean proofgithub.com · RelativeGeneration.leanlink only, reading not recorded
Method
The manuscript “Relative generation and the generator problem for finite factors”, dated September 23, 2026, is listed in CONTENTS.md of the openai/math repository. The repository supplies lean/docs/296.md, which “describes the scope of the Lean formalization”. The repository also holds two Comparator statements: lean/ComparatorChallenges/FactorGeneration.lean and lean/ComparatorChallenges/RelativeGeneration.lean. 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).
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 296, 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 290 of 372, by family number
- 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)
- Not evaluated : A counterexample to Voiculescu’s free-entropy equality conjecture (family 298)
- Not evaluated : The Kirchberg–Rørdam character criterion (family 299)
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