Not evaluated
The Popa–Vaes quadratic strong-operator paving conjecture (family 300)
The gist
In its release of October 6, 2026, OpenAI presents two manuscripts, dated September 25, 2026, on paving over arbitrary maximal abelian subalgebras.
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-300-popavaes-quadratic-strong-operator-paving-r1
@misc{discoveria-oai-fam-300-popavaes-quadratic-strong-operator-paving-r1,
author = {{DiscoverIA}},
title = {The Popa–Vaes quadratic strong-operator paving conjecture (family 300)},
howpublished = {DiscoverIA registry, entry oai-fam-300-popavaes-quadratic-strong-operator-paving},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-300-popavaes-quadratic-strong-operator-paving#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 were correct, their results would apply, going by their titles, to arbitrary maximal abelian subalgebras, not to one particular subalgebra. The precise scope depends on statements that the sources read do not give.
What remains unclear
No third-party evaluation was read and no Lean file is provided for this family. The sources read do not show where the question stood before the announcement.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · README.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 · Approximation-Paving-over…link only, reading not recorded
- Repositorygithub.com · Quadratic-Strong-Operator…link only, reading not recorded
Method
The stated origin is an unreleased internal model from OpenAI. The openai/math repository holds two manuscripts dated September 25, 2026. They are titled “Approximation Paving over Arbitrary Maximal Abelian Subalgebras” and “Quadratic Strong-Operator Paving over Arbitrary Maximal Abelian Subalgebras”. There is no lean/docs/300.md; 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: “Not all have accompanying Lean formalizations.”).
Limits
DiscoverIA has not checked this result itself.
Key facts
- Claimed by
- OpenAI (unreleased internal model)
announced on Oct 6, 2026 - Nature
- new result
- Field
- Mathematics (Operator algebras)
- In openai/math
- family 300, section “Operator algebras”, 2 manuscripts dated Sep 25, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 3 : 3 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with no Lean proof supplied. No third-party evaluation read.
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 294 of 372, by family number
- 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)
- Not evaluated : The Popa–Vaes quadratic strong-operator paving conjecture (family 300)
- Not evaluated : Classification by trace cones after Razak–Jacelon stabilization (family 301)
- Not evaluated : The Phillips–Toms formula for minimal integer actions (family 302)
- Not evaluated : From ordinary to strong pure infiniteness (family 303)
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