Not evaluated
A counterexample to the hyperinvariant-subspace problem (family 293)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, 2 manuscripts dated September 27, 2026 on invariant-projection counterexamples and a transitive commutant.
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-293-counterexample-hyperinvariant-subspace-r1
@misc{discoveria-oai-fam-293-counterexample-hyperinvariant-subspace-r1,
author = {{DiscoverIA}},
title = {A counterexample to the hyperinvariant-subspace problem (family 293)},
howpublished = {DiscoverIA registry, entry oai-fam-293-counterexample-hyperinvariant-subspace},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-293-counterexample-hyperinvariant-subspace#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
The set of operators that commute with a given operator is called its commutant. If the manuscripts were correct, the first would give invariant-projection counterexamples for every irrational rotation and the second a transitive commutant.
What remains unclear
The manuscript titles do not name the hyperinvariant-subspace problem (a closed subspace stable under every operator that commutes with a given operator), and the sources read do not say how the two are linked. The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI only; formalization.yaml carries the note “review: status: unchecked”, and no third-party assessment is recorded.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 293.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 · Invariant-projection…link only, reading not recorded
- Repositorygithub.com · Backward-intertwiners-and…link only, reading not recorded
- Lean proofgithub.com · 293.mdpage read word for word
- Lean proofgithub.com · BackwardIntertwiners.leanlink only, reading not recorded
- Lean proofgithub.com · ContinuousCircleWeight.lea…link only, reading not recorded
- Lean proofgithub.com · FiniteFactor.leanlink only, reading not recorded
- Lean proofgithub.com · HyperinvariantSubspaces.le…link only, reading not recorded
- Lean proofgithub.com · IrrationalRotation.leanlink only, reading not recorded
- Lean proofgithub.com · ProductBrown.leanlink only, reading not recorded
Method
The openai/math repository contains 2 manuscripts: “Invariant-projection counterexamples for every irrational rotation” and “Backward intertwiners and a transitive commutant”. OpenAI supplies lean/docs/293.md and 6 Comparator files, including lean/ComparatorChallenges/HyperinvariantSubspaces.lean and lean/ComparatorChallenges/IrrationalRotation.lean. According to history.md, no revision is reported. 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 293, section “Operator algebras”, 2 manuscripts dated Sep 27, 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
- 10 : 1 read word for word, 9 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 287 of 372, by family number
- 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)
- Not evaluated : The generator problem for finite factors (family 296)
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