Not evaluated
The cotype–cotype conjecture under the approximation property (family 326)
The gist
On October 6, 2026, OpenAI published a manuscript on the cotype–cotype conjecture under the approximation property, 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-326-cotypecotype-conjecture-under-approximation-r1
@misc{discoveria-oai-fam-326-cotypecotype-conjecture-under-approximation-r1,
author = {{DiscoverIA}},
title = {The cotype–cotype conjecture under the approximation property (family 326)},
howpublished = {DiscoverIA registry, entry oai-fam-326-cotypecotype-conjecture-under-approximation},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-326-cotypecotype-conjecture-under-approximation#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 functional analysis (section “Functional analysis” of overview.tex). If its result were correct, it would concern the conjecture in the case where the approximation property is assumed.
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 · 326.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 · The-cotype-cotype…link only, reading not recorded
- Lean proofgithub.com · 326.mdpage read word for word
- Lean proofgithub.com · Cotype.leanlink only, reading not recorded
Method
The manuscript “The cotype–cotype conjecture under the approximation property”, dated September 23, 2026, is listed in CONTENTS.md of the openai/math repository. The repository supplies lean/docs/326.md, which “describes the scope of the Lean formalization”, and one Comparator statement: lean/ComparatorChallenges/Cotype.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 (Functional analysis)
- In openai/math
- family 326, section “Functional analysis”, 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 320 of 372, by family number
- Not evaluated : Relative independence of the separable quotient problem (family 323)
- Not evaluated : Lipschitz equivalence without linear isomorphism (family 324)
- Not evaluated : The complete Crouzeix conjecture (family 325)
- Not evaluated : The cotype–cotype conjecture under the approximation property (family 326)
- Not evaluated : Markov type characterizes superreflexivity (family 327)
- Not evaluated : Fixed points of nonexpansive maps in reflexive Banach spaces (family 328)
- Not evaluated : A counterexample to Pietsch's metric-entropy duality conjecture (family 329)
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