Not evaluated
Markov type characterizes superreflexivity (family 327)
The gist
OpenAI claims, on October 6, 2026, in a manuscript dated September 23, 2026, that nontrivial Markov type forces superreflexivity.
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-327-markov-type-characterizes-superreflexivity-r1
@misc{discoveria-oai-fam-327-markov-type-characterizes-superreflexivity-r1,
author = {{DiscoverIA}},
title = {Markov type characterizes superreflexivity (family 327)},
howpublished = {DiscoverIA registry, entry oai-fam-327-markov-type-characterizes-superreflexivity},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-327-markov-type-characterizes-superreflexivity#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 10 s reading time, estimated
What it changes
If the manuscript held, it would link two properties of functional analysis by an implication: nontrivial Markov type and superreflexivity.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI alone, with the mention “review: status: unchecked” in formalization.yaml. No third-party verification has been read.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 327.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 · Nontrivial-Markov-Type…link only, reading not recorded
- Lean proofgithub.com · 327.mdpage read word for word
- Lean proofgithub.com · MarkovType.leanlink only, reading not recorded
Method
The manuscript “Nontrivial Markov Type Forces Superreflexivity”, dated September 23, 2026, is the only one in family 327. A Comparator statement accompanies it (lean/ComparatorChallenges/MarkovType.lean, described in lean/docs/327.md); the family is present in the sources of formalization.yaml. 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 (Functional analysis)
- In openai/math
- family 327, 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 321 of 372, by family number
- 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)
- Not evaluated : A negative answer to Kalton's Lipschitz-free approximation question (family 330)
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