Not evaluated
Asymptotic midpoint uniform convexity without asymptotically uniformly convex renorming (family 331)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, seven manuscripts on “asymptotic midpoint uniform convexity” without “asymptotically uniformly convex” renorming.
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-331-asymptotic-midpoint-uniform-convexity-r1
@misc{discoveria-oai-fam-331-asymptotic-midpoint-uniform-convexity-r1,
author = {{DiscoverIA}},
title = {Asymptotic midpoint uniform convexity without asymptotically uniformly convex renorming (family 331)},
howpublished = {DiscoverIA registry, entry oai-fam-331-asymptotic-midpoint-uniform-convexity},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-331-asymptotic-midpoint-uniform-convexity#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
If the manuscripts were correct, they would bring new results in functional analysis, the field where OpenAI's repository files this family. A renorming replaces the norm of a space (its way of measuring lengths) by an equivalent norm, one comparable to the first up to a constant factor.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) was supplied by OpenAI itself and carries the mark “unchecked” in formalization.yaml; no third-party verification is recorded. The sources read do not say whether the seven Lean statements cover the seven manuscripts, nor whether those manuscripts claim the same result.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 331.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 · Asymptotic-midpoint…link only, reading not recorded
- Repositorygithub.com · Midpoint-lenses-in…link only, reading not recorded
- Repositorygithub.com · Diamond-distortion-from…link only, reading not recorded
- Repositorygithub.com · Exact-asymptotic-moduli…link only, reading not recorded
- Repositorygithub.com · …bounded-tree-potentials…link only, reading not recorded
- Repositorygithub.com · Independent-products-in…link only, reading not recorded
- Repositorygithub.com · …two-recursive-potentials…link only, reading not recorded
- Lean proofgithub.com · 331.mdpage read word for word
- Lean proofgithub.com · BoundedTreePotentials.leanlink only, reading not recorded
- Lean proofgithub.com · DaugavetModuli.leanlink only, reading not recorded
- Lean proofgithub.com · DiamondDistortion.leanlink only, reading not recorded
- Lean proofgithub.com · ForestSpace.leanlink only, reading not recorded
- Lean proofgithub.com · IndependentProducts.leanlink only, reading not recorded
- Lean proofgithub.com · MidpointLenses.leanlink only, reading not recorded
- Lean proofgithub.com · RecursivePotentials.leanlink only, reading not recorded
Method
In openai/math, family 331 comprises seven manuscripts dated September 27, 2026, including “Asymptotic midpoint uniform convexity and unbounded diamond distortion in a reflexive tree space” and “Independent products in real L1: asymptotic midpoint convexity without AUC renormings”. The Lean supplied comprises lean/docs/331.md and seven Comparator files, including lean/ComparatorChallenges/DaugavetModuli.lean. For formalization.yaml: family present in the “sources”; 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: “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 331, section “Functional analysis”, 7 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
- 16 : 1 read word for word, 15 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 325 of 372, by family number
- 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)
- Not evaluated : Asymptotic midpoint uniform convexity without asymptotically uniformly convex renorming (family 331)
- Not evaluated : Metric Markov cotype two for ℓ_1 (family 332)
- Not evaluated : Smooth isometric immersions of surfaces into ℝ⁴ (family 333)
- Not evaluated : A smooth surface metric with no local immersion in ℝ³ (family 334)
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