Not evaluated
A counterexample to Bang's cylinder-covering bound (family 100)
The gist
On October 6, 2026, OpenAI published four manuscripts from an unreleased internal model, presented as a counterexample to Bang's cylinder-covering bound.
DiscoverIA status on October 12, 2026: not evaluated, meaning no third-party evaluation found.
Text written by an AI, reviewed by Antoine Olivier,
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-100-counterexample-bangs-cylinder-covering-bound-r1
@misc{discoveria-oai-fam-100-counterexample-bangs-cylinder-covering-bound-r1,
author = {{DiscoverIA}},
title = {A counterexample to Bang's cylinder-covering bound (family 100)},
howpublished = {DiscoverIA registry, entry oai-fam-100-counterexample-bangs-cylinder-covering-bound},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-100-counterexample-bangs-cylinder-covering-bound#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 the counterexample held, Bang's cylinder-covering bound would not be valid as stated. OpenAI presents it as a new result in convex and metric geometry, not as the formalisation of an already known result.
What remains unclear
The Lean formalisation (Lean is a language in which a computer checks every step of a proof) is supplied by OpenAI alone, and the repository marks its review "unchecked". No third-party verification is recorded.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 100.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 · Finite-angular-cylinder…link only, reading not recorded
- Repositorygithub.com · Finite-cylinder…link only, reading not recorded
- Repositorygithub.com · Slope-field-perturbations…link only, reading not recorded
- Repositorygithub.com · Finite-triangular…link only, reading not recorded
- Lean proofgithub.com · 100.mdpage read word for word
- Lean proofgithub.com · CylinderCovering.leanlink only, reading not recorded
- Lean proofgithub.com · RuledCovering.leanlink only, reading not recorded
- Lean proofgithub.com · TriangularCovering.leanlink only, reading not recorded
Method
In the openai/math release (719 manuscripts, 372 families), family 100 has four manuscripts dated September 27, 2026: "Finite angular cylinder covers below the half-area bound", "Finite cylinder approximation of ruled sets", "Slope-field perturbations of the two-cylinder covering" and "Finite triangular approximation of radial sweeps". It also includes three Lean Comparator files (CylinderCovering, RuledCovering, TriangularCovering) described in lean/docs/100.md. It is absent from the sources of formalization.yaml, and history.md reports no revision of its manuscripts. 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 (Convex and metric geometry)
- In openai/math
- family 100, section “Convex and metric geometry”, 4 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
- 9 : 1 read word for word, 8 links only
- This entry
- Reviewed by Antoine Olivier, Oct 18, 2026
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 97 of 372, by family number
- Not evaluated : The Euclidean Steinitz–Bergström conjecture (family 097)
- Not evaluated : A negative answer to the Lang–Plaut problem (family 098)
- Not evaluated : The sharp distortion of edit distance into ℓ_1 (family 099)
- Not evaluated : A counterexample to Bang's cylinder-covering bound (family 100)
- Not evaluated : The sharp simplex conjecture for isotropic constants (family 101)
- Not evaluated : Claimed proof of the Unique Games Conjecture (family 102)
- Not evaluated : Derandomization of logarithmic space: L=RL=BPL (family 103)
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