Not evaluated
Sharp symplectic ball-packing criteria in higher dimensions (family 343)
The gist
In its release of October 6, 2026, OpenAI presents a manuscript, from an unreleased internal model, on symplectic ball packings in higher dimensions.
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-343-sharp-symplectic-ball-packing-criteria-r1
@misc{discoveria-oai-fam-343-sharp-symplectic-ball-packing-criteria-r1,
author = {{DiscoverIA}},
title = {Sharp symplectic ball-packing criteria in higher dimensions (family 343)},
howpublished = {DiscoverIA registry, entry oai-fam-343-sharp-symplectic-ball-packing-criteria},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-343-sharp-symplectic-ball-packing-criteria#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
According to the family title, “Sharp symplectic ball-packing criteria in higher dimensions”, the manuscript would deal with criteria for packing symplectic balls. If the manuscript held, it would supply these criteria in higher dimensions, in differential geometry; the sources read do not specify what “sharp” means.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) was supplied by OpenAI itself, and its tracking file marks it “unchecked”. No third-party verification is recorded. The sources read do not say whether the Lean statements match the manuscript's statements.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 343.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 · Symplectic-Ball-Packings…link only, reading not recorded
- Lean proofgithub.com · 343.mdpage read word for word
- Lean proofgithub.com · BallPacking.leanlink only, reading not recorded
- Lean proofgithub.com · BallPackingNecessity.leanlink only, reading not recorded
Method
The openai/math repository holds the manuscript “Symplectic Ball Packings in Higher Dimensions”, dated September 23, 2026. The file lean/docs/343.md describes the Lean formalisation, with two Comparator statements: lean/ComparatorChallenges/BallPacking.lean and lean/ComparatorChallenges/BallPackingNecessity.lean. In formalization.yaml the family is not among the listed sources; history.md reports no revision of this manuscript. 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 (Differential geometry)
- In openai/math
- family 343, section “Differential geometry”, 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
- 5 : 1 read word for word, 4 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 337 of 372, by family number
- Not evaluated : Counterexample to the nearby Lagrangian conjecture (family 340)
- Not evaluated : Donaldson's hypersymplectic deformation conjecture (family 341)
- Not evaluated : Donaldson's tamed-to-compatible conjecture (family 342)
- Not evaluated : Sharp symplectic ball-packing criteria in higher dimensions (family 343)
- Not evaluated : The metric Blaschke conjecture (family 344)
- Not evaluated : Infinitely many closed geodesics on spheres and three-manifolds (family 345)
- Not evaluated : Sharp singular-set bounds for stationary integral varifolds (family 346)
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