Not evaluated
Petty's projection-volume conjecture and simplex counterexamples (family 088)
The gist
On October 6, 2026, OpenAI presents two manuscripts, one on Petty's conjecture, the other claiming a counterexample to the simplex maximum for projection-body volume.
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-088-pettys-projection-volume-conjecture-simplex-r1
@misc{discoveria-oai-fam-088-pettys-projection-volume-conjecture-simplex-r1,
author = {{DiscoverIA}},
title = {Petty's projection-volume conjecture and simplex counterexamples (family 088)},
howpublished = {DiscoverIA registry, entry oai-fam-088-pettys-projection-volume-conjecture-simplex},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-088-pettys-projection-volume-conjecture-simplex#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
A simplex is the analogue, in any dimension, of the triangle and the tetrahedron; a projection body is a convex body built from the shadows of a body in all directions. If the manuscripts were correct, one would supply a product counterexample to the simplex maximum for projection-body volume, and the other would treat Petty's conjecture in dimensions at least four.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI itself: its review field reads “unchecked”, and no third-party verification is recorded.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 088.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 · Pettys-projection-volume…link only, reading not recorded
- Repositorygithub.com · A-product-counterexample…link only, reading not recorded
- Lean proofgithub.com · 088.mdpage read word for word
- Lean proofgithub.com · PettyProjectionVolume.leanlink only, reading not recorded
- Lean proofgithub.com · ProjectionCounterexample.l…link only, reading not recorded
- Lean proofgithub.com · ProjectionVolume.leanlink only, reading not recorded
Method
The two manuscripts are dated September 24, 2026 and attributed to an unreleased internal OpenAI model: “Petty’s projection-volume conjecture in dimensions at least four” and “A product counterexample to the simplex maximum for projection-body volume”. The formalisation is in lean/docs/088.md and in three files, lean/ComparatorChallenges/PettyProjectionVolume.lean, lean/ComparatorChallenges/ProjectionCounterexample.lean and lean/ComparatorChallenges/ProjectionVolume.lean (3 Comparator statements); the family appears in the sources of formalization.yaml, and 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 (Convex and metric geometry)
- In openai/math
- family 088, section “Convex and metric geometry”, 2 manuscripts dated Sep 24, 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
- 7 : 1 read word for word, 6 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 85 of 372, by family number
- Not evaluated : Endpoint regularity of the planar centered maximal function (family 085)
- Not evaluated : An L³ bound for the trilinear Hilbert transform (family 086)
- Not evaluated : The Mahler conjectures and symplectic width (family 087)
- Not evaluated : Petty's projection-volume conjecture and simplex counterexamples (family 088)
- Not evaluated : Bounded-distortion L_1 embeddings of planar and bounded-treewidth graphs (family 089)
- Not evaluated : Universal optimality of the triangular lattice (family 090)
- Not evaluated : The logarithmic Brunn–Minkowski conjecture (family 091)
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