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Not evaluated

The Mahler conjectures and symplectic width (family 087)

The gist

On October 6, 2026, OpenAI announced, from an unreleased internal model, three manuscripts on the Mahler conjectures, with Lean files supplied by OpenAI.

DiscoverIA status on October 12, 2026: not evaluated, meaning no third-party evaluation found.

Status detailsDetails

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.

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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

DiscoverIA. (2026, October 12). The Mahler conjectures and symplectic width (family 087) [Status: Not evaluated, snapshot 1]. DiscoverIA registry. https://discoveria.ai/entry/oai-fam-087-mahler-conjectures-symplectic-width#releve-1

BibTeX @misc, key discoveria-oai-fam-087-mahler-conjectures-symplectic-width-r1

@misc{discoveria-oai-fam-087-mahler-conjectures-symplectic-width-r1,
  author       = {{DiscoverIA}},
  title        = {The Mahler conjectures and symplectic width (family 087)},
  howpublished = {DiscoverIA registry, entry oai-fam-087-mahler-conjectures-symplectic-width},
  note         = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
  year         = {2026},
  url          = {https://discoveria.ai/entry/oai-fam-087-mahler-conjectures-symplectic-width#releve-1},
  urldate      = {2026-10-12}
}

Dated link opens this snapshot in the history

https://discoveria.ai/entry/oai-fam-087-mahler-conjectures-symplectic-width#releve-1

To understand ≈ 30 s reading time, estimated

What it changes

The Mahler conjecture concerns the product of the volume of a convex body (a shape with no dents) and that of its polar, its dual shape. If the manuscripts were correct, they would bring results on its symmetric version, equality cases included, and on its version for general convex bodies, with a link to symplectic width according to their titles.

What remains unclear

The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI alone: it is marked “unchecked” in the repository, and no third-party verification is recorded. The sources read do not detail how far this formalisation reaches relative to the manuscripts.

For experts

Sources, method, key facts, status history, report an error

Status

Not evaluated

Recorded on · github.com · 087.md

Step 1 of 4 on the scale: not evaluated. Next step: under review.

  1. Announced
  2. Recordednot evaluated
  3. 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.

Full history

Proofs
manuscrit : The symmetric Mahler conjecture and its equality cases (preprints/The-symmetric-Mahler-conjecture-and-its-equality-cases-September-22-2026), manuscrit : The Mahler Conjecture for General Convex Bodies (preprints/The-Mahler-Conjecture-for-General-Convex-Bodies-September-22-2026), manuscrit : Symplectic Balls in Symmetric Polar Products (preprints/Symplectic-Balls-in-Symmetric-Polar-Products-September-22-2026), résumé de raisonnement famille 087 (reasoning_traces/symmetric-and-general-mahler-conjectures.pdf), Lean fourni par le revendicateur : lean/docs/087.md, 4 énoncé(s) Comparator (non vérifié par un tiers)

Sources

Method

The openai/math repository contains three manuscripts dated September 22, 2026: “The symmetric Mahler conjecture and its equality cases”, “The Mahler Conjecture for General Convex Bodies” and “Symplectic Balls in Symmetric Polar Products”, together with a reasoning summary (reasoning_traces/symmetric-and-general-mahler-conjectures.pdf). The Lean is described in lean/docs/087.md and spread over four files in the lean/ComparatorChallenges folder (GeneralMahler.lean, MahlerConjecture.lean, SymmetricMahlerEquality.lean, SymmetricPolar.lean), that is four Comparator statements. history.md reports no revision of these 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 087, section “Convex and metric geometry”, 3 manuscripts dated Sep 22, 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
AI draft, not reviewed

Status history

Only one observation so far.

  1. 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 84 of 372, by family number

See all 372 entries

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