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Not evaluated

The three-quarter diameter exponent for honeycomb walks (family 237)

The gist

On October 6, 2026, OpenAI announced 13 manuscripts on walks on the honeycomb lattice, filed under the title “The three-quarter diameter exponent for honeycomb walks”.

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 three-quarter diameter exponent for honeycomb walks (family 237) [Status: Not evaluated, snapshot 1]. DiscoverIA registry. https://discoveria.ai/entry/oai-fam-237-three-quarter-diameter-exponent-honeycomb#releve-1

BibTeX @misc, key discoveria-oai-fam-237-three-quarter-diameter-exponent-honeycomb-r1

@misc{discoveria-oai-fam-237-three-quarter-diameter-exponent-honeycomb-r1,
  author       = {{DiscoverIA}},
  title        = {The three-quarter diameter exponent for honeycomb walks (family 237)},
  howpublished = {DiscoverIA registry, entry oai-fam-237-three-quarter-diameter-exponent-honeycomb},
  note         = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
  year         = {2026},
  url          = {https://discoveria.ai/entry/oai-fam-237-three-quarter-diameter-exponent-honeycomb#releve-1},
  urldate      = {2026-10-12}
}

Dated link opens this snapshot in the history

https://discoveria.ai/entry/oai-fam-237-three-quarter-diameter-exponent-honeycomb#releve-1

To understand ≈ 20 s reading time, estimated

What it changes

If the manuscripts held, they would describe how the diameter of these walks grows with their length. An exponent is a number r such that the diameter behaves roughly like the length raised to the power r.

What remains unclear

The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI alone, and formalization.yaml marks it “unchecked”. No third-party evaluation is read, and the sources do not say what each of the 13 manuscripts establishes.

For experts

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

Status

Not evaluated

Recorded on · github.com · 237.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 : Radial transfer estimates and polygon length laws for honeycomb walks (preprints/Radial-transfer-estimates-and-polygon-length-laws-for-honeycomb-walks-September-26-2026), manuscrit : Critical honeycomb chords with prescribed boundary endpoints (preprints/Critical-honeycomb-chords-with-prescribed-boundary-endpoints-September-26-2026), manuscrit : Cylinder loop weights and planar nesting (preprints/Cylinder-loop-weights-and-planar-nesting-September-26-2026), manuscrit : Mass and covering exponents for fixed-length honeycomb walks (preprints/Mass-and-covering-exponents-for-fixed-length-honeycomb-walks-September-26-2026), manuscrit : Signed cylinder propagation and marked polygons on the honeycomb lattice (preprints/Signed-cylinder-propagation-and-marked-polygons-on-the-honeycomb-lattice-September-26-2026), manuscrit : Cylinder amplitudes and logarithmic bridge-length windows on the honeycomb lattice (preprints/Cylinder-amplitudes-and-logarithmic-bridge-length-windows-on-the-honeycomb-lattice-September-26-2026), manuscrit : Marked polygon correlations and one-arc bounds (preprints/Marked-polygon-correlations-and-one-arc-bounds-September-26-2026), manuscrit : Disk transfer representations and confined bridge mass (preprints/Disk-transfer-representations-and-confined-bridge-mass-September-26-2026), manuscrit : Polynomial vacuum representations and bridge mass for honeycomb walks (preprints/Polynomial-vacuum-representations-and-bridge-mass-for-honeycomb-walks-September-26-2026), manuscrit : Renewal and changes of law for critical honeycomb walks (preprints/Renewal-and-changes-of-law-for-critical-honeycomb-walks-September-26-2026), manuscrit : Critical strip-crossing mass on the honeycomb lattice (preprints/Critical-strip-crossing-mass-on-the-honeycomb-lattice-September-26-2026), manuscrit : Uniform marked-polygon estimates and sharp finite bridge moments (preprints/Uniform-marked-polygon-estimates-and-sharp-finite-bridge-moments-September-26-2026), manuscrit : Cap-selected amplitudes and triangle chords for honeycomb walks (preprints/Cap-selected-amplitudes-and-triangle-chords-for-honeycomb-walks-September-26-2026), Lean fourni par le revendicateur : lean/docs/237.md, 4 énoncé(s) Comparator (non vérifié par un tiers)

Sources

Method

13 manuscripts dated September 26, 2026, including “Radial transfer estimates and polygon length laws for honeycomb walks”, “Mass and covering exponents for fixed-length honeycomb walks” and “Critical strip-crossing mass on the honeycomb lattice”. Lean supplied by OpenAI: 4 Comparator statements (CriticalStripMass.lean, HoneycombBridgeFiniteness.lean, HoneycombBridgeMassSupport.lean, HoneycombFreeEnergy.lean), described in lean/docs/237.md; family present in the “sources” of formalization.yaml. 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 (Probability and statistical mechanics)
In openai/math
family 237, section “Probability and statistical mechanics”, 13 manuscripts dated Sep 26, 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
19 : 1 read word for word, 18 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 231 of 372, by family number

See all 372 entries

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