Not evaluated
No bigeodesics and smooth limit shapes in planar first-passage percolation (family 212)
The gist
On October 6, 2026, OpenAI announced, from an unreleased internal model, 2 manuscripts dated September 24, 2026 on planar first-passage percolation.
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-212-no-bigeodesics-smooth-limit-shapes-planar-r1
@misc{discoveria-oai-fam-212-no-bigeodesics-smooth-limit-shapes-planar-r1,
author = {{DiscoverIA}},
title = {No bigeodesics and smooth limit shapes in planar first-passage percolation (family 212)},
howpublished = {DiscoverIA registry, entry oai-fam-212-no-bigeodesics-smooth-limit-shapes-planar},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-212-no-bigeodesics-smooth-limit-shapes-planar#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 30 s reading time, estimated
What it changes
A bigeodesic is a path, infinite in both directions, that stays the fastest route between any two of its points. If the manuscripts were correct, the first would rule out bigeodesics in this model and the second would show that the “exponential” limit shape (the shape of the region reached in a given time, rescaled to a fixed size as that time grows) is strictly convex and differentiable.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is supplied by OpenAI only; formalization.yaml carries the note “review: status: unchecked”, and no third-party assessment is recorded. The sources read do not say which part of the 2 manuscripts the 2 Comparator statements cover.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 212.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 · No-bigeodesics-in-planar…link only, reading not recorded
- Repositorygithub.com · Strict-convexity-and…link only, reading not recorded
- Lean proofgithub.com · 212.mdpage read word for word
- Lean proofgithub.com · GammaPassage.leanlink only, reading not recorded
- Lean proofgithub.com · PlanarFirstPassage.leanlink only, reading not recorded
Method
The openai/math repository contains 2 manuscripts: “No bigeodesics in planar first-passage percolation” and “Strict convexity and differentiability of the planar exponential first-passage limit shape”. OpenAI supplies lean/docs/212.md, which “describes the scope of the Lean formalization”, and 2 Comparator files: lean/ComparatorChallenges/GammaPassage.lean and lean/ComparatorChallenges/PlanarFirstPassage.lean. According to history.md, no revision is reported. 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).
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 212, section “Probability and statistical mechanics”, 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
- 6 : 1 read word for word, 5 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 206 of 372, by family number
- Not evaluated : Integral counterexamples to Gersten’s conjecture (family 209)
- Not evaluated : Foulkes’ conjecture for sixth powers and quadratic stabilization (family 210)
- Not evaluated : Geometry, diffusion, and spectra of random planar maps (family 211)
- Not evaluated : No bigeodesics and smooth limit shapes in planar first-passage percolation (family 212)
- Not evaluated : No infinite critical clusters on quasi-transitive graphs (family 213)
- Not evaluated : The Benjamini–Schramm nonuniqueness conjecture (family 214)
- Not evaluated : Massive continuum limits and exact mass asymptotics for planar O(n) models (family 215)
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