Not evaluated
No infinite critical clusters on quasi-transitive graphs (family 213)
The gist
On October 6, 2026, OpenAI claimed no percolation at criticality on quasi-transitive graphs; a second manuscript covers critical bond and site percolation on the cubic lattice.
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-213-no-infinite-critical-clusters-quasi-r1
@misc{discoveria-oai-fam-213-no-infinite-critical-clusters-quasi-r1,
author = {{DiscoverIA}},
title = {No infinite critical clusters on quasi-transitive graphs (family 213)},
howpublished = {DiscoverIA registry, entry oai-fam-213-no-infinite-critical-clusters-quasi},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-213-no-infinite-critical-clusters-quasi#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
If the result held, it would concern the critical value itself, the threshold at which an infinite cluster becomes possible: no infinite cluster would form there on these graphs. The titles do not give the exact assumptions, nor what the second manuscript establishes on the cubic lattice.
What remains unclear
The Lean (a language in which a computer checks every step of a proof) is provided by OpenAI alone, and its review is marked “unchecked”; it is not known whether a third party has checked it.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · 213.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 · Critical-bond-and-site…link only, reading not recorded
- Repositorygithub.com · No-percolation-at…link only, reading not recorded
- Lean proofgithub.com · 213.mdpage read word for word
- Lean proofgithub.com · CriticalPercolation.leanlink only, reading not recorded
- Lean proofgithub.com · CriticalZ3.leanlink only, reading not recorded
Method
Two manuscripts dated September 24, 2026: “Critical bond and site percolation on the cubic lattice” and “No percolation at criticality on quasi-transitive graphs”. The repository provides lean/docs/213.md and two Comparator files, CriticalPercolation.lean and CriticalZ3.lean; the family is noted as “présente des `sources` de formalization.yaml”. No revision is recorded in history.md. 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 213, 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 207 of 372, by family number
- 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)
- Not evaluated : Critical logarithmic corrections and BKT scaling for the planar XY model (family 216)
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