Not evaluated
Conformal limits of square-lattice random-cluster interfaces (family 223)
The gist
On October 6, 2026, OpenAI presented six manuscripts on the interfaces of random-cluster (FK) models on the square lattice, and on their conformal limits.
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-223-conformal-limits-square-lattice-random-r1
@misc{discoveria-oai-fam-223-conformal-limits-square-lattice-random-r1,
author = {{DiscoverIA}},
title = {Conformal limits of square-lattice random-cluster interfaces (family 223)},
howpublished = {DiscoverIA registry, entry oai-fam-223-conformal-limits-square-lattice-random},
note = {Status “Not evaluated”, snapshot 1, recorded on October 12, 2026. New result},
year = {2026},
url = {https://discoveria.ai/entry/oai-fam-223-conformal-limits-square-lattice-random#releve-1},
urldate = {2026-10-12}
}Dated link opens this snapshot in the history
To understand ≈ 20 s reading time, estimated
What it changes
The titles name subjects (nested loops, occupation measures, SLE, a family of random curves) without stating a result. It is therefore not possible to say what would change if the manuscripts held up.
What remains unclear
No Lean (a language in which a computer checks every step of a proof) is provided, and no third-party assessment is recorded in the sources read, so it is not known whether these results hold up.
For experts
Sources, method, key facts, status history, report an error
Status
Not evaluated
Recorded on · github.com · README.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 · Square-lattice-FK…link only, reading not recorded
- Repositorygithub.com · Self-dual-random-cluster…link only, reading not recorded
- Repositorygithub.com · Quenched-SLE-Universality…link only, reading not recorded
- Repositorygithub.com · Thermal-FK-Ising…link only, reading not recorded
- Repositorygithub.com · Natural-Occupation…link only, reading not recorded
- Repositorygithub.com · Conformal-Limits-of…link only, reading not recorded
Method
The family comprises six manuscripts; two are dated September 23, 2026: “Square-lattice FK interfaces and nested loops for 1 <= q < 4” and “Self-dual random-cluster interfaces below one”. Two are dated October 5, 2026: “Quenched SLE Universality for Weakly Disordered FK–Ising Interfaces” and “Thermal FK–Ising interfaces and massive SLE”. The last two: “Natural Occupation Measures for Critical Square-Lattice FK Interfaces” and “Conformal Limits of Critical Square-Lattice Random-Cluster Interfaces”. 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: “Not all have accompanying Lean formalizations.”).
Limits
DiscoverIA has not checked this result itself.
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 223, section “Probability and statistical mechanics”, 6 manuscripts dated Sep 23, 2026
- Lean proof
- none supplied
- Revisions
- none reported by the claimant
- Checked by
- no verifier identified
- Sources
- 7 : 7 links only
- This entry
- AI draft, not reviewed
Status history
Only one observation so far.
- 01
First observation:Not evaluatedCurrent status
Family with no Lean proof supplied. No third-party evaluation read.
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 217 of 372, by family number
- Not evaluated : Directional zero–one laws and ballisticity in random environments (family 220)
- Not evaluated : The Mézard–Parisi formula for diluted spin glasses (family 221)
- Not evaluated : Perceptron free energies and microscopic jamming (family 222)
- Not evaluated : Conformal limits of square-lattice random-cluster interfaces (family 223)
- Not evaluated : Critical and near-critical universality for Voronoi percolation (family 224)
- Not evaluated : Gaussian free field limits for the balanced six-vertex model (family 225)
- Not evaluated : The double-dimer CLE_4 conjecture in the half-plane (family 226)
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