Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 223-06. Conformal Limits of Critical Square-Lattice Random-Cluster Interfaces
Manuscript map · lines 6615–6624
OpenAI@2026-10-07#rem:oai-p-223-06
Authors: OpenAI. Family 223.
Title: Conformal Limits of Critical Square-Lattice Random-Cluster Interfaces.
Abstract: For every fixed $1{}le q{}le4$, critical square-lattice random-cluster Dobrushin interfaces converge to chordal ${}mathop{{}mathrm{SLE}}{}nolimits _{{}kappa(q)}$, where ${}kappa(q)=4{}pi/{}arccos(-{}sqrt q/2)$, and the complete nested plane loop collections converge to whole-plane ${}mathop{{}mathrm{CLE}}{}nolimits _{{}kappa(q)}$. The results hold under uniform marked Jordan boundary approximation and retain loop multiplicities and traversals. At q = 1 we obtain Cardy's formula for square-lattice bond percolation with free boundary edges.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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