OpenAI · 218-05 · 2026-09-23 · Probability and statistical mechanics
SLE3 universality for weak finite-range Ising interactions
preprints/SLE3-universality-for-weak-finite-range-Ising-interactions-September-23-2026
Family 218. Conformal universality for weakly interacting and disordered Ising models.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Weak finite-range square-symmetric even multispin perturbations of the square-lattice Ising model preserve critical bulk spin and energy limits; weak square-symmetric contour interactions also yield chordal interface limits. With sufficiently weak iid bond disorder of any fixed bounded nondegenerate mean-zero law, critical spin interfaces converge to the same law in probability over environments.
We prove that every sufficiently small, square-symmetric finite-range perturbation of the planar Ising contour energy has a domain-independent inverse temperature at which its spin interface converges to chordal SLE3. The result allows interactions of either sign, arbitrary admissible exterior contours, and uniformly approximated Jordan domains. Convergence holds for the full oriented curve law in uniform distance modulo increasing reparametrization.
Preprint source and Lean scope
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A Lean scope note is stored for family 218, but it does not name this preprint. It names 218-06. This page still has the full preprint source. No compilation is asserted. O.1 stays NOT_CLOSED.