Remark: Family 232. Gaussian fields and SLE interfaces for Lipschitz heights

Proves Gaussian free field limits on bounded smooth simply connected domains for triangular-lattice height models: uniform odd heights with increments $0,\pm 2$ and two-arc boundary values $\pm 1$, and zero-boundary integer Lipschitz heights weighted by fixed $x\in [1/\sqrt{2},1]$. Uniform real Lipschitz heights also converge to a Gaussian field; at a tuned opposite-boundary amplitude, their interface converges to chordal ${\mathrm{SLE}}_4$, establishing Schramm’s real-field/interface predictions.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.