Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 232-03. Uniform real Lipschitz surfaces on the triangular lattice
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OpenAI@2026-10-07#rem:oai-p-232-03
Authors: OpenAI. Family 232.
Title: Uniform real Lipschitz surfaces on the triangular lattice.
Abstract: We prove the Gaussian free field and SLE$_4$ scaling limits for uniformly sampled real nearest-neighbor Lipschitz heights on the triangular lattice, resolving Schramm's Problem 2.3. On approximations of smooth simply connected domains, the centered height field converges as a random distribution to a multiple of the Dirichlet Gaussian free field. At one tuned two-arc boundary amplitude, the zero-height interface converges in uniform curve distance to chordal SLE$_4$. We identify the relation between the field variance and the boundary height in terms of an implicit stationary tangent-flux coefficient.
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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