Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 232-02. The Gaussian free field limit of integer Lipschitz heights with two-arc boundary data
Manuscript map · lines 6845–6854
OpenAI@2026-10-07#rem:oai-p-232-02
Authors: OpenAI. Family 232.
Title: The Gaussian free field limit of integer Lipschitz heights with two-arc boundary data.
Abstract: We prove that the centered uniform odd integer height function on triangular-lattice approximations of a smooth simply connected domain, with neighboring differences zero or two and boundary values +1 and −1 on two arcs, converges to a universal multiple of the Dirichlet Gaussian free field. This resolves the field part of Schramm's Problem 2.2. We give an absolutely convergent finite-volume formula for the normalization. The proof combines reflection positivity, a spectral sum rule, and boundary comparison with Gaussian moment identities.
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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