OpenAI · 225-01 · 2026-09-23 · Probability and statistical mechanics

The Gaussian free field limit of the balanced six-vertex model with variance multiplier 1/arcsin(c/2)

preprints/The-Gaussian-free-field-limit-of-the-balanced-six-vertex-model-with-variance-multiplier-1-over-arcsin-c-over-2-September-23-2026

Family 225. Gaussian free field limits for the balanced six-vertex model.

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

The balanced square-lattice six-vertex height field with $a = b = 1$ and $0 < c \leq 2$ converges to a Gaussian free field, including at the endpoint $c = 2$ . The plane state is defined by balanced-torus limits. For unit height increments and Green kernel $- (2 π)^{- 1} lo g ∣ x - y ∣$ , the exact variance multiplier is $1/ arcsin (c /2)$ .

We prove that the height function of the square-lattice six-vertex model with weights $a = b = 1$ and $0 < c \leq 2$ , in the plane state obtained from balanced tori, converges to a multiple of the Gaussian free field. For unit height jumps and Green kernel $- (2 π)^{- 1} lo g ∣ x - y ∣$ , the squared multiplier is $1/ arcsin (c /2)$ .

Preprint source and Lean scope

The abstract above is the catalogue abstract. The sections below are the full preprint source, 0 sections. This page is not only the abstract. The manuscript file is loading.

No Lean scope note is in the repository for this family. The preprint source below is still the full manuscript, not only the abstract. No compilation is asserted.