Gaussian free field limits throughout the balanced six-vertex regime

What OpenAI claims

The balanced square-lattice six-vertex height field with a=b=1 and 0 < c ≤ 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 -(2π)^-1 log|x-y|, the exact variance multiplier is 1/arcsin(c/2).

Paper

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

   23 September 2026 · Preprint, not peer reviewed · PDF

   OpenAI's abstract We prove that the height function of the square-lattice six-vertex model with weights a=b=1 and 0 < c ≤ 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 -(2π)^-1 log|x-y|, the squared multiplier is 1/arcsin(c/2).

Status

Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.