Gaussian free field limits throughout the balanced six-vertex regime
OpenAI research collection · 1 manuscript · Source checked 2026-10-19
OpenAI's result summary
The balanced square-lattice six-vertex height field with a=b=1 and 0< c\le2 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).
Read the manuscripts
Short excerpts below come from OpenAI's abstracts. The full abstract and original PDF preserve the paper's precise scope.
MANUSCRIPT 01
The Gaussian free field limit of the balanced six-vertex model with variance multiplier 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\le2, 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).
This exact PDF is not listed in the imported formalization catalogue. Family scope notes may contain further information.
New mathematical reasoning could help AI tackle harder scientific and computational problems. How reliably these skills transfer beyond mathematics will determine how much they contribute to general intelligence.