# Six-vertex height variance reference

Family 225: Gaussian free field limits throughout the balanced six-vertex regime. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Lattice-model researchers can use the exact GFF variance multiplier to check balanced six-vertex simulations with fixed height and Green-kernel conventions.

## Applicability and commercial boundary

Balanced torus limits, a=b=1 and 0<c<=2 are specific. c approaching zero changes the multiplier, and finite-grid observations require error control.

## Initial business decision

Conditional engineering. Buyer budget, commercial novelty and profitability are unvalidated.

## Next verification action

Implement a convention-aware variance reference and compare finite simulations across several c values.

## Evidence scope

The catalog statement was individually reviewed. This record does not imply a manuscript proof review or formal-scope comparison. No independent Lean check was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

## Main source

[The Gaussian free field limit of the balanced six-vertex model with variance multiplier 1/arcsin(c/2)](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Gaussian-free-field-limit-of-the-balanced-six-vertex-model-with-variance-multiplier-1-over-arcsin-c-over-2-September-23-2026/The-Gaussian-free-field-limit-of-the-balanced-six-vertex-model-with-variance-multiplier-1-over-arcsin-c-over-2-September-23-2026.pdf).