  The six-vertex model is an important toy-model in statistical mechanics for
two-dimensional ice with a natural parameter $\Delta$. When $\Delta = 0$, the
so-called free-fermion point, the model is in natural correspondence with
domino tilings of the Aztec diamond. Although this model is integrable for all
$\Delta$, there has been very little progress in understanding its statistics
in the scaling limit for other values. In this work, we focus on the six-vertex
model with domain wall boundary conditions at $\Delta = 1/2$, where it
corresponds to alternating sign matrices (ASMs). We consider the level lines in
a height function representation of ASMs. We show that the maximum of the
topmost level line for a uniformly random ASMs has the GOE Tracy--Widom
distribution after appropriate rescaling. A key ingredient in our proof is
Zeilberger's proof of the ASM conjecture. As far as we know, this is the first
edge fluctuation result away from the tangency points for the domain-wall
six-vertex model when we are not in the free fermion case.
