The external Arctic curve envelope conjecture for generic six-vertex domains

Let $\Lambda$ be a generic domain for the six-vertex model, and consider a south side ending at a corner, with the relevant external portion of the Arctic curve lying above that side and to the right of its contact point, when present, and visible from the side. Let $H^{(r)}$, $h(z)$, and $r(z)$ denote the corresponding one-point boundary-correlation quantities, with coordinates rescaled using the same size parameter as in $r(z)$. Let $t$ and $\Delta$ be the six-vertex model parameters, and let $x,y$ be rescaled coordinates. External Arctic Curve Envelope Conjecture. For this system, the specified portion of the Arctic curve is the geometric caustic, or envelope, of the one-parameter family of lines

$$F(x,y;z)=x-\frac{z(t^2-2\Delta t+1)}{(z-1)(t^2-2\Delta t+z)}y-r(z),$$

with parameter $z\in[1,+\infty)$. This extends the Tangent Method description from the square domain to external arcs of generic domains; the source presents it at the same level of rigour as the square-domain derivation and bases it on a suitable restatement of the tangent assumption.