Macroscopic boundary conjecture for the left side of the t-split two-periodic Aztec diamond

Let $t$, $x$, and $y$ denote the split parameter and macroscopic coordinates, and let $r_{\alpha,2}(z)$ and $r_{\beta,2}(z)$ be the functions appearing in the correlation-kernel asymptotics. Define the saddle function

$$\varphi_{\alpha,\beta}(z;x,y)=(1+y)\log z-\log(z-1)+(t-x)\log r_{\alpha,2}(z)+(1/2-t)\log r_{\beta,2}(z).$$

Macroscopic boundary conjecture. The macroscopic boundary of the $t$-split two-periodic Aztec diamond to the left of the interface is governed by this saddle function: the boundary corresponds to the coalescence of critical points, as in the two-periodic model. This conjecture predicts that the left macroscopic boundary can be identified through the saddle-point analysis of the limiting kernel, extending the corresponding mechanism from the two-periodic model to the split model. The source gives no resolution status.