The voter-model interface straight-line convergence conjecture

Let $B_L$ be the rhombic region of scale $L$, and let $Z_L$ denote the voter-model interface curve in $B_L$. Straight-line convergence conjecture. As $L\rightarrow\infty$, the interface curve $Z_L$ converges to a straight line.

This conjecture is suggested by the preceding convergence theorem and describes the macroscopic shape of the voter-model interface in the scaling limit. The source provides no resolution of the conjecture.