The phase limit set conjecture for discriminant coamoebas

Let $A\subset\mathbb{Z}^m$ be a nondefective configuration with Gale dual $B\subset\mathbb{Z}^d$. For $d>2$, write ${\it c}\mathscr{A}(D_B)$ for the discriminant coamoeba of the discriminant $D_B$, and let $\mathscr{P}^{\infty}(D_B)$ denote its phase limit set.

Phase limit set conjecture. The closure of the discriminant coamoeba equals the phase limit set:

$$\overline{{\it c}\mathscr{A}(D_B)}=\mathscr{P}^{\infty}(D_B).$$

This conjecture is motivated by computations and is an analogue of the solidity of discriminant amoebas. The surrounding results describe the components and $d$-dimensional strata of the phase limit set, but the equality is not established in general; it is known in the case $d=3$ through the results discussed in the paper.