The pole formula for Zelevinsky representations

Let $\mathfrak{m},\mathfrak{n}\in\mathcal{M}\mathrm{ult}(\rho)$ be multisegments, let $\mathrm{Z}(\mathfrak{m})$ denote the corresponding representation, and let $C(\mathfrak{m})$ be the associated irreducible component. Write $\Lambda$ for the order of the pole at $s=0$ of the intertwining operator, and $\operatorname{hom}_\Pi$ for the corresponding generic Hom dimension.

Zelevinsky pole conjecture. One has

$$\Lambda(\mathrm{Z}(\mathfrak{m}),\mathrm{Z}(\mathfrak{n}))=\operatorname{hom}_\Pi(C(\mathfrak{n}),C(\mathfrak{m})).$$

The source proves this equality when at least one of $\mathfrak{m},\mathfrak{n},\mathfrak{m}^*,\mathfrak{n}^*$ is balanced, and then proposes the unrestricted multisegment formula. The general statement remains open in the supplied text.