The maximal rank conjecture for multiplication maps of general linear series

Let $X$ be a general curve of genus $g$, and let $V \subset \mathcal{L}(D_X)$ be a general linear series of rank $r \geq 3$ and degree $d$. For every positive integer $m$, consider the multiplication map

$$\mu_m: \operatorname{Sym}^m V \longrightarrow \mathcal{L}(mD_X).$$

Here maximal rank means that the map is injective or surjective.

Maximal rank conjecture. The multiplication maps $\mu_m$ have maximal rank for all $m$.

The paper presents this as the algebraic maximal rank conjecture and seeks to prove it using tropical independence. The supplied text gives no resolution status.