The rational-point invariance conjecture for tropical linear series

Let $\Delta$ be a tropical complex and let $D$ be a Weil divisor on $\Delta$. Define $h^0(\Delta,D)$ as the smallest cardinality of a set of rational points that is not contained in any effective divisor linearly equivalent to $D$, or infinity if no such finite set exists. The conjecture concerns replacing rational points by arbitrary points in this definition. Rational-point invariance conjecture. The definition of $h^0$ is equivalent to the analogous definition where the points are allowed to be arbitrary, not necessarily rational, points. This would remove a technical rationality restriction from the definition of $h^0$; the source gives no resolution of the conjecture.