Dimension-equality conjecture for tropical plane-curve gonality loci

Let $\mathbb{M}^{\mathrm{nd}}_g$ be the moduli space of genus-$g$ smooth tropical plane curves. For $d\geq 1$, let $\mathbb{M}^{\mathrm{nd}}_{g,d}$ denote the locus of curves of divisorial gonality $d$, and let $\mathbb{M}^{\mathrm{nd}}_{g,\underline d}$ denote the locus obtained by taking the union over Newton polygons of genus $g$ and expected gonality $d$.

Dimension-equality conjecture. For every $g\geq 0$ and $d\geq 1$,

$$\dim\bigl(\mathbb{M}^{\mathrm{nd}}_{g,d}\bigr)=\dim\bigl(\mathbb{M}^{\mathrm{nd}}_{g,\underline d}\bigr).$$

The paper proves this equality when $d\geq3$ and $g\geq\max\{d^3,32\}$, verifies it in several low-genus cases, and notes that the cases $d=1$ and $d=2$ are known. The assertion for all $g$ and $d$ is presented as a weaker consequence of the expected-gonality conjecture and remains open in general.