The boundary complex conjecture for tropical unramified $p$-covers

Let $\mathcal{M}_{g,\mathbb{Z}/p}$ be the moduli space of smooth genus-$g$ curves equipped with an unramified $\mathbb{Z}/p$-cover, and let $\overline{\mathcal{M}}_{g,\mathbb{Z}/p}$ be its admissible-covers compactification. Write

$$D=\overline{\mathcal{M}}_{g,\mathbb{Z}/p}\backslash\mathcal{M}_{g,\mathbb{Z}/p}$$

for the normal crossings boundary, and let $\Delta(D)$ be its dual intersection complex. Let $\Delta_{g,p}$ denote the symmetric $\Delta$-complex associated with tropical unramified $p$-covers. Boundary complex conjecture. There is an isomorphism of symmetric $\Delta$-complexes

$$\Delta(D)\longrightarrow\Delta_{g,p}.$$

If true, this identifies the boundary-complex model controlling the top-weight cohomology of $\mathcal{M}_{g,\mathbb{Z}/p}$ with the tropical moduli complex, yielding an analogue of the corresponding result for the ordinary moduli space of curves. The source states that the proof is subject to ongoing work.