Multiplicity conjecture for Proudfoot-Speyer degenerations of scattering equations

Let $L_m$ be the relevant linear space arrangement, let $\mathbb{L}_s$ be the linear space determined by the kinematic data $s$, and let $I_r(W)$ be a type (ii) flat, with associated stratum ${\cal R}_{(L_m)_{I_r(W)}}^\circ$. The intersection $\mathbb{L}_s \cap {\cal R}_{L_m}$ contains ${(m-3-r)!}$ points in this open stratum, corresponding to the scattering equations of ${\cal M}_{0,m-r}$. Multiplicity conjecture. The multiplicity of $\mathbb{L}_s \cap {\cal R}_{L_m}$ at each of these ${(m-3-r)!}$ points equals $r!$. This predicts the local intersection multiplicities in the Proudfoot-Speyer degeneration and is stated after identifying the points in each type (ii) stratum; no resolution or proof is supplied in the given text.