Factorization conjecture for LS discriminants of rational Landau diagrams

Let $\mathcal{L}$ be a rational Landau diagram, and let $V_G$ be the associated variety with irreducible components $V_{G,\sigma}$. Let $\Delta_{\mathcal{L}}$ denote its LS discriminant, and let $\Delta_{\mathcal{L},\mathrm{mix}}$ denote the mixed LS discriminant. Factorization conjecture. On each irreducible component of $V_G$, the LS discriminant has the form given in equation

$$, and the mixed LS discriminant has the analogous form given in equation$$

, with both products ranging over all external colorings admissible for $\mathcal{L}$. This is presented as a generalization of the triangle case; the source gives no resolution.