Freeness implies supersolvability for ψ-graphical arrangements

Let $\mathcal{A}_{G,\psi}$ be a $\psi$-graphical arrangement, and call it free when its cone is a free arrangement. Recall that an arrangement is supersolvable when the intersection lattice of its cone contains a maximal chain of modular elements. The freeness–supersolvability conjecture. If $\mathcal{A}_{G,\psi}$ is free, then $\mathcal{A}_{G,\psi}$ is supersolvable. This would extend to $\psi$-graphical arrangements the fact that every free graphical arrangement is supersolvable; the paper presents it as a second conjecture and remarks that it may not be difficult to prove.