Yoshinaga's sharp-pair conjecture on monodromy of real arrangements

Let ${\mathcal A}$ be a real affine line arrangement and let $\overline{{\mathcal A}}$ be its projective arrangement. A sharp pair of lines is a pair of projective lines satisfying the sharpness condition for the arrangement. An arrangement is a-monodromic when it has no nontrivial monodromy, and let $h_1$ denote the monodromy operator on first homology. Yoshinaga's conjecture. If $\overline{{\mathcal A}}$ has a sharp pair of lines and ${\mathcal A}$ is not a-monodromic, then the eigenvalues of $h_1$ are cubic roots of unity. The conjecture is one of the statements motivating the paper's study of sharp arrangements; its status is open in the supplied source.