The supersolvable line arrangement double-point conjecture

Let ${\mathcal A}$ be a supersolvable line arrangement consisting of $d=|{\mathcal A}|$ lines, and suppose that ${\mathcal A}$ is not a pencil. Denote by $n_2$ the number of intersection points of multiplicity two. Double-point conjecture. Then

$$n_2 \geq \frac{d}{2}.$$

This conjecture was checked for all non-pencil supersolvable arrangements that are either real or have at most $12$ lines. It is also established in several classes, including the cases described in the paper, but remains open in general.