Cuntz–Geis bound for sporadic simplicial line arrangements

Let $\mathcal{L}$ be a sporadic simplicial line arrangement in $\mathbb{P}^{2}_{\mathbb{R}}$, meaning a simplicial line arrangement outside the known infinite families, and let $d$ be its number of lines. Cuntz–Geis conjecture. Then

$$d\leqslant 37.$$

This is a stronger conjecture related to Grünbaum's catalogue conjecture, predicting a uniform upper bound on the number of lines in a sporadic simplicial arrangement. The source does not state a resolution.