Lattice-determined minimal Jacobian-relation degree conjecture for line arrangements

Let $\mathcal A:f=0$ be a line arrangement of degree $d$ in the complex projective plane. Let $\operatorname{mdr}(f)$ denote the minimal degree of a Jacobian relation for $f$, and write $r=\operatorname{mdr}(f)$. Minimal-degree conjecture. For any line arrangement $\mathcal A:f=0$, the integer $r$ is determined by the intersection lattice whenever $r<d/2$.

This is presented as a stronger claim that would imply Terao's freeness conjecture through the characterization of free curves by maximal total Tjurina number in the relevant range. Its resolution is not given in the supplied text.