Terao-type conjecture for the invariant ν of line arrangements

Let $C:f=0$ be a line arrangement in $\mathbb{P}^2$. The invariant $\nu(C)$ is a combinatorial invariant of $C$.

Terao-type conjecture. The invariant $\nu(C)$ is combinatorially determined.

This is presented as a stronger version of H. Terao's conjecture that freeness of a line arrangement is combinatorially determined. The source gives no resolution status for this stronger statement.