Papadima–Suciu conjecture on prime-power roots of line-arrangement Alexander polynomials

Let $C$ be a line arrangement that is not a union of concurrent lines, and let ${\alpha}$ be a root of its Alexander polynomial $\Delta^1_C(t)$. Suppose that the order of ${\alpha}$ has the form $p^s$, where $p$ is a prime number and $s>0$ is an integer. Papadima–Suciu conjecture. Then

$$p^s\in\{2,3,4\}.$$

This conjecture predicts that prime-power orders of roots of Alexander polynomials of non-pencil line arrangements are severely restricted. The surrounding discussion notes that the Alexander polynomial is trivial for most line arrangements, while non-trivial cases have highly restricted possible roots; the source gives no resolution of this conjecture.