Top-computability conjecture for arrangements and free locally quasi-homogeneous divisors

Let $f$ be the defining polynomial of either an arrangement ${\mathcal A}:f=0$ of $d$ hyperplanes in $\mathbb{P}^n$, or a free locally quasi-homogeneous divisor $V:f=0$ of degree $d$ in $\mathbb{P}^n$. For a positive integer $k$, let $(k,1)$-top-computable mean that the relevant top-degree information is determined by the second page of the spectral sequence $E_*(f)$ as specified by the paper's definition. Top-computability conjecture. The polynomial $f$ is $(k,1)$-top-computable for every positive integer $k$ satisfying

$$1\leq k\leq d.$$

This is presented as the paper's main conjecture. The preceding discussion says that the property is verified in the computed examples and gives supporting evidence, but no proof is supplied.