The indecomposable central arrangement hyperplane conjecture

Let $F=(f_1, 3ellots,f_r)$, where each $f_j$ is a not necessarily reduced central hyperplane arrangement in $\mathbb{C}^n$ of degree $d_j$, and suppose that $\prod_{j=1}^rf_j$ is a central essential indecomposable hyperplane arrangement. Central arrangement Bernstein-Sato conjecture.

$$\{d_1s_1+\ldots+d_rs_r+n=0\}\subset V(B_F).$$

This is presented as a multivariable generalization of the cited one-variable conjecture and has implications for the multivariable strong monodromy conjecture. The assertion remains open in the source.