The Strong Monodromy Conjecture for local motivic zeta functions

Let $f: X \longrightarrow \mathbb{C}$ be a non-constant regular function and let $x \in X$. Denote by $Z_{\textnormal{mot}, x}(f; s)$ the local motivic zeta function and by $b_{f, x}(s)$ the local Bernstein–Sato polynomial. Strong Monodromy Conjecture. If $s_0$ is a pole of $Z_{\textnormal{mot}, x}(f; s)$, then $s_0$ is a root of $b_{f, x}(s)$, and the order of the pole is at most its multiplicity as a root of $b_{f, x}(s)$. The first assertion is known for plane curves by Loeser's work, whereas the multiplicity assertion is the stronger remaining prediction in general.