The Bernstein–Sato divisibility conjecture for regular sequences

Let $X$ be the smooth variety and let $f_1,\dots,f_r\in \mathscr{O}_X(X)$ be a regular sequence. Set $g=f_1\cdots f_r$ and let $U$ denote the open subset on which the relevant restriction $g\vert_U$ is defined. Let $b_g(s)$ and $b_{g\vert_U}(s)$ be the corresponding Bernstein–Sato polynomials. Bernstein–Sato divisibility conjecture. We have

$$b_g(s) \mid b_{g\vert_U}(s)(s+r).$$

Equivalently, the set $I$ is either empty or the singleton $\\{0\\}$. This conjecture predicts that no factor $s+r+j$ with $j>0$ can occur without forcing additional integer roots in the restricted Bernstein–Sato polynomial, constraining the possible discrepancy between the global and restricted polynomials.