Upper semicontinuity of Euler–Koszul multiplicities

Let $A$ be fixed, let $L$ be a filtration, let $\tau$ be the corresponding face or stratum, and let $\mu^{L,\tau}_{A,0}(\beta)$ denote the multiplicity of the associated component in the $L$-characteristic cycle of the $A$-hypergeometric system with parameter $\beta$. Upper-semicontinuity conjecture. For fixed $A$, $L$ and $\tau$, $\mu^{L,\tau}_{A,0}(\beta)$ is upper semicontinuous in $\beta$. This would strengthen the proved fact that the multiplicity is minimal at generic parameters; the paper presents upper semicontinuity as conjectural.