Combinatorial description of slopes of projectivized A-hypergeometric systems

Let $A$ be an integer matrix, let $\mathcal{M}_A(\beta)$ be the projectivized $A$-hypergeometric system with parameter $\beta$, and let $Y$ be a coordinate variety. For a filtration $L=pF+qV$ with $p/q\in\mathbb{Q}_{>0}\cup\{\infty\}$, where $V$ is the $V$-filtration along $Y$, let $\Phi^Y_A(p/q)$ be the subset of the relevant faces $\tau$ that are not pyramids with vertex in the specified coordinate index set. Slope-description conjecture. The slopes of the projectivized $A$-hypergeometric system $\mathcal{M}_A(\beta)$ along a coordinate variety $Y$ are the jump parameters $p/q\in\mathbb{Q}_{>0}\cup\{\infty\}$ of $\Phi^Y_A(p/q)$. The claim is motivated by the belief that non-$(F,V)$-bihomogeneous components are irrelevant for these slopes, but the source does not establish the proposed combinatorial description.