Zero-count conjecture for Fox's H-function

Let $\mathbf A=(A_1,\textellipsis,A_p)$ and $\mathbf B=(B_1,\textellipsis,B_q)$ have positive entries, let $\mathbf a=(a_1,\textellipsis,a_p)$ and $\mathbf b=(b_1,\textellipsis,b_q)$ have nonnegative entries, and let $\mu$, $\rho$, and $Q(t)$ be the parameters and function used in the Fox $H$-function representation. Assume

$$\mu\ge0,\qquad \rho\le1,\qquad \sum_{i=1}^{p}A_i=\sum_{j=1}^{q}B_j.$$

Zero-count conjecture. The number of zeros of

$$H_{q,p}^{p,0}\left(x\left|\begin{array}{l}(\mathbf B,\mathbf b)\\(\mathbf A,\mathbf a)\end{array}\right.\right)$$

on $(0,\rho)$ is at most the number of zeros of $Q(t)$ on $(0,1)$.

The paper presents this as a stronger assertion than the known implication from nonnegativity of $Q$ to nonnegativity of the $H$-function. It is supported by numerical evidence, while its general validity remains open.