Li-Sheng's Beauville-number conjecture

Let $\lambda$ be a parameter, written in characteristic $p$ as a lifting $(\lambda_0,\lambda_1)$, and let $M_p(\lambda_0,\lambda_1)$ denote the matrix associated with the periodicity condition for the corresponding parabolic Higgs bundle. A Beauville number is a parameter arising from the Beauville-number condition. Li-Sheng's conjecture. $\lambda$ is a Beauville number if and only if

$$\det M_p(\lambda_0,\lambda_1)=0$$

for almost all places $\mathfrak{p}$. The statement relates an arithmetic condition on $\lambda$ to periodicity in the positive-characteristic parabolic non-abelian Hodge correspondence; the supplied text does not state whether the conjecture has been proved or disproved.