Grothendieck–Katz conjecture for iterative q-difference modules

Let $(\mathcal{M}, \phi_M, \delta_M^*)$ be an iterative $q$-difference module defined over $K(t)$. For each finite place $v$, let $\pi_v$ be its corresponding uniformizer and let

$$\psi_{\pi_v}:=(\delta_M^{(n)})^{p_v}$$

be the $\pi_v$-curvature, where $p_v$ is the residue characteristic at $v$.

Grothendieck–Katz conjecture for iterative q-difference modules. The iterative $q$-difference module $\mathcal{M}$ is isotrivial, meaning that it becomes trivial after a finite base field extension, if and only if, for almost all finite places $v$, the $\pi_v$-curvature $\psi_{\pi_v}$ induces the zero map on the reduction of $\mathcal{M}$ modulo $\pi_v$.

This is proposed as an analogue of the Grothendieck–Katz conjecture for differential equations, relating isotriviality to the vanishing of curvatures at almost all finite places. The supplied text does not state whether the conjecture has been proved or disproved.