Taelman's class number conjecture for abelian t-modules

Let $K$ be a finite separable extension of $\mathbf{F}_q(t)$, let $A=\mathbf{F}_q[t]$, and let $K_\infty$ and $O_K$ denote the completions and the ring of integers used in the definition of the associated $t$-module. Let $E$ be a uniformizable abelian $t$-module over $K$ whose associated $t$-motive $M$ has everywhere good reduction. Define

$$W_E=\operatorname{Lie}_E/(t-\theta)\operatorname{Lie}_E$$

and let $w:\operatorname{Lie}_E\to W_E$ be the canonical projection. Taelman's class number conjecture. There exists a sub-$A$-module $Z\subset\operatorname{Lie}_E(K_\infty)$ of rank $\dim W_E$ such that $\exp_E(Z)\subset E(O_K)$ and

$$\bigwedge_A^{\dim W_E}w(Z)=L(E,0)\cdot\left(\bigwedge_A^{\dim W_E}W_E(O_K)\right)$$

as $A$-lattices inside the one-dimensional $F_\infty$-vector space

$$\bigwedge_{K_\infty}^{\dim W_E}W_E(K_\infty).$$

This is a function-field analogue of a class number formula: the special value $L(E,0)$ is predicted to measure the covolume of an exponential lattice associated with integral points of $E$. The source presents the claim as a conjecture and gives numerical evidence, but no resolution is supplied here.