Taelman's conjecture for finite uniformizable t-modules

Let $K={\mathbb F}_q(\theta)$, let $F$ be a finite extension of $K$, let ${\cal O}_F$ be an integral closure of $A$ in $F$, and let $F_{\infty}=F\otimes_K K_{\infty}$. Let $\Upsilon$ be a finite uniformizable $\mathbf{t}$-module over ${\cal O}_F$. Set

$$W_{\Upsilon}(F_{\infty}):={\mathrm{Lie}}(\Upsilon)(F_{\infty})/(\partial_{\Upsilon}(\theta)-\theta I_d){\mathrm{Lie}}(\Upsilon)(F_{\infty})$$

and let $w:{\mathrm{Lie}}(\Upsilon)(F_{\infty})\to W_{\Upsilon}(F_{\infty})$ be the projection. Write $r:=\dim_{K_{\infty}}W_{\Upsilon}(F_{\infty})$. Taelman's conjecture. There exist an element $a\in A\backslash\{0\}$ and a sub-$A$-module $Z\subset {\mathrm{Lie}}(\Upsilon)(F_{\infty})$ of rank $r$ such that

$$\exp_{\Upsilon}(Z)\subset {\mathrm{Lie}}(\Upsilon)({\cal O}_F)$$

and

$${\bigwedge}_A^r w(Z)=a\cdot L(\Upsilon/{\cal O}_F)\cdot {\bigwedge}_A^r W_{\Upsilon}({\cal O}_F).$$

This conjecture predicts an arithmetic description of a suitable lattice in the Lie algebra of a finite uniformizable $\mathbf{t}$-module, relating its exterior power to the associated $L$-value. The supplied text does not state whether the conjecture has been proved or disproved.