Vanishing-order bound for P-adic L-series of Anderson t-modules

Let $E$ be the Anderson $t$-module under consideration over $L/K$, let $P$ be a prime of $A$, and let $\Omega_E$ be the period lattices associated with $E$. Write $r_{\Omega_E}$ for the rank of these period lattices. Vanishing-order bound. We have

$$\operatorname{ord}_{z=1}L_P(\widetilde{E}/\widetilde{\mathscr{O}_L})\leq [L:K]r_{\Omega_E}d.$$

The statement is presented in the paper as a conjecture in the list following the independence conjecture. No resolution or supporting special cases are supplied in the provided text.