Lehmer inequality for Drinfeld modules

Let $K$ be a finitely generated field, let $A$ be the coefficient ring of a Drinfeld module, and let $\phi:A\rightarrow K\{\tau\}$ be a Drinfeld module. For a point $x\in K^{\operatorname{alg}}$, write $\operatorname{\widehat{h}}(x)$ for its canonical height, and call $x$ non-torsion if it is not a torsion point for the Drinfeld-module action. Lehmer inequality for Drinfeld modules. There exists a constant $C>0$ depending only on $\phi$ such that every non-torsion point $x\in K^{\operatorname{alg}}$ satisfies

$$\operatorname{\widehat{h}}(x)\geq\frac{C}{[K(x):K]}.$$

This is the general Lehmer-type conjecture formulated for Drinfeld modules; the paper presents inequalities intended to establish Mordell–Weil-type structure results, but the stated general form is not resolved here.