The component-module conjecture for Drinfeld modules

Let $K$ be the function field of a curve over a finite field $\mathbb{F}_q$, let $A$ be the ring of functions regular away from a chosen point at infinity, and let $L/K$ be a finite extension. For a Drinfeld $A$-module $\phi/L$, let $\mu(\phi,N,\mathfrak{a})$ denote the proportion of the finite height contribution of its moduli point arising from places whose component module is annihilated by $\mathfrak{a}$, after allowing $N$ exceptional places.

Component-module conjecture. There exists an integer $N\geq 0$ and an ideal $\mathfrak{a}\subseteq A$ such that

$$\mu(\phi,N,\mathfrak{a})\geq 1/q$$

for every Drinfeld $A$-module $\phi/L$.

Together with the theorem stated immediately before it, this conjecture would imply Poonen's uniform boundedness conjecture for torsion. The paper proves the relevant torsion bound under the displayed $\mu$-condition, but does not establish uniform choices of $N$ and $\mathfrak{a}$ in general.