Newman's conjecture for function-field L-functions

Let $\mathcal F$ be a family of $L$-functions over a function field $\mathbb F_q[x]$. For each parameter $D\in\mathcal F$, let $\Lambda_D$ denote the associated De Bruijn–Newman constant. Newman's conjecture for function fields. One has

$$\sup_{D\in\mathcal F}\Lambda_D=0.$$

Unlike the number-field setting, individual function-field constants may equal $-\infty$, so the supremum over a family is the appropriate analogue. The source presents this as a generalized conjecture of Andrade, Chang and Miller and does not state a resolution here.