Uniform-discreteness conjecture for zeros of Paley–Wiener extremal functions

Let $0<p<\infty$, and let a solution mean a function solving the extremal problem defined earlier in the paper. Uniform-discreteness conjecture. The zero set of any solution of the extremal problem is uniformly discrete for all $0<p<\infty$. The source states that this is known for $p\geq1/2$ and remains conjectural in the full range.