Divergence conjecture for non-equidistant sampling in system approximation

Let t_k_{k\in\mathbb{Z}}\subset\mathbb{R} be an ordered complete interpolating sequence for $\mathcal{PW}_{\pi}^{2}$, let $\phi_k$ be as defined in the source, and let $0<\sigma<\pi$. Divergence conjecture. For every $t\in\mathbb{R}$, there exist a stable LTI system $T_*:\mathcal{PW}_{\pi}^{1}\to\mathcal{PW}_{\pi}^{1}$ and a signal $f_*\in\mathcal{PW}_{\sigma}^{1}$ such that

$$\limsup_{N\to\infty}\left|(T_*f_*)(t)-\sum_{k=-N}^{N}f_*(t_k)(T_*\phi_k)(t)\right|=\infty.$$

This conjecture asserts pointwise divergence of the digital approximation process for every complete interpolating sampling sequence; the paper states that it is proved in the cited section, so its database status is solved.