Screening conjecture under directional derivative predictability

Let $Z$ be a spatial process with spectral density $f$ satisfying condition (f-cond), let $N_\varepsilon$ be a set of observations approaching the origin, and let $b(r)$ denote the frequency ball of radius $r$. Assume that, for each coordinate direction $x_j$, $j=1,\ldots,n$, every mean square derivative of $Z$ at the origin in that direction can be predicted from $Z(N_\varepsilon)$ with mean squared error tending to $0$ as $\varepsilon\downarrow0$. Screening conjecture. For every $r>0$,

$$\lim_{\varepsilon\downarrow0} \frac{Ee\{N_\varepsilon\cup b(r)^c\}^2}{Ee\{N_\varepsilon\}^2}=1.$$

The conjecture proposes a sufficient condition for screening by nearby observations: once all directional mean square derivatives are asymptotically predictable, observations outside any fixed frequency ball should contribute negligibly to the prediction error. The source presents it as consistent with all examples discussed, but supplies no resolution.