Large ensemble decoupling for the paraboloid

Let $R$ be a large parameter, let $B_R$ be a ball or cube of radius or side length $R$ in ${\mathbb R}^3$, and let $E_SF$ denote the Fourier extension operator associated to the two-dimensional paraboloid, restricted to $S\subset[0,1]^2$. A large ensemble is a disjoint union of $1/\sqrt{R}$-squares from the partition ${\mathcal Q}_R$ of $[0,1]^2$. Let $N=O(R)$, and let $S_1,\ldots,S_N$ be a partition of $[0,1]^2$ into large ensembles. Large ensemble decoupling for the paraboloid. For $2\le p\le3$, one has

$$\|EF\|_{L^p(B_R)}\lesssim_{\epsilon}R^{\epsilon}\left(\sum_{i=1}^N\|E_{S_i}F\|_{L^p(B_R)}^2\right)^{1/2}.$$

This would extend canonical $l^2$ decoupling from canonical caps to arbitrary unions of such caps, including thin rectangles and disconnected sets. The source provides no resolution status for this conjecture.