Sharp small-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 $E_SF$ be the extension operator for the two-dimensional paraboloid restricted to $S\subset[0,1]^2$. Assume each $S_i$ is a $\sqrt{R}$-set, meaning a large ensemble containing $\sqrt{R}$ canonical $1/\sqrt{R}$-squares, with the sets $S_i$ forming the family under consideration. Sharp small-ensemble decoupling for the paraboloid. For $2\le p\le10/3$, one has

$$\|EF\|_{L^p(B_R)}\lesssim_{\epsilon}R^{\frac12(\frac12-\frac1p)+\epsilon}\left(\sum_{i=1}^{R^{1/2}}\|E_{S_i}F\|_{L^p(B_R)}^p\right)^{1/p}.$$

The estimate would be particularly significant at $p=10/3$, where the corresponding case is linked to the sharp restriction estimate. The source gives no resolution status for this conjecture.