The sharp Vinogradov mean value bound for integer sets

For positive integers $s$ and $k$ with $s\geq k(k+1)/2$, let $A$ be a finite non-empty subset of $\mathbb Z$. Let $J_{s,k}(A)$ denote the number of solutions in $A$ to

$$x_1^j+\cdots+x_s^j=y_1^j+\cdots+y_s^j\qquad(1\leq j\leq k).$$

Sharp Vinogradov mean value conjecture. For every $\epsilon>0$, if $|A|$ is sufficiently large, then

$$J_{s,k}(A)\leq |A|^{2s-k(k+1)/2+\epsilon}.$$

This would remove the paper's sparsity or diameter restriction and give the expected sharp estimate for the Vinogradov system. The supplied text presents it as a conjectural strengthening of the available upper bound; no resolution is stated.