Uniform, degenerate, and sublevel set decoupling for polynomial graphs

Let $n,d\ge 1$. For each $n$, let $U(n)$ denote uniform decoupling for the polynomial class $\mathcal P_{n,d}$, let $Z(n)$ denote uniform degenerate decoupling for $\mathcal P_{n,d}$, meaning uniform decoupling with the additional condition $\det D^2\phi\equiv 0$, and let $S(n)$ denote uniform sublevel set decoupling for $\mathcal P_{n,d}$, as defined above. Decoupling conjecture. The statements $U(n)$, $Z(n)$ and $S(n)$ hold for all $n\ge 1$. Uniform and degenerate decoupling are known in dimensions $n=1,2$, and sublevel set decoupling is also known in dimensions $n=1,2$; the conjecture concerns the general case.