Uniform decoupling conjecture for the parabola below scale $N^2$

Let $s\in[1,2)$ and $2\le p\le 2+2s$. Write $D(N,N^s,p)$ for the decoupling constant associated with the parabola at spatial scale $N^s$ and exponent $p$. Uniform decoupling conjecture. There exists $C(s)>0$ such that

$$D(N,N^s,p)\le C(s).$$

The conjecture asserts that the relevant decoupling constants remain uniformly bounded in $N$ for scales strictly below $N^2$ throughout the indicated range of exponents. The surrounding discussion notes that the preceding superlevel-set estimates are not sharp in this regime, apart from endpoint-type cases.