Bilinear restriction range conjecture

Let $n\geq2$, let $Q=[-1,1]^{n-1}$, and let $\Phi$ be an elliptic phase. For $O(1)$-separated subcubes, write $R^*(p\times p\to q)$ for the bilinear adjoint restriction estimate

$$\|\operatorname{Re}^*f\,\operatorname{Re}^*g\|_q<_\sim\|f\|_p\|g\|_p.$$

Bilinear restriction range conjecture. If $n\geq2$, then $R^*(p\times p\to q)$ holds whenever

$$q\geq\frac{n}{n-1},$$ $$\frac{n+2}{2q}+\frac{n}{p}\leq n,$$ $$\frac{n+2}{2q}+\frac{n-2}{p}\leq n-1.$$

By the theorem in the source, this conjecture is verified for $q\geq2$ (and hence for $n=2$), while the general range remains open.