Discrete Fourier restriction conjecture for the monomial curve

Let $d\geq 3$ be an integer, let $N\in\mathbb N$, let $a_1,\ldots,a_N\in\mathbb C$, and write $\mathbb T^2$ for the two-dimensional torus. For $p\geq 2(d+1)$ and every $\varepsilon>0$, the discrete Fourier restriction conjecture asserts that

$$\left\|\sum_{n=1}^N a_n e^{2\pi i x_1 n+2\pi i x_2 n^d}\right\|_{L^p(\mathbb T^2)}\lesssim N^\varepsilon\left(\sum_{n=1}^N|a_n|^2\right)^{\frac12}.$$

This is a mean-value estimate for exponential sums on the discrete curve $(n,n^d)$ and is of interest in additive number theory because it would yield a substantial improvement in Waring's problem. It is also a discrete Fourier restriction problem; the source does not state whether the conjecture has been resolved.