All-degrees elliptope conjecture for the Montanari–Sen witness

Let $\alpha,\delta \in (0,1)$ and let $d \in 2\mathbb{N}$. The random matrix $\bm{M}^{(\alpha,\delta)}(\bm{W})$ is the proposed degree-$d$ witness, and $\mathscr{E}_d^N$ is the degree-$d$ elliptope. All-degrees elliptope conjecture.

$$\lim_{N\to\infty}\mathbb{P}\left[\bm{M}^{(\alpha,\delta)}(\bm{W})\in\mathscr{E}_d^N\right]=1.$$

This conjecture asserts that the adjusted Montanari–Sen construction is asymptotically feasible at every even degree. It is proposed as evidence for the expected behavior of higher-degree sum-of-squares relaxations, but no resolution is given in the source.