The adjacency conjecture for X(n) and X(n+1)

Let $X(n)$ denote the standard spectra in the Ravenel sequence, and let $\langle E\rangle$ denote the Bousfield class of a spectrum $E$.

X(n)-adjacency conjecture. The spectra $X(n)$ and $X(n+1)$ are adjacent in the Bousfield lattice: if

$$\langle E\rangle>\langle X(n+1)\rangle,$$

then

$$\langle E\rangle\geq\langle X(n)\rangle.$$

The source uses this conjecture to derive consequences for acyclic complements and related Bousfield classes, but gives no resolution.