Gordon's conjecture on toroidal and Seifert Dehn fillings

Let $M$ be a hyperbolic knot manifold, meaning a compact, connected, orientable $3$-manifold with torus boundary whose interior admits a complete finite-volume hyperbolic structure. Let $\beta$ and $\beta$ be slopes on $\partial M$, and write $M(\alpha)$ and $M(\beta)$ for the corresponding Dehn fillings; let $\Delta(\alpha,\beta)$ denote the distance between the slopes. Gordon's conjecture. Suppose that $M(\beta)$ is a toroidal manifold and $M(\alpha)$ is a Seifert manifold. If

$$\Delta(\alpha,\beta)>5,$$

then $M$ is the figure-eight knot exterior. The conjecture concerns the exceptional-filling distance for hyperbolic knot manifolds; the supplied text gives no resolution status, so it is recorded as open.