C. McA. Gordon's small Seifert–toroidal distance conjecture

Let $M$ be a hyperbolic knot manifold, and let $\alpha,\beta$ be slopes on $\partial M$. The distance $\Delta(\alpha,\beta)$ is the minimal geometric intersection number of representatives of the two slopes. A Dehn filling $M(\alpha)$ is small Seifert if it admits a Seifert structure with base orbifold of the form $S^2(a,b,c)$, and $M(\beta)$ is toroidal if it contains an incompressible torus.

C. McA. Gordon's conjecture. Suppose that $M$ is a hyperbolic knot manifold $M$ and $\alpha, \beta$ are slopes on $\partial M$ such that $M(\alpha)$ is small Seifert and $M(\beta)$ toroidal. If $\Delta(\alpha, \beta) > 5$, then $M$ is the figure eight knot exterior.

This is the small Seifert–toroidal case implied by the exceptional-slope bounds. The source describes related distance bounds and indicates that this case is the subject of the paper; no resolution is supplied in the provided context.