Strong Gordon conjecture for the figure-8 knot complement

A non-hyperbolic Dehn filling is a Dehn filling of a $1$-cusped hyperbolic $3$-manifold that does not remain hyperbolic. Strong Gordon conjecture. The figure-$8$ knot complement is the unique $1$-cusped hyperbolic $3$-manifold which realizes the maximal number of non-hyperbolic Dehn fillings. This is proposed as a strong form of the Gordon conjecture, building on the theorem that a one-cusped hyperbolic $3$-manifold has at most $10$ non-hyperbolic Dehn fillings; uniqueness of the maximizer remains open in the source.