The non-integral boundary slope conjecture for hyperbolic link exteriors

Let a hyperbolic link exterior be the complement of a hyperbolic link in the 3-sphere, and let an $n$-punctured sphere be a sphere with $n$ boundary components properly embedded in that exterior. A boundary slope is non-meridional if it is not a meridian and non-integral if it is not an integral slope.

Non-integral boundary slope conjecture. There does not exist an essential $n$-punctured sphere with non-meridional, non-integral boundary slope in a hyperbolic link exterior in the 3-sphere.

This conjecture concerns restrictions on essential surfaces in hyperbolic link exteriors and is related to the classification of link exteriors containing essential punctured spheres with non-integral boundary slopes. The supplied text gives no resolution status.