Motegi's boundary-slope bound conjecture for exceptional surgeries

Let $K$ be a hyperbolic knot in $S^3$. A boundary slope is a slope represented by the boundary curves of an essential embedded surface in the exterior of $K$, and an exceptional surgery is a rational Dehn surgery slope whose filling is non-hyperbolic and non-meridional. Motegi's conjecture. There exist boundary slopes $b_1,b_2$ with $b_1<b_2$ such that all exceptional surgeries occur, as rational numbers, in the interval

$$[b_1,b_2].$$

This conjecture concerns the location of non-trivial exceptional surgeries relative to boundary slopes. The paper presents evidence for it, including examples where exceptional slopes form a sequence bounded by boundary slopes; its general status remains open.