Baker's lens space cabling conjecture

Let $K$ be a knot in a lens space $L$ and let surgery on $K$ produce a non-prime $3$-manifold $Y$. A knot $K$ is hyperbolic if its exterior admits a complete finite-volume hyperbolic structure. Baker's lens space cabling conjecture. If $K$ is hyperbolic, then

$$Y=L(r,1)\#L(s,1).$$

Otherwise, either $K$ is a torus knot, a Klein bottle knot, or a cabled knot and the surgery is along the boundary slope of an essential annulus in the exterior of $K$, or $K$ is contained in a ball. The non-hyperbolic case has been proved by Baker, but a counterexample is known in the hyperbolic case, so the conjecture is refuted.