The Gonzales-Acuña–Short cabling conjecture for knots in the 3-sphere

Let $K$ be a knot in $S^3$. A surgery on $K$ may produce a non-prime $3$-manifold.

Gonzales-Acuña–Short's cabling conjecture. If a knot in $S^3$ admits a surgery to a non-prime $3$-manifold, then the knot is either a torus knot or a cabled knot.

Greene proved this in the special case where the surgery produces a non-trivial connected sum of lens spaces. The conjecture motivates the proposed lens-space generalization discussed in the paper.