Hom–Lidman–Vafaee conjecture on satellite L-space knots

Given a pattern knot $P$ and a companion knot $C$, both in the three-sphere, let $P(C)$ denote the resulting satellite knot. Hom–Lidman–Vafaee conjecture. If $P(C)$ is an L-space knot, then $P$ and $C$ are L-space knots as well. This conjecture concerns when the L-space-knot property is inherited by the pattern and companion of a satellite knot; the source gives no resolution, so its status is open.