Lidman–Vafaee satellite L-space knot necessity conjecture

Let $P$ be a pattern in the solid torus, let $K$ be a knot, let $U$ denote the unknot, and write $P(K)$ and $P(U)$ for the corresponding satellite knots. An L-space knot is a knot admitting a positive surgery yielding an L-space. Lidman–Vafaee's conjecture. If $P(K)$ is an L-space knot, then both $P(U)$ and $K$ are L-space knots. This gives a necessary condition for a satellite knot to be an L-space knot; the source presents it as a conjecture attributed to the author, Lidman, and Vafaee, and its status is not resolved here.