Satellite L-space knot converse conjecture

Let $P$ be a pattern in the solid torus and let $K$ be a knot, with satellite knot $P(K)$. An L-space knot is a knot admitting a positive Dehn surgery yielding an L-space. Satellite L-space knot conjecture. If $P(K)$ is an L-space knot, then $K$ and $P$ are L-space knots. The paper also conjectures a converse when the pattern is embedded “nicely” in the solid torus, for example as a strongly quasipositive braid closure, and is sufficiently positively twisted, but does not make these conditions precise. The claim is posed as a generalization of the preceding construction of L-space knots by Berge–Gabai satellite operations.