Precise satellite L-space knot characterization conjecture

Let $P$ be a pattern in the solid torus, let $K$ be a knot of genus $g$, let $U$ denote the unknot, and write $P(U,-n)$ for the pattern knot after $-n$ full twists. Satellite L-space knot characterization conjecture. The satellite knot $P(K)$ is an L-space knot if and only if all of the following hold: $K$ is an L-space knot; $P(U,-2g+1)$ is an L-space knot; adding $-2g+1$ full twists to $P$ yields a strongly quasipositive braid in $D^2\times S^1$; and $P(U,-n)$ is a negative L-space knot for all sufficiently large integers $n$. This is the paper's more precise formulation of a proposed converse, but the third condition contains a question mark in the source and should be checked against the original manuscript.