Gordon–Lidman conjecture on cyclic branched covers of satellite knots

Let $K$ be a prime satellite knot in $S^3$, and for each positive integer $n$ let $\Sigma_n(K)$ denote the $n$-fold cyclic branched cover of $S^3$ branched over $K$. A Gordon–Lidman conjecture. Every cyclic branched cover $\Sigma_n(K)$ is excellent. Here, excellent means that the manifold is neither an $L$-space nor has a non-left-orderable fundamental group, in the terminology used for cyclic branched covers; the statement is presented as an expected generalization of known results for torus knots, and its resolution is not supplied in the source.