Miyazaki's torsion conjecture for cables

Let $K$ be a knot, let $p$ and $q$ be relatively prime integers with $|p|>1$, and let $K_{p,q}$ denote the $(p,q)$-cable of $K$. Let $\mathcal{C}$ denote the smooth knot concordance group. Miyazaki's torsion conjecture. The $(p,q)$-cable of $K$ is torsion in $\mathcal{C}$ if and only if $K$ is slice and $|q|=1$. This strengthens the question of whether a $(p,1)$- or $(p,-1)$-cable can be slice only when the companion knot is slice. The paper proves infinite-order and linear-independence results for many odd cables, but the stated equivalence is not resolved here.