The universal rank-expansion conjecture for winding-zero satellite operators

Let $\mathcal{C}$ be the smooth knot concordance group. A satellite operator $P$ is rank-expanding along $\{nK\}_{n\in\mathbb{Z}}$ if $\{nK\}_{n\in\mathbb{Z}}$ is a rank-one subgroup of $\mathcal{C}$ and $\{P(nK)\}_{n\in\mathbb{Z}}$ has infinite rank. Universal rank-expansion conjecture. Any non-constant winding number zero satellite operator is rank-expanding along every rank-one subgroup $\{nK\}_{n\in\mathbb{Z}}$. This would strengthen the preceding existence conjecture by requiring rank expansion for every nontorsion knot $K$. The paper proves rank expansion for many patterns and companion families, but this universal assertion remains open.