to the fact that the techniques of [@VanCott2008] can also be employed in the study of the Rasmussen concordance invariant, $s(K)$. This latter invariant is defined using Khovanov homology [@RasSlice], and while it shares several important properties of $\tau$ the two invariants are independent [@Stau]. Indeed, we expect the behavior of the corresponding functions $\cs{n}$ to be quite different from that of $\ctau{n}$. Our intuition comes from the fact that the Alexander polynomial of cable knots is determined by the formula $$\label{eq:satpoly}
\Delta_{K_{p,q}}(t)=\Delta_{T_{p,q}}(t)\cm\Delta_K(t^p).$$ On the other hand, there cannot exist a formula which computes the Jones polynomial of cables of $K$ in terms of the Jones polynomial of $K$. Since knot Floer homology and Khovanov homology categorify the Alexander and Jones polynomial, respectively, we expect any invariant derived from these theories, e.g. $\tau$ and $s$, to have quite different behavior under cabling. For this reason, we expect invariants derived from $s$ of cables to be very interesting new concordance invariants, and a pursuit of effective means of computation is well-motivated. In fact, one can ask:

Does the Rasmussen concordance invariant, applied to all iterated cables of $K$, determine if $K$ is smoothly slice?

This question has many variants obtained by 