we will work with null-homologous knots equipped with a fixed Seifert surface, $F$, though more general constructions are possible [@RationalSurgeries]. This paper, and its predecessor [@Cabling], study the knot Floer filtration induced by a class of knots called cable knots.

Let $K$ be a knot. Recall that the $(p,q)$ cable of $K$, denoted $K_{p,q}$, is a satellite knot with pattern the $(p,q)$ torus knot, $T_{p,q}$. More precisely, $K_{p,q}$ is the image of a torus knot living on the boundary of a tubular neighborhood of $K$.[^1] Thus $p$ is the number of times $K_{p,q}$ traverses the longitudinal direction of $K$, and $q$ the meridional number. Throughout, we will assume $p>0$.[^2] Our original motivation for studying cable knots and, more generally, satellite knots, lay in the fact that their complements decompose as the union of two three-manifolds joined along a torus, and hence provide a testing ground for the topological quantum field theoretic (TQFT) behavior of the Heegaard Floer invariants in $(2+1)$ dimensions.

The knot Floer filtration is, in fact, a $\Z\oplus\Z$ filtration of $\CFinf(Y,\spinc)$, and it is the filtered chain homotopy type of this $\Z\oplus\Z$ filtration which is the primary knot invariant coming from Heegaard Floer homology. The existence of two 