The colored cable colimit conjecture

Let $\mathbf{K}$ be a framed, oriented knot, and let $\chi\mathbf{K}$ denote the knot with framing increased by one. For $b\geq0$, consider the directed system whose terms alternate between the trivial and sign isotypic components of the deformed homology complexes of successive $b$-cables, with maps induced by the bottom eigenmap for the $b$-strand full twist. Colored cable colimit conjecture. The homotopy colimit of this system is quasi-isomorphic to the $b$-colored curved Rickard complex $\EuScript Y C_{\mathrm{KR}}(\mathbf{K},b)$, as complexes of modules over

$$\mathbb{Q}[x_1,\ldots,x_b]^{\mathfrak{S}_b}\otimes\mathbb{Q}[v_1,\ldots,v_b].$$

The conjecture extends the undeformed cable relation to deformed colored triply-graded homology; it is supported by the paper's results for colored Hopf links but remains unproved in general.