The power conjecture for colored HOMFLY homology of rational knots and links

Let $L$ be a rational knot or link. For each $j$, let $\tilde{P}_j(L)(a,Q,t)$ denote the Poincaré polynomial of reduced triply graded $\Lambda^j$-colored HOMFLY homology with a corrected $Q$-grading, and let $P_j(L)(a,q,t)$ denote the ordinary Poincaré polynomial.

Power conjecture. There exists a corrected $Q$-grading such that

$$\tilde{P}_j(L)(a,Q,t)=\bigl(\tilde{P}_1(L)(a,Q,t)\bigr)^j.$$

In particular,

$$P_j(L)(a,1,t)=\bigl(P_1(L)(a,1,t)\bigr)^j.$$

The conjecture asserts that higher-color homologies of rational knots and links are governed by powers of the uncolored homology. The supplied text gives no evidence of resolution, so its status remains open.