Hopf-divisibility conjecture for rational tangle relations

Let $[n_1,n_2,\dots,n_r]$ and $\epsilon[n_1,n_2,\dots,n_r]$ be two diagrams of rational links, where $\epsilon=1$ if $r$ is odd and $\epsilon=-1$ otherwise. The Rational Tangle Algorithm computes these diagrams as elements of the cubic skein module. Hopf-divisibility conjecture. The relation

$$[n_1,n_2,\dots,n_r]-\epsilon[n_1,n_2,\dots,n_r]$$

is divisible by the Hopf Relation. Therefore, the Rational Tangle Algorithm produces no relations beyond the Hopf Relation. This conjecture describes the relations detected by the rational tangle computations, while other relations in the full cubic skein module are known to occur outside the ideal generated by the Hopf Relation.