The three-component skein invariant sum conjecture

Let $L_1$ and $L_2$ be links with three components. For each $c$, let $\Sigma^c(L)$ denote the sum of the elements of the set $\mathbf{F}^c_p$ associated with $L$, where $p$ records the relevant coloring type. Three-component sum conjecture. If

$$\Sigma^1(L_1)=\Sigma^1(L_2),$$

then

$$\Sigma^3(L_1)-\Sigma^2(L_1)=\Sigma^3(L_2)-\Sigma^2(L_2).$$

The conjecture proposes an identity among the sums of the colored-link skein invariant values for three-component links; the supplied text does not state whether it has been proved or disproved.