Resolution conjecture for generalized Kauffman brackets with multiple double points

Let $L^{(j,0)}$ be a singular link with $j\geq 1$ transverse double points, and let $Z\left(L^{(j,0)}\right)$ denote its generalized Kauffman bracket. Resolving one chosen transverse double point produces links $L^{(j-1,0)}$ with positive and negative crossings.

Resolution conjecture. The generalized Kauffman bracket is given by

$$Z\left(L^{(j,0)}\right)=\frac{1}{e(\frac{1}{2})+e(-\frac{1}{2})}\left(Z\left(L^{(j-1,0)}\right)_{+}+Z\left(L^{(j-1,0)}\right)_{-}\right).$$

This extends the resolution rule from one transverse double point to an arbitrary number of double points. The supplied text presents the formula as an expectation, and gives no evidence that it has been proved or disproved.