Star-placement symmetry conjecture for knotoid potentials

Let $K$) be a knotoid diagram in $S^2$. Let $K_1$ and $K_2$ be the starred knotoid diagrams obtained from $K$ by placing a star in the regions incident to the tail and head of $K$, respectively. The potential $abla_L(W,B)$ of a starred diagram $L$ is defined by the state \sum over all states of $L$.

Star-placement symmetry conjecture. The potentials satisfy

$$\nabla_{K_{1}}(W,B)=\nabla_{K_{2}}(-B,-W).$$

This conjecture expresses the observed symmetry between the potentials associated with the two possible endpoint-adjacent star placements. The paper notes that the potential is introduced partly because of this graph-theoretic phenomenon; no resolution is supplied in the given text.