Full HOMFLY invariance under mutation for connected simple plabic graphs

Let $G$ and $G'$ be connected simple plabic graphs whose quivers $Q_G$ and $Q_{G'}$ are mutation equivalent. Let $L^{\operatorname{plab}}_G$ and $L^{\operatorname{plab}}_{G'}$ be their associated plabic graph links. Full HOMFLY invariance conjecture.

$$P(L^{\operatorname{plab}}_G;a,z)=P(L^{\operatorname{plab}}_{G'};a,z).$$

This asserts that the full HOMFLY polynomial, unlike the link itself in general, is determined by the mutation class of the quiver for connected simple plabic graphs. The supplied source gives no resolution status.