The tropical F-polynomial identity for nondegenerate quivers with potential

Let $\delta$ and $\check{\epsilon}$ be weights for a quiver with potential, and write $\check{f}_{\delta}$ and $f_{\check{\epsilon}}$ for the dual and ordinary tropical $F$-polynomials associated with general representations of weights $\delta$ and $\check{\epsilon}$, respectively. Let $\hom(\delta,\check{\epsilon})$ denote the relevant homomorphism invariant. Tropical F-polynomial conjecture. For a nondegenerate quiver with potential, and any $\delta$ and $\check{\epsilon}$, one has

$$\check{f}_{\delta}(\check{\epsilon})=\hom(\delta,\check{\epsilon})=f_{\check{\epsilon}}(\delta).$$

The identity would relate the dual and ordinary tropical $F$-polynomials through the homomorphism invariant; the source gives no resolution.