Abstract duality invariance conjecture for the interior polynomial

Let $G=(V_0,V_1,E)$ be a connected bipartite graph inducing hypergraphs $d4a2_0$ and $d4a2_1$ by taking the neighborhoods of the vertices in $V_0$ and $V_1$, respectively. The interior polynomial assigns a polynomial $I_{\mathscr G}$ to a hypergraph $\mathscr G$. Abstract duality conjecture. The two induced hypergraphs have the same interior polynomial:

$$I_{\mathscr G_0}=I_{\mathscr G_1}.$$

Equivalently, the interior polynomial should be an invariant of the underlying connected bipartite graph, independent of which color class is regarded as the vertex set of the hypergraph. The paper presents this as a conjectural extension of the equality of the previously established coefficients; no resolution is given here.