Entropy maximality conjecture for periodic regular graphs

Let $G$ and $G_0$ satisfy the assumptions of the theorem preceding this statement, and let $h_G(p)$ and $h_{G_0}(p)$ denote their monomer–dimer entropies at density $p$. Entropy maximality conjecture. For every $p\in[0,1]$,

$$h_G(p)\leq h_{G_0}(p).$$

The statement is presented as a consequence of the preceding theorem and the transfer-matrix comparison; however, the theorem's assumptions and the definitions of $G$, $G_0$, and $h_G(p)$ are not included in the supplied context. Its status therefore cannot be determined from this span.