Champanerkar–Kofman–Lalín's bipyramid volume conjecture for periodic alternating links

Let $\mathcal{L}$ be a $\mathbb{Z}^2$-periodic alternating link, with toroidally alternating quotient link $L$. Let $P(z,w)$ be the characteristic polynomial of the toroidal dimer model constructed from the associated periodic bipartite graph. The Champanerkar–Kofman–Lalín conjecture.

$$2\pi M(P(z,w)) \geq \operatorname{vol}^{\lozenge}(L).$$

Here $M(P(z,w))$ is the Mahler measure of $P(z,w)$, and $\operatorname{vol}^{\lozenge}(L)$ is the sum of the volumes of the regular ideal bipyramids associated with the faces of $L$. The conjecture compares the dimer-model Mahler measure with the bipyramid volume of the quotient link and was proposed for $\mathbb{Z}^2$-periodic alternating links; its resolution is not specified in the source.