The Toroidal Volume–Determinant Conjecture for biperiodic alternating links

Let $\mathcal L$ be a biperiodic alternating link with alternating quotient link $L$, and let $K_n$ be alternating hyperbolic links satisfying $K_n\stackrel{\rm F}{\longrightarrow}\mathcal L$. Let $p(z,w)$ be the characteristic polynomial of the associated toroidal dimer model, and let $m(p(z,w))$ denote its Mahler measure. Toroidal Vol-Det Conjecture.

$$\operatorname{vol}((T^2\times I)-L)\leq 2\pi\,m(p(z,w)).$$

This inequality is motivated by the volume-density and determinant-density limits established for the infinite square weave and, more generally, for biperiodic alternating links. The supplied source gives no resolution status.