Large-weight spanning-forest free-energy conjecture

Let $f(w)$ be the spanning-forest free energy per site on a regular lattice of dimension $d\geq2$ and coordination number $r$, and let $f_0$ denote the entropy per site for spanning trees on that lattice. The large-weight expansion conjecture. As $|w|\to\infty$,

$$f(w)=\log|w|+f_0+\frac{1}{2r}\frac{1}{w}+O(w^{-2}).$$

The conjecture is motivated by numerical fits for the square and triangular lattices and predicts the universal first inverse-$w$ coefficient in terms of the coordination number.