Large-parameter limit of the beta-skewed free maximal spanning forest

Determine whether, for every locally finite connected graph with a transitive nonunimodular automorphism subgroup, the local limit of the beta-skewed free maximal spanning forest as beta tends to infinity exists and almost surely equals the free w-maximal spanning forest.

Background

The paper establishes the large-beta local limit for the wired beta-skewed maximal spanning forest in full generality, and for the free version under additional hypotheses, including equality of the wired and free w-maximal spanning forests or discrete weight values. The authors explain that, without such assumptions, subsequential limits exist but the existence of the full limit is unclear. The question asks whether the stronger conclusion always holds in the general setting of the wired-limit theorem.