Expander and wired-tree local-limit conjecture for the minimum spanning algorithm

Let $G_n$ be an expander sequence converging locally to the $d$-regular tree. Consider the local limits associated with item c., a sequence of $d$-regular expanders with $n$ vertices, and item d., a $d$-regular tree of height $n$ whose leaves are glued or wired together, both with i.i.d. continuously distributed weights with positive support. Expander–wired-tree local-limit conjecture. The local limit for the expander sequence in item c. matches the local limit for the wired $d$-regular-tree sequence in item d. This is posed as a natural extension of the main theorem to other graph classes; the existence of a local limit for the wired-tree case with i.i.d. Exponential$(1)$ weights is stated to be known, but a more detailed description and the claimed identification with the expander limit remain open.