ALE scaling-limit conjecture for the folded dimer model on $\hat{\mathcal G}$

Let $\hat{\mathcal G}$ be obtained by adjoining to a graph $\mathcal G$ its reflection across the real axis while retaining one copy of vertices on the real axis. Let $M$ be an infinite-volume dimer cover of $\hat{\mathcal G}$, and define its reflected superposition by

$$\hat{\Sigma}=M|_{\mathbb H}\cup(-M)|_{-\mathbb H}.$$

The boundary-touching curves of $\hat{\Sigma}$ are the curves of interest. Folding ALE conjecture. In the scaling limit, the collection of boundary-touching curves in $\hat{\Sigma}$ converges to the Arc Loop Ensemble, denoted by $\mathrm{ALE}$, in the upper half-plane. The associated height function is expected to converge to a Neumann Gaussian free field normalization, motivating the ALE prediction; the source gives no resolution.