GHPL convergence of unmarked loop O(n) planar maps to the LQG disk

Let $n\in(0,2)$, let $(g,h)\in\mathcal{D}\cup\{(g_*,h_*)\}$, and let $(T_\ell,\Gamma_\ell)\sim p^{-,n,g,h}_{0,\ell}$. Set $\kappa=\kappa(n,g,h)$ and $a(\kappa)=2\wedge(8/\kappa)$. View $(T_\ell,\Gamma_\ell)$ as a loop-decorated metric measure space, with graph distance multiplied by $c\ell^{-2/d(\kappa)}$ and counting measure multiplied by $c'\ell^{-a(\kappa)}$.

Unmarked planar-map scaling-limit conjecture. There exist unique constants $d(\kappa)>0$ and $c,c'>0$ such that the rescaled spaces converge in law to $\bar{\operatorname{M}}_{0,1}^{-,\kappa}$, normalized to be a probability measure, as $\ell\to\infty$ in the GHPL topology.

This gives a precise metric-measure scaling-limit prediction for the unmarked loop $O(n)$ model in the dense and dilute regimes described by the parameter set $\mathcal{D}$ and its non-generic critical point.