Supercritical fully packed $O(2)$ maps scaling-limit conjecture

Fix $s>1$, and let $(M_k',L_k')$ be sampled from the modified iteration procedure. Let $\mathbf c_{\mathrm L}\in(1,25)$ be the central charge parameter determined by $s$ through

$$s=\exp\mathopen{}\mathclose\bgroup\originalleft(\frac{\sqrt{4-Q^2}}{Q}\pi\aftergroup\egroup\originalright),\qquad Q=\sqrt{\frac{\mathbf c_{\mathrm L}-1}{6}}.$$

A CLE$_4$-decorated supercritical LQG disk is the continuum surface with the corresponding central charge parameter, decorated by CLE$_4$. Supercritical map scaling-limit conjecture. Under an appropriate scaling limit as $k\to\infty$, $(M_k',L_k')$ converges to a CLE$_4$-decorated supercritical LQG disk, with central charge parameter $\mathbf c_{\mathrm L}\in(1,25)$ depending on $s$ as above. The conjecture is motivated by the modified iteration, the previously stated fully packed $O(2)$ conjecture, and the Markov property of the CLE$_4$-decorated supercritical LQG disk; it remains open.