Infinite-volume scaling limit conjecture for the uniform infinite meandric system

Let $(\mathcal M,P,\Gamma)$ be the infinite random planar map decorated by a bi-infinite Hamiltonian path and the loops and possibly bi-infinite paths associated to the UIMS. Uniform infinite meandric-system scaling limit conjecture. Under an appropriate scaling limit, $(\mathcal M,P,\Gamma)$ converges to an independent triple consisting of a $\sqrt2$-LQG cone, a whole-plane SLE$_8$ from $\infty$ to $\infty$, and a whole-plane CLE$_6$. This is the infinite-volume analogue of the finite-volume scaling-limit prediction and is consistent with the conjecture that all UIMS components are finite loops; it remains open.