Borot–Garcia-Failde's fully simple maps conjecture for loop models

Consider ordinary maps carrying self-avoiding loop configurations, whose topological-recursion initial data are given by the generating series of disks and cylinders with loops. Let $(x,w)$ be the corresponding spectral-curve variables, and let fully simple maps carrying the same loop model mean maps whose boundaries satisfy the fully simple restriction.

Fully simple loop-model conjecture. After the symplectic transformation

$$(x,w)\longmapsto(w,x),$$

in the initial data of topological recursion for ordinary maps with loops, the topological-recursion amplitudes enumerate fully simple maps carrying a loop model.

The claim generalizes the fully simple-map conjecture from ordinary maps to maps with self-avoiding loops. The disk and cylinder cases follow from the source's proved base cases, whereas the general loop-model statement remains open.