Critical loop-model correlation-function basis conjecture

Let $M$ be a combinatorial map and $W$ a choice of loop weights, and write $Z_{M,W}$ for the associated loop-model correlation function. Assume the critical limit exists. The corresponding conformal-bootstrap equations are those determined by the external data and spectra associated with the map family $\mathcal{M}_{g,n}(r_1,\ldots,r_n)$. Critical loop-model correlation-function basis conjecture. When it exists, the critical limit of $Z_{M,W}$ is a solution of the conformal-bootstrap equations. Moreover,

$$\left\{\lim_{\mathrm{critical}} Z_{M,W}\right\}_{M\in\mathcal{M}_{g,n}(r_1,\ldots,r_n)}$$

is a basis of the corresponding solution space. The statement is conditional on existence of the critical limit, and no resolution is given in the supplied text.