Exceptional-speed solution-space conjecture for multiple-SLE null-state PDEs

Let $\mathcal{S}_N$ be the SLE partition-function solution space, let $\mathcal{B}_N$ be the distinguished family of solutions, and let $\mathcal{R}_N\subset\mathcal{S}_N$ be the solution space for the infinite collection of null-state PDEs governing the correlation function of $2N$ one-leg boundary operators. Let $\kappa_{q,q'}$ denote an exceptional speed, and suppose $\kappa=\kappa_{q,q'}\in(0,8)$ with $q\leq N+1$. Exceptional-speed solution-space conjecture. Then

$$\operatorname{span}\mathcal{B}_N=\mathcal{R}_N.$$

The conjecture would identify the span of the Coulomb-gas solutions with the full solution space of all null-state equations at exceptional speeds. The paper verifies or discusses special cases, including the $\mathcal{M}(3,2)$ case, but does not establish the assertion in general.