Classification conjecture for multiple radial SLE null-vector solutions

Let $n$ growth points and $m$ screening variables define the null-vector equations and Ward identities for multiple radial SLE, and let $u\in\mathbb{H}$ be the marked interior point. Write $\operatorname{LP}(n,m)$ for the corresponding link patterns and let $\operatorname{Rad}(u,\mathbb{H})=i(\bar u-u)$. Classification conjecture. For every solution $\psi$ to the null-vector equations and Ward identities, there is a real constant $\alpha$ such that

$$\tilde{\psi}=\operatorname{Rad}(u,\mathbb{H})^{\alpha}\psi$$

belongs to one of four types: radial ground solutions, radial excited solutions, radial ground solutions with spin $\eta$, each of dimension $|\operatorname{LP}(n,m)|={n\choose m}$ for $1\leq m\leq n/2$, or chordal solutions of dimension $|\operatorname{LP}(2k,k)|=\frac{1}{k+1}{2k\choose k}$ when $n=2k$. This conjecture proposes a complete classification of the solution space, while the paper constructs the listed families by screening operations; whether they span all solutions remains open.