Multiple-SLE crossing-probability formula

Let $\kappa\in(0,8)$, and consider a multiple-SLE$_\kappa$ process growing $2N$ curves in the upper half-plane from points $x_1<x_2<\ldots<x_{2N}$, with SLE$_\kappa$ partition function $F\in\mathcal{S}_N$. For each connectivity index $\varsigma\in\{1,2,\ldots,C_N\}$, let $[\mathscr{L}_{\varsigma}]F$ be the corresponding connectivity weight and let $\Pi_{\varsigma}$ be the associated connectivity function. The multiple-SLE crossing-probability conjecture. The probability that the curves eventually join pairwise in the $\varsigma$th connectivity is

$$P_{\varsigma}(x_1,x_2,\ldots,x_{2N})=[\mathscr{L}_{\varsigma}]F\,\frac{\Pi_{\varsigma}(x_1,x_2,\ldots,x_{2N})}{F(x_1,x_2,\ldots,x_{2N})}.$$

Equivalently, using the decomposition of $F$ into connectivity functions, this yields the normalized crossing probabilities described in the paper. The formula matches the crossing-probability expression previously conjectured for multiple SLE, but its validity is not established here.