Schramm's FK interface convergence conjecture

Fix $q\in[0,4]$. A critical FK interface is the exploration interface in a Dobrushin domain for FK percolation with cluster-weight $q$. Schramm's conjecture. The law of critical FK interfaces with cluster-weight $q$ converges to Schramm–Loewner evolution with parameter

$$\kappa=\frac{4\pi}{\arccos(-\sqrt q/2)}.$$

The source derives this prediction from the conjectured scaling limit of the parafermionic observable and the associated martingale. Establishing convergence of the discrete interfaces is described as the final goal of the program and remains open in the supplied text.