Square-lattice FK interfaces and nested loops for 1 ≤ q < 4

For every fixed $1\le q<4$, critical square-lattice random-cluster Dobrushin interfaces converge as ordered curves to chordal $\SLE_{\kappa(q)}$, where $\kappa(q)=4\pi/\arccos(-\sqrt q/2)$, confirming the Rohde--Schramm prediction in this parameter range. This holds in every bounded Jordan domain under uniform marked boundary approximation. The complete nested plane loop collections converge to whole-plane $\CLE_{\kappa(q)}$ in a spherical matching topology retaining multiplicities and traversals. At $q=1$ we obtain Cardy's formula for square-lattice bond percolation with free boundary edges.