Super-strong separation lemma for critical percolation interfaces

Let $B(R_2)$ and $B(R_1)$ be concentric planar regions with $R_1>R_2$, and let an arbitrary starting configuration $\Theta$ of faces surround $B(R_2)$, with any number of faces. Consider the interfaces starting from the endpoints of these faces and reaching $B(R_1)$.

Super-strong separation lemma. Conditioned on at least four of these interfaces reaching $B(R_1)$, the set of interfaces reaching $R_1$ has positive quality with positive probability.

This is an expected strengthening of the separation result for critical planar percolation interfaces. The source states that it is not known how to prove this version; its precise meaning depends on the previously defined notion of the quality of a set of interfaces.