Yang's test-map discreteness conjecture for subgroups of $SL(2,\mathbb C)$

Let $G$ be a non-elementary subgroup of $SL(2,\mathbb C)$ containing elliptic elements, and let $f$ be a loxodromic or elliptic transformation. For each elliptic element $g\in G$, consider the subgroup $\langle f,g\rangle$. Yang's test-map discreteness conjecture. If $\langle f,g\rangle$ is discrete for every elliptic element $g\in G$, then $G$ is discrete. This conjecture concerns whether discreteness of the rank-two subgroups detected by a fixed test map forces discreteness of the whole non-elementary Möbius group. It was proposed as a generalization of earlier discreteness criteria using partial information about rank-two subgroups; the supplied text gives no resolution.