Schwartz's conjectural picture for complex hyperbolic triangle groups

Assume $p_1\le p_2\le p_3$, and let $\iota_1,\iota_2,\iota_3$ be the complex reflections generating a $(p_1,p_2,p_3)$-representation. Define

$$w_A=\iota_3\iota_2\iota_3\iota_1,\qquad w_B=\iota_1\iota_2\iota_3.$$

Schwartz's conjectural picture. A $(p_1,p_2,p_3)$-representation is a discrete embedding if and only if neither $w_A$ nor $w_B$ is elliptic. The corresponding parameter values form a closed symmetric interval. If $w_A$ becomes elliptic before $w_B$, call the triple type A; otherwise call it type B. The triple is of type A if $p_1<10$ and of type B if $p_1>13$. For a type A triple, there is a countable collection of parameters for which the representation is infinite and discrete but not injective; for a type B triple, there are no discrete but non-injective representations of this kind.

This is the conjectural description, attributed in the source to Richard Schwartz, of the parameter space and discreteness behavior of complex hyperbolic triangle groups. The supplied material does not establish its resolution status.