Extra discrete representations conjecture for complex reflection triangle groups

Let $(p,q,r)$ be a triple with $p\leq q\leq r$, let $\rho_t(p,q,r)$ be the associated family, and classify the triple as type A or type B according to the critical-interval definition. Extra representations conjecture. If $(p,q,r)$ has type A, then there is a countable collection of parameters $t_1,t_2,t_3,\ldots$ for which $\rho_{t_j}(p,q,r)$ has infinite image, is discrete, and is not injective. If $(p,q,r)$ has type B, then every infinite discrete representation $\rho_t(p,q,r)$ is an embedding and is covered by the discreteness interval conjecture. The proviso excluding finite-image degeneracies is necessary because the source notes an always-available quotient onto $\mathbb{Z}/2$.