Tan–Wong–Zhang's Cantor-set conjecture for end invariants

Let $\rho$ be an $SL(2,\mathbb{C})$-representation of \pi_1(\text{\boldmathT}), and let $\mathcal{E}(\rho)$ be its set of end invariants in the projective lamination space $\mathcal{PL}$ of \text{\boldmathT}. An element of $\mathcal{PL}$ is an end invariant if it is the limit of distinct essential simple loops whose traces under $\rho$ have uniformly bounded absolute value. Tan–Wong–Zhang's conjecture. If $\mathcal{E}(\rho)$ has at least two accumulation points, then $\mathcal{E}(\rho)$ is either a Cantor set in $\mathcal{PL}$ or all of $\mathcal{PL}$. This conjecture concerns the possible homeomorphism types of end-invariant sets; the cited context reports related structural results but does not state a resolution.