Tan–Wong–Zhang end-invariant conjecture for two-bridge link representations

Let $\rho$ be a $\mathrm{PSL}(2,\mathbb{C})$-representation of \pi_1(\text{\boldmathT}), and let $\mathcal{E}(\rho)\subset\mathcal{PL}$ denote its set of end invariants. An accumulation point is a limit point of $\mathcal{E}(\rho)$ in the projective lamination space $\mathcal{PL}$. Tan–Wong–Zhang's end-invariant conjecture. If $\mathcal{E}(\rho)$ has at least two accumulation points, then either

$$\mathcal{E}(\rho)=\mathcal{PL}$$

or $\mathcal{E}(\rho)$ is a Cantor set contained in $\mathcal{PL}$. Tan, Wong, and Zhang proved that $\mathcal{E}(\rho)$ is closed and established the asserted dichotomy for discrete representations under a stronger hypothesis; the general statement remains open.