The eigencurve intersection conjecture for one-dimensional local representations

Let $l$) and $p$ be distinct rational primes, let $S$ be a finite set of places of $\mathbb{Q}$ containing $p$, $l$ and $\infty$, and let $\mathcal{E}$ be the cuspidal eigencurve lying over a modular two-dimensional residual representation $V_{\mathbb{F}}$. Each point $x\in\mathcal{E}$ has an associated two-dimensional Frobenius semisimple Weil–Deligne representation $(\rho_{x,l},N_x)$.

Eigencurve intersection conjecture. If $x\in\mathcal{E}$ is such that $\pi(\rho_{x,l},N_x)$ is one dimensional, then there exist irreducible components $\mathcal{Z},\mathcal{Z}'\subset\mathcal{E}$, generically special and principal series respectively, such that $x\in\mathcal{Z}\cap\mathcal{Z}'$.

This conjecture predicts that every failure of local-to-global compatibility arising from a one-dimensional local representation occurs at an intersection of a generically special component and a generically principal-series component of the eigencurve. The supplied text gives no resolution of the conjecture.