Classicality conjecture for de Rham strictly dominant points

Let $Y(U^p,\overline{\rho})$ be the eigenvariety locus considered in the paper, with points $x=(\rho,\underline{\delta})$ consisting of a Galois representation and a locally $\mathbb{Q}_p$-analytic character parameter. A point is called de Rham strictly dominant when $\rho$ is de Rham and the parameter is strictly dominant in the sense defined in the paper; a point is classical when it admits a nonzero morphism factoring through the locally $\mathbb{Q}_p$-algebraic quotient. Classicality conjecture. Every de Rham strictly dominant point $x\in Y(U^p,\overline{\rho})$ is classical. This predicts that sufficiently dominant de Rham points on the eigenvariety arise from classical automorphic representations; the supplied passage does not state a resolution.