Density conjecture for regular crystalline points in framed deformation spaces

Let $p$ be a prime, let $n$ be a positive integer, let $K$ be a finite extension of $\mathbf{Q}_p$, and let $\overline\rho:G_K\to\operatorname{GL}_n(k_L)$ be a continuous representation as in the Böckle–Juschka conjecture. Let $\mathcal{X}^{\square}_{\overline\rho}$ be its framed deformation space; a crystalline point is regular when its labeled Hodge–Tate weights are distinct. Regular crystalline density conjecture. The set of regular crystalline points is dense in $\mathcal{X}^{\square}_{\overline\rho}$. The conjecture is motivated by the goal of showing that crystalline points are dense in the entire unrestricted local deformation space: regular crystalline points are expected to meet every irreducible component. The source presents this as a conjecture and gives no resolution of it in the supplied text.