The salvaged residual-representation ghost conjecture

Let $p\geq 5$, and let $\overline{\rho}$ be a residual Galois representation that is regular in the sense specified in the paper. For each $\kappa\in\mathcal W_{b(\overline{\rho})}$, write $w_\kappa=\kappa(1+2p)-1$, and let $G_{\overline{\rho}}(w,t)$ be the ghost series associated with $\overline{\rho}$. Let $S_\kappa^\dagger(\overline{\rho})$ denote the $\overline{\rho}$-isotypic component of the overconvergent $p$-adic cuspforms of weight $\kappa$. The salvaged residual-representation ghost conjecture. For every $\kappa\in\mathcal W_{b(\overline{\rho})}$, the Newton polygon of $G_{\overline{\rho}}(w_\kappa,t)$ equals the Newton polygon of the characteristic series of the $U_p$-operator acting on $S_\kappa^\dagger(\overline{\rho})$. This is the paper's proposed correction to the original ghost conjecture; the regularity condition is included because the original prediction fails in the oversight cases, while the conjecture is supported by theoretical and computational evidence.