Zel'manov's classification conjecture for just-infinite pro-$p$ groups of finite width

Let $G$ be a just-infinite pro-$p$-group of finite width, meaning a just-infinite pro-$p$-group whose finite-index subgroup growth layers have uniformly bounded width. Zel'manov's classification conjecture. $G$ is either solvable, $p$-adic analytic, or commensurable to a positive part of a loop group or to the Nottingham group. This conjecture concerns the classification of just-infinite pro-$p$ groups under a finite-width hypothesis. The source presents it as a conjecture discussed by many mathematicians and stated by Zel'manov in 1996; the supplied text gives no resolution.