Greenberg's semisimplicity conjecture for the cyclotomic Selmer module

Let $A$ be as in the cyclotomic Iwasawa setting, let $X(A/F_\mathrm{cyc})$ have a pseudo-isomorphism with elementary factors including $\bigoplus_{j=1}^t\mathbb{Z}_p\llbracket\Gamma\rrbracket/f_j^{\beta_j}$, where each $f_j$ is irreducible and is not an associate of $p$. Greenberg's conjecture. One has $\beta_j=1$ for every $j$. This semisimplicity condition would rule out repeated powers among the non-$p$ elementary factors and implies the auxiliary assumption used in the paper; its general status is left unresolved here.