Mann's polynomial bound conjecture for Möbius values of open subgroups

Let $G$ be a positively finitely generated (PFG) group, and let $bc$ be the Mobius function on the lattice of open subgroups of $G$. For an open subgroup $H\leq G$, write $|G:H|$ for its index.

Mann's conjecture. The quantity $|\mu(H,G)|$ is bounded by a polynomial function of $|G:H|$, and the number of subgroups $H$ of $G$ of index $m$ satisfying $\mu(H,G)\neq 0$ grows at most polynomially in $m$.

This conjecture concerns polynomial control of both individual Mobius values and the number of open subgroups contributing nontrivially at each index in finitely generated profinite groups. Its resolution is not specified in the source.