Bounded packing conjecture for subgroups of virtually polycyclic groups

Let $P$ be a virtually polycyclic group. A subgroup $H\leq P$ has bounded packing in $P$ if, for every $D>0$, there is a bound on the number of distinct left cosets of $H$ that are pairwise at distance less than $D$ in the corresponding coset metric.

Bounded packing conjecture for virtually polycyclic groups. Each subgroup of $P$ has bounded packing in $P$.

This conjecture is presented as an expected affirmative result after posing the broader question of whether every subgroup of every solvable group has bounded packing. Its resolution is not given in the supplied text.