Conjecture on nilpotent conjugacy growth and lower-central ranks

Let $G$ be a finitely generated nilpotent group, and for each $i$ let $r_i$ be the torsion-free rank of the quotient $G^{(i+1)}/G^{(i)}$. Nilpotent conjugacy-growth rank conjecture. The conjugacy growth of $G$ depends only on the numbers $r_i$. The conjecture would imply that conjugacy growth is a quasi-isometry invariant among finitely generated nilpotent groups, extending the results discussed in the source for virtually abelian groups and for class 2 nilpotent groups with infinite cyclic derived subgroup; it remains open in the source.