Conjecture on Busemann points of free two-step nilpotent groups

Let $N_{2,r}$ be the free nilpotent group of step $2$ and rank $r$, equipped with its standard generating set. Its Busemann points are the horofunctions arising as limits of geodesic or almost-geodesic rays.

Free two-step nilpotent Busemann-point conjecture. The set of Busemann points of $N_{2,r}$ with respect to the standard generating set is countable.

This conjecture is proposed as a tool for extending the classification of Busemann points from particular two-step nilpotent groups to general finitely generated two-step nilpotent groups, using quotients of the free two-step nilpotent group. The source provides no resolution, so its status remains open.