  We bring evidence that the recently discovered property of natural stability
of the high-energy resummation is directly connected to the fragmentation
mechanism of heavy hadrons. As a phenomenological support, we provide
predictions for differential distributions sensitive to heavy-hadron tags,
calculated at the next-to-leading logarithmic level of the hybrid
high-energy/collinear factorization (NLL/NLO), as implemented in the JETHAD
multimodular code. We show that the stabilizing mechanism is encoded in gluon
channels of both heavy-flavor collinear fragmentation functions extracted from
data and the ones evolved from a non-relativistic QCD input.
