  We show that the regular separability problem of VASS reachability languages
is decidable and $\mathbf{F}_{\omega}$-complete. At the heart of our decision
procedure are doubly-marked graph transition sequences, a new proof object that
tracks a suitable product of the VASS we wish to separate. We give a
decomposition algorithm for DMGTS that not only achieves perfectness as known
from MGTS, but also a new property called faithfulness. Faithfulness allows us
to construct, from a regular separator for the $\mathbb{Z}$-versions of the
VASS, a regular separator for the $\mathbb{N}$-versions. Behind faithfulness is
the insight that, for separability, it is sufficient to track the counters of
one VASS modulo a large number that is determined by the decomposition.
