  We explore whether a tree-level expression for the gluon two-point function,
supposed to express effects of an horizon term introduced to eliminate the
Gribov ambiguity, is consistent with the propagator obtained in simulations of
lattice-regularised quantum chromodynamics (QCD). In doing so, we insist that
the gluon two-point function obey constraints that ensure a minimal level of
consistency with parton-like behaviour at ultraviolet momenta. In consequence,
we are led to a position which supports a conjecture that the gluon mass and
horizon scale are equivalent emergent mass-scales, each with a value of roughly
$0.5\,$GeV; and wherefrom it appears plausible that the dynamical generation of
a running gluon mass may alone be sufficient to remove the Gribov ambiguity.
