  In principle, the strong-interaction sector of the Standard Model is
characterised by a unique renormalisation-group-invariant (RGI) running
interaction and a unique form for the dressed--gluon-quark vertex,
$\Gamma_\mu$; but, whilst much has been learnt about the former, the latter is
still obscure. In order to improve this situation, we use a RGI
running-interaction that reconciles both top-down and bottom-up analyses of the
gauge sector in quantum chromodynamics (QCD) to compute dressed-quark gap
equation solutions with 1,660,000 distinct Ansaetze for $\Gamma_\mu$. Each one
of the solutions is then tested for compatibility with three physical criteria
and, remarkably, we find that merely 0.55% of the solutions survive the test.
Plainly, therefore, even a small selection of observables places extremely
tight bounds on the domain of realistic vertex Ansaetze. This analysis and its
results should prove useful in constraining insightful contemporary studies of
QCD and hadronic phenomena.
