  We discuss near-conformal gauge theories beyond the standard model (BSM)
where interesting results on the twelve-flavor $\beta$-function of massless
fermions in the fundamental representation of the SU(3) color gauge group and
dilaton tests of the light scalar with two massless fermions in the two-index
symmetric tensor (sextet) representation can be viewed as parts of the same BSM
paradigm under investigation. We report results from high precision analysis of
the twelve-flavor $\beta$-function \cite{Fodor:2016zil} refuting its published
IRFP \cite{Cheng:2014jba,Hasenfratz:2016dou}. We present our objections to
recent claims \cite{Hasenfratz:2017mdh,Hasenfratz:2017qyr} for non-universal
behavior of staggered fermions used in our analysis. We also report our first
analysis of dilaton tests of the light $0^{++}$ scalar in the sextet model and
comment on related post-conference developments. The dilaton test is the main
thrust of this conference contribution including presentation #405 on the
$n_f=12$ $\beta$-function and presentation #260 on dilaton tests of the sextet
model. They are both selected from the near-conformal BSM paradigm.
