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.
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