  The Electroweak interactions of a strongly coupled gauge theory are discussed
with outlook beyond the Standard Model (BSM) under global and gauge anomaly
constraints. The theory is built on a minimal massless fermion doublet of the
SU(2) BSM flavor group (bsm-flavor) with a confining gauge force at the TeV
scale in the two-index symmetric (sextet) representation of the BSM SU(3) color
gauge group (bsm-color). The intriguing possibility of near-conformal sextet
gauge dynamics could lead to the minimal realization of the composite Higgs
mechanism with a light $0^{++}$ scalar, far separated from strongly coupled
resonances of the confining gauge force in the 2-3 TeV range, distinct from
Higgsless Technicolor. In previous publications we have presented results for
the meson spectrum of the theory, including the light composite scalar, perhaps
the emergent Higgs impostor. Here we discuss the critically important role of
the baryon spectrum in the sextet model investigating its compatibility with
what we know about thermal evolution of the early Universe including its
galactic and terrestrial relics. For an important application, we report the
first numerical results on the baryon spectrum of this theory from
non-perturbative lattice simulations with baryon correlators in the staggered
fermion implementation of the strongly coupled gauge sector. The quantum
numbers of composite baryons and their spectroscopy from lattice simulations
are required inputs for exploring dark matter contributions of the sextet BSM
model, as outlined for future work.
