  The Glashow-Salam-Weinberg model for N=2 generations is extended to 8
composite Higgs multiplets by using a one-to-one correspondence between its
complex Higgs doublet and very specific quadruplets of bilinear quark
operators. This is the minimal number required to suitably account,
simultaneously, for the pseudoscalar mesons that can be built with 4 quarks and
for the masses of the $W$ gauge bosons. They are used as input, together with
elementary low energy considerations, from which all other parameters, masses
and couplings can be calculated. We focus in this work on the spectrum of the 8
Higgs bosons, on the mixing angles, and on the set of "horizontal" and
"vertical" entangled symmetries that, within the chiral $U(4)_L \times U(4)_R$
group, strongly frame this extension of the Standard Model. In particular, the
$u-c$ ($\theta_u$) and $d-s$ ($\theta_d$) mixing angles satisfy the robust
relation $\tan(\theta_d+\theta_u)\tan(\theta_d-\theta_u) =
\Big(\frac{1}{m_{K^\pm}^2}-\frac{1}{m_{D^\pm}^2}\Big) \big/
\Big(\frac{1}{m_{\pi^\pm}^2}-\frac{1}{m_{D_s^\pm}^2}\Big)$. Light scalars
(below $90 MeV$) arise and the mass of (at least) one of the Higgs bosons grows
like that of the heaviest $\bar q\gamma_5 q$ bound state. $\theta_u$ cannot be
safely tuned to zero and several parameters have no reliable expansion in terms
of "small" parameters like $m_\pi$ or the mixing angles. This study does not
call for extra species of fermions. The effective couplings of scalars, which
depend on the non-trivial normalization of their kinetic terms, can be
extremely weak. For the sake of (relative) brevity, their rich content of
non-standard physics (including astrophysics), the inclusion of the 3rd
generation and the taming of quantum corrections are left for a subsequent
work.
