  Exploiting certain robust topological inputs from the skyrmion description of
compressed baryonic matter with a scale-chiral symmetric Lagrangian, we predict
the equation of state that is consistent with the properties of nuclear matter
at the equilibrium density, supports the maximum mass of massive compact star
$\sim 2 M_\odot$ and surprisingly gives the sound velocity close to the
"conformal velocity" $1/\sqrt{3}$ at densities $\gtrsim 3 n_0$. At the core of
this result is the observation that parity-doubling occurs in the nucleon
structure as density goes above $\sim 2n_0$ with a chiral-singlet mass $m_0
\sim (0.6-0.9) m_N$, hinting at a possible up-to-date unsuspected source of
proton mass and an emergence at high density of scale symmetry and flavor local
symmetry, both hidden in the QCD vacuum.
