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.
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