  The hadron-quark/gluon duality formulated in terms of a topology change at a
density $n\gsim 2n_0$ $n_0\simeq 0.16$fm$^{-3}$ is found to describe the core
of massive compact stars in terms of quasiparticles of fractional baryon
charges, behaving neither like pure baryons nor like deconfined quarks. This
can be considered as the Cheshire-Cat mechanism~\cite{CC} for the hadron-quark
continuity arrived at bottom-up from skyrmions that is equivalent to the
"MIT-bag"-to-skyrmion continuity arrived at top-down from quarks/gluons. Hidden
symmetries, both local gauge and pseudo-conformal (or broken scale), emerge and
give rise both to the long-standing "effective $g_A^\ast\approx 1$" in nuclear
Gamow-Teller transitions at $\lsim n_0$ and to the pseudo-conformal sound
velocity $v_{pcs}^2/c^2\approx 1/3$ at $\gsim 3n_0$. It is suggested that what
has been referred to, since a long time, as "quenched $g_A$" in light nuclei
reflects what leads to the dilaton-limit $g_A^{\rm DL}=1$ at near the
(putative) infrared fixed point of scale invariance. These properties are
confronted with the recent observations in Gamow-Teller transitions and in
astrophysical observations.
