  When baryon-quark continuity is formulated in terms of a topology change
without invoking "explicit " QCD degrees of freedom at a density higher than
twice the nuclear matter density $n_0$ the core of massive compact stars can be
described in terms of fractionally charged particles, behaving neither like
pure baryons nor deconfined quarks. Hidden symmetries, both local gauge and
pseudo-conformal (or broken scale), lead to the pseudo-conformal (PC) sound
velocity $v_{pcs}^2/c^2\approx 1/3$ at $\gsim 3n_0$ in compact stars. We argue
these symmetries are "emergent" from strong nuclear correlations and conjecture
that they reflect hidden symmetries in QCD proper exposed by nuclear
correlations. We establish a possible link between the quenching of $g_A$ in
superallowed Gamow-Teller transitions in nuclei and the precocious onset at
$n\gsim 3n_0$ of the PC sound velocity predicted at the dilaton limit fixed
point. We propose that bringing in explicit quark degrees of freedom as is done
in terms of the "quarkyonic" and other hybrid hadron-quark structure and our
topology-change strategy represent the "hadron-quark duality" formulated in
terms of the Cheshire-Cat mechanism~\cite{CC} for the smooth cross-over between
hadrons and quarks. Confrontation with currently available experimental
observations is discussed to support this notion.
