  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 make the suggestion for 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 implementing explicit quark degrees of freedom for
baryon-quark continuity as is done in terms of the "quarkyonic" and other
hybrid structure belongs to the class of the Cheshire Cat mechanism or what may
be called "Cheshire Catism." Confrontation with currently available
experimental observations is discussed to support this notion.
