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When baryon-quark continuity is formulated in terms of a topology changewithout invoking "explicit " QCD degrees of freedom at a density higher thantwice the nuclear matter density $n_0$ the core of massive compact stars can bedescribed in terms of fractionally charged particles, behaving neither likepure baryons nor deconfined quarks. Hidden symmetries, both local gauge andpseudo-conformal (or broken scale), lead to the pseudo-conformal (PC) soundvelocity $v_{pcs}^2/c^2\approx 1/3$ at $\gsim 3n_0$ in compact stars. We arguethese symmetries are "emergent" from strong nuclear correlations and conjecturethat they reflect hidden symmetries in QCD proper exposed by nuclearcorrelations. We establish a possible link between the quenching of $g_A$ insuperallowed Gamow-Teller transitions in nuclei and the precocious onset at$n\gsim 3n_0$ of the PC sound velocity predicted at the dilaton limit fixedpoint. We propose that bringing in explicit quark degrees of freedom as is donein terms of the "quarkyonic" and other hybrid hadron-quark structure and ourtopology-change strategy represent the "hadron-quark duality" formulated interms of the Cheshire-Cat mechanism~\cite{CC} for the smooth cross-over betweenhadrons and quarks. Confrontation with currently available experimentalobservations is discussed to support this notion.

The sound speed and core of massive compact stars: A manifestation of hadron-quark duality