  We review the recent exploration of a possible "domain-wall structure" of
compressed baryonic matter in massive compact stars in terms of fractional
quantum Hall droplets and skyrmions for baryons in medium. The theoretical
framework is anchored on an effective nuclear effective field theory that
incorporates two hidden symmetries, flavor local symmetry and scale symmetry
conjectured to be dual to the gluons and quarks of QCD. It hints at a basically
different, hitherto undiscovered structure of nuclear matter at low as well as
high densities. Hidden "genuine dilaton (GD)" symmetry and hidden local
symmetry (HLS) gauge-equivalent at low density to nonlinear sigma model
capturing chiral symmetry, put together in nuclear effective field theory, are
seen to play an increasingly important role in providing hadron-quark duality
in baryonic matter. This strongly motivates incorporating both symmetries in
formulating "first-principles" approaches to nuclear dynamics encompassing from
the nuclear matter density to the highest density stable in the Universe.
