  I discuss a novel scenario on how baryonic matter could turn into a Fermi
liquid of fractionalized baryons driven by high density inside compact stars.
It involves the "hidden" local vector bosons $\rho$ and $\omega$ together with
the "hidden" scale symmetry dilaton $\chi$, both taken to be "dual" to the
quarks and gluons of QCD in the sense of quark $\leftrightarrow$ hadron duality
and offers a possibility, exploiting the "Cheshire Cat Principle", to unify the
"dichotomy" of baryons described in terms of skyrmions and fractional quantum
Hall (FQH) droplets {\it and} to explore how the baryonic matter could behave
as density goes way beyond the normal nuclear matter density to the density
regime where "deconfined" quarks are presumed to figure. The question is raised
as to whether the fractionalized characteristics of the "stuff" -- whatever
they are -- can be "probed" in the dense star core of compact stars.
