  In a previous article, the 4D half-skyrmion (or 5D dyonic salt) structure of
dense baryonic matter described in crystalline configuration in the large $N_c$
limit was shown to impact nontrivially on how anti-kaons behave in compressed
nuclear matter with a possible implication on an "ice-9" phenomenon of deeply
bound kaonic matter and condensed kaons in compact stars. We extend the
analysis to make a further prediction on the scaling properties of hadrons that
have a surprising effect on the nuclear tensor forces, the symmetry energy and
hence on the phase structure at high density. We treat this problem relying on
certain topological structure of chiral solitons. Combined with what can be
deduced from hidden local symmetry for hadrons in dense medium and the "soft"
dilatonic degree of freedom associated with the trace anomaly of QCD, we
uncover a novel structure of chiral symmetry in the "supersoft" symmetry energy
that can influence the structure of neutron stars.
