  We propose and examine a new high-density composite of $\Lambda^* \equiv K^-p
= (s \bar{u}) \otimes (uud)$, which may be called {\it Kaonic Proton Matter
(KPM)}, or simply, {\it $\Lambda^* $-Matter}, where substantial shrinkage of
baryonic bound systems originating from the strong attraction of the
$(\bar{K}N)^{I=0}$ interaction takes place, providing a ground-state neutral
baryonic system with a huge energy gap. The mass of an ensemble of $(K^-p)_m$,
where $m$, the number of the $K^-p$ pair, is larger than $m \approx 10$, is
predicted to drop down below its corresponding neutron ensemble, $(n)_m$, since
the attractive interaction is further increased by the Heitler-London type
molecular covalency, as well as by chiral symmetry restoration of the QCD
vacuum. Since the seed clusters ($K^-p$, $K^-pp$ and $K^-K^-pp$) are
short-lived, the formation of such a stabilized relic ensemble, $(K^-p)_m$, may
be conceived during the Big-Bang Quark Gluon Plasma (QGP) period in the early
universe before the hadronization and $quark$-$anti$-$quark$ annihilation
proceed. At the final stage of baryogenesis a substantial amount of primordial
($\bar{u},\bar{d}$)'s are transferred and captured into {\it KPM}, where the
anti-quarks find places to survive forever. The expected {\it KPM} state may be
{\it cold, dense and neutral $\bar{q} q$-hybrid ({\it Quark Gluon Bound (QGB)})
states, $[s(\bar{u} \otimes u) ud]_m$,} to which the relic of the disappearing
anti-quarks plays an essential role as hidden components. The {\it KPM} may
also be produced during the formation and decay of neutron stars.
