mass spectral exponent for the finite metastable quark-gluon bag with the colored SU ( N$_{c}$ ) state is reduced to α$_{non}$ = 1 / 2 (i.e. simply colored SU ( N$_{c}$ ) states). The metastable colored bags are expected to emerge before they expand smoothly and overlap each other and eventually form quark-gluon plasma. Nonetheless, the fuzzy and center of mass corrections modify the mass spectral exponent α significantly [2]. The center of mass correction has been introduced by Kapusta [5]. Therefore, it is expected that when the fuzzy and center of mass corrections are considered, the exponents α for the orthogonal, unitary and symplectic Hagedorn states overlap with each other under certain conditions in the hot and compressed nuclear matter. This leads to a smooth transmutation from certain composite bag’s internal symmetry to another one. The complexity of the color-flavor coupling structure for the large µ$_{B}$ is illustrated in Fig. (4). The color-flavor coupling is simplified drastically by correlating the bag’s color and flavor symmetries to form the Sp ( N ) symmetry group. The mass spectrum for the color superconductivity physics is simplified drastically by considering the colorless Sp ( N ) state. It is evident that the mass spectral exponent α for the continuous high-lying mass spectrum ρ$_{(}$$_{II}$$_{)}$ = c m − $^{α}$eb m depends essentially on µ$_{B}$ and T . The order of phase transition is sensitive to the exponent α . This sensitivity indicates the existence of the tri-critical point in the phase transition diagram. The order of deconfinement phase transition is found first order for the Hagedorn states with the exponent α > 7 $_{2}$. The second and third order phase transitions are found for Hagedorn states with exponents 7 2 ≥ α > 3 and 3 ≥ α > 17 6 , respectively. Moreover, the n th order phase transition takes place for 5 2 + 1 n − 1 ≥ α > 5 2 + 1 $_{n}$. There is no direct (explosive) deconfinement phase transition to quark-gluon plasma for the hadronic matter that is populated by Hagedorn states with the mass spectral exponent α ≤ 5 $_{2}$. The phase transition for the Hagedorn states with the mass spectral exponent α ≤ 5 2 is smooth (i.e. smooth cross-over phase transition). In this case, the Hagedorn bags expand smoothly and they are gently thermally excited without an abrupt phase transition to explosive quark-gluon plasma. If the unitary Hagedorns freeze out they undergo Gross- Witten phase transition to the low-lying mass spectrum hadronic matter. The means that the Hagedorn bags evaporate to the discrete low-lying mass spectrum particles and this resembles the black hole evaporation in AdS/CFT duality. It is reasonable to assume that the thermal excitation may change the Hagedorn bag’s internal structure. For instance under certain circumstances the nuclear matter that is 51