the smooth cross-over phase transition which usually takes place at small baryonic density (i.e. µ$_{B}$ ≈ 0), the color charges are capable to escape and subsequently the color neutrality is violated. In this case, the color-singlet constraint is loosed and the bag’s internal symmetry is broken violently above the right hand side of the tri-critical point in the following way: When the system is compressed and cooled down further more and becomes extremely dense and saturated (i.e. µ$_{B}$ becomes significantly large), the unitary Hagedorn matter transmutes to another one that is dominated by the symplectic Hagedorn states due to the modification of the quark and gluon bag’s internal structure and the coupling of color symmetry with other symmetries such as but not limited to the flavor symmetry as follows In fact the symplectic symmetry restores additional N 2 − N adjoint degrees of freedom (for instance partially breaking the flavor invariance SU ( N$_{f}$ ) × SU ( N$_{f}$ ) and leaving U (1) N$_{f}$ − 1 invariance) besides the original N 2 c − 1 adjoint color degrees of freedom. The phase transition from the unitary Hagedorns to the colorless symplectic states (i.e. symplectic Hagedorns) may take place through more complicated multi-processes in the Hagedorn matter. Further- more, the mass spectral exponent α will continue to increase when additional symmetries are incorporated as the nuclear matter becomes denser. Probably, the Hagedorn matter with a certain complex internal symmetry passes to a new physics regime such as forming fluid of stable black holes or dark matter. The deformation of the quark and gluon bag’s boundary surface besides other corrections such as the center of mass correction modify the mass spectral exponent α smoothly. The smooth modification of the mass spectral exponent α guarantees the continuity of various hadronic phases which are dominated by orthogonal, unitary and symplectic etc Hagedorns. Moreover, it is worth to mention that the symplectic Hagedorn matter is very rich due to the color-flavor coupling or color-angular coupling etc. The emergence of the color-superconductivity and other related physics can be explained in terms of the complex internal structure such as the symplectic Hagedorn matter. The analysis of the chiral phase transition at low µ$_{B}$ and high T demonstrates that in the case of the mass spectral exponent α ≤ 7 / 2 such as the mass spectrum for orthogonal Hagedorn states, the chiral restoration phase transition takes place far away below the de- confinement phase transition but at the threshold or above Gross-Witten point. Therefore, 60 colorless: color-singlet SU ( N$_{c}$ ) → colored SU ( N$_{c}$ ) . (169) SU ( N$_{c}$ ) × SU$_{L}$ ( N$_{f}$ ) × SU$_{R}$ ( N$_{f}$ ) → Sp ( N ) × [ conserved: U (1) N$_{f}$ − 1 ] . (170)