other hand, the quark and gluon bag’s internal structure is mutated from the colorless unitary state (unitary Hagedorn) to the colorless symplectic state (symplectic Hagedorn) under the extreme compressed nuclear matter (i.e. when the unitary Hagedorn matter becomes saturated) such that one is found in the compact stars. It is evident that the mass spectral exponent α increases with respect to µ$_{B}$ when the system is compressed and cooled down. This exponent decreases when the system is heated up. The Hagedorn states which are expected to be produced in the ultra-relativistic heavy ion collisions and beyond have a rather low mass spectral exponent. In the RHIC or LHC energy, it is expected that the dilute hadronic matter which is dominated at first by the unitary Hagedorn states at small µ$_{B}$ passes Hagedorn phase transition to another nuclear matter that is dominated by the orthogonal Hagedorns when the medium is heated up to higher temperature. The resultant orthogonal Hagedorn matter acts as the Coulomb liquid. At small baryonic density, the hot nuclear matter which is dominated by the colorless orthogonal (Hagedorn) states undergoes higher order phase transition to the colored SU ( N$_{c}$ ) states with total color-neutral quark-gluon plasma. The colored SU ( N$_{c}$ ) states are colored quark-gluon bags (i.e.: color-non-singlet states). The conserved color charges are adjusted by the color chemical potentials. The colored quark-gluon bags with color-non-singlet states are not Hagedorn states. Aftermath the deconfinement phase transition, the medium is enriched by colored quarks and gluons. In this sense the bag’s color-singlet constraint is badly broken and the bag becomes a colored one where the colored quarks can be liberated or exchanged. The phase transition from the hadronic matter which is dominated by the colorless Hage- dorns to another matter that is populated by the colored bags is associated with the breaking of the color-singlet constraint. The breaking of Hagedorn bag’s internal symmetry from the color-singlet state of the unitary symmetry to the colored unitary state probably takes place through several intermediate processes in the following way: colorless SU ( N$_{c}$ ) → colorless O$_{(}$$_{S}$$_{)}$ ( N$_{c}$ ) + 1 2 N$_{c}$ ( N$_{c}$ + 1) gluons , → colorless U (1) N$_{c}$ + N$_{c}$ ( N$_{c}$ − 1) gluons , → colored SU ( N$_{c}$ ) (i.e. color-non-singlet states) , → N$_{c}$ quarks + ( N 2 c − 1) gluons , (168) where the unimodular-like constraint is imposed in all the symmetries are involved in the 58