the Gross-Witten point (i.e. a continuous line in the µ$_{B}$ − T plane) is likely to be dominated by the unitary Hagedorns (i.e. colorless unitary SU ( N$_{c}$ ) states). When the dilute SU ( N$_{c}$ ) Hagedorn matter is heated up, the Hagedorn states mutate their internal symmetry from the colorless SU ( N$_{c}$ ) symmetry to the colorless O ( N$_{c}$ ) symmetry. Nevertheless, the flavor symmetry maintains its optimal invariance in the hot nuclear bath. Hence, the unitary Hagedorn matter undergoes phase transition to another Hagedorn matter that is dominated by the colorless orthogonal O ( N$_{c}$ ) states and becomes orthogonal Hagedorn matter. The phase transition from unitary Hagedorn matter to orthogonal Hagedorn matter is shown by the light dotted line (yellow online) on the top left of the µ$_{B}$ − T phase transition diagram. At higher temperature, the Hagedorn matter that is dominated by the colorless orthogonal states undergoes deconfinement phase transition to the quark-gluon plasma where the color- singlet constraint is broken in order to form colored SU ( N$_{c}$ ) states. When the color singlet constraint is broken badly, the colored quarks and gluons are liberated and/or the quark- gluon bags become colored ones. The order of the deconfinement phase transition is supposed to be varied and it is shown by several gray circles on the top and left of the µ$_{B}$ − T phase transition diagram. Two major factors likely modify the order of phase transition: The first factor comes mainly from the Hagedorn internal symmetry modification to either the colorless SU ( N$_{c}$ ), colorless O ( N$_{c}$ ) or colorless Sp ( N$_{c}$ ) states. It is also possible to assume that the heat can release most of the gluonic contents of the Hagedorn states and mutates them to the colorless U (1) N$_{c}$ quark bags in the case of the dilute nuclear matter where µ$_{B}$ ≈ 0 (i.e. further reduction in the adjoint degrees of freedom). Eventually, the heat can break the color- singlet constraint and the metastable colored (color-non-singlet-sate) SU ( N$_{c}$ ) quark-gluon bags (with initial total zero color charges: i.e. color-neutral bags) emerge in the system. The second factor is actually originated from the deformation of the Hagedorn cavity boundary surface. The situation is completely different when the nuclear system is compressed and cooled to lower temperatures. This is marked by the light dotted line (yellow online) on the lower right side of the µ$_{B}$ − T diagram in particular when the baryonic chemical potential µ$_{B}$ becomes relatively large. The flavor degree of freedom becomes more important albeit the system tends somehow to maintain the optimal flavor invariance and restores the chiral symmetry. Furthermore, the strangeness degree of freedom is essential, though it is not mentioned explicitly throughout the present work. Furthermore, along the µ$_{B}$ direction, the nuclear matter also passes the Gross-Witten Hagedorn phase transition from the hadronic 48