the chiral mass is generated through the multiple phase transition processes from the or- thogonal Hagedorn states to the unitary Hagedorn states and subsequently to the low-lying mass spectrum states at the Gross-Witten point. The order and shape of the ( µ$_{B}$ − T ) phase transition diagram depends basically on the internal structure of the quark and gluon bags such as but not limited to the color, flavor and angular symmetries. The Hagedorn’s mass spectral exponent α is found to depend essentially on the medium. Furthermore, the multi-intermediate processes in the phase transition diagram from the low-lying hadrons to the eventual quark-gluon plasma is found very rich and not trivial. The complexity of the multi-process phase transitions increases along the temperature axis with the rather small baryonic chemical potential µ$_{B}$ ∼ 0 (i.e. dilute nuclear matter). It is evident that the Hagedorn’s internal structure is significantly modified with respect to both T and µ$_{B}$ . The mass spectral exponent seems to increase significantly at large baryonic density µ$_{B}$ ≫ 0 and relatively low temperature (i.e. the extreme dense nuclear matter that is relevant to the compact stars). The order and shape of the phase transition is basically medium dependent. It is associated with complicated multi- processes of symmetry reconfiguration along the chemical potential µ$_{B}$ and temperature T axes. Therefore, the QCD phase transition diagram is proved to be very rich, tricky and non-trivial one. The partial support from Alexander von Humboldt foundation is acknowledged. Acknowledgments [1] I. Zakout and C. Greiner, Phys. Rev. C78 , 034916 (2008), arXiv:0709.0144 [nucl-th] [nucl-th]. [2] I. Zakout, C. Greiner, and J. Schaffner-Bielich, Nucl. Phys. A781 , 150 (2007), arXiv:nucl-th/0605052. [3] C. Amsler et al. (Particle Data Group), Phys. Lett. B667 , 1 (2008). [4] J. I. Kapusta, Phys. Rev. D23 , 2444 (1981). [5] J. I. Kapusta, Nucl. Phys. B196 , 1 (1982). [6] D. J. Gross and E. Witten, Phys. Rev. D21 , 446 (1980). [7] A. Andronic et al. (2009), arXiv:0911.4806 [hep-ph] [hep-ph]. 61