matter which is dominated by the discrete low-lying mass spectrum hadrons to another one that is dominated by the continuous high-lying mass spectrum Hagedorns. The continuous high-lying mass (and volume) spectrum phase is initially dominated by the colorless SU ( N$_{c}$ ) states in particular just above the mete of the Gross-Witten point. Evidently the system undergoes phase transition to another Hagedorn matter that is populated by colorless Sp ( N ) states when the color and flavor degrees of freedom are coupled to form Sp ( N ) symmetry group. The phase domain of the new colorless Sp ( N$_{c}$ ) states is immured by the light dotted line (online green) on the lower-right side of the µ$_{B}$ − T diagram. It sounds that the nuclear matter which is dominated by the colorless Sp ( N ) states overlaps and matches the color- superconductivity, non-CFL quark liquid and CFL alike phases. The complexity of the color-flavor coupling and the nontrivial Sp ( N ) structure increases significantly when the system is compressed to form denser nuclear matter. Fig. (2) focuses on the flavor symmetry besides the color symmetry. It is shown that the Hagedorn matter is initially dominated by the mesonic Hagedorn states for small µ$_{B}$ . When µ$_{B}$ increases, the baryonic Hagedorn states appear in the system besides the existing mesonic Hagedorn states. It follows from Eq.(137) that mass spectral exponent increases by α → α + 1 2 when the Hagedorn states attain specific baryonic number and it is also modified by α → α + 1 2 when the strangeness number is included. The strangeness turns to be impor- tant when the system is compressed to larger µ$_{B}$ and is heated up to higher temperature. Furthermore, the Hagedorn matter tends to maintain the optimal flavor invariance in the dilute hot nuclear matter keeping in mind that the Hagedorn states are colorless regardless of the type of the internal color structure symmetry or if the color degrees of freedom are coupled to other degrees of freedom. When the the maximum flavor invariance is maintained at high temperature, the classical Maxwell-Boltzmann statistics becomes a good approxi- mation under certain circumstances. The classical statistics approximation also suits the exotic Hagedorn states. It is likely that the hadronic matter which is dominated by the col- orless orthogonal states undergoes smooth phase transition to the colored (non-color-singlet) SU ( N$_{c}$ ) quark-gluon matter with initial neutral color charges (i.e. color-neutral) for µ$_{B}$ ≈ 0 at the critical temperature T$_{c}$ . The alternate scenario is that the colorless U (1) N$_{c}$ quark bags may emerge above the orthogonal Hagedorn states and below the deconfinement phase transition where the color-singlet constraint of the colorless states is broken and the colored (i.e. color-non-singlet) states appear abundantly in the system. This kind of intermediate 49