  The critical sector of strong interactions at high temperatures is explored
in the frame of two complementary paradigms: Statistical Bootstrap for the
hadronic phase and Lattice QCD for the Quark-Gluon partition function. A region
of thermodynamic instability of hadronic matter was found, as a direct
prediction of Statistical Bootstrap. As a result, critical end point solutions
for nonzero chemical potential were traced in the phase diagram of strongly
interacting matter, consistently with chiral QCD and recent lattice
calculations. The relevance of these solutions for current and future
experiments with nuclei at high energies is also discussed.
