Physics aspects of a JINR project to reach the planned 5A GeV energy for the Au and U beams and to increase the bombarding energy up to 10A GeV are discussed. The project aims to search for a possible formation of a strongly interacting mixed quark-hadron phase. The relevant problems are exemplified. A need for scanning heavy-ion interactions in bombarding energy, collision centrality and isospin asymmetry is emphasized.
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