This contribution discusses baryon-rich matter in the context of recent astrophysical observations of neutron stars (NSs) and the structure of the equation of state that arises from these observations. We show that, generating an ensemble of equations of state that fulfill multimessenger constraints, the speed of sound and trace anomaly can reach their conformal values at the center of maximally massive NSs. The local peak of the speed of sound appears at values of the energy and particle densities being consistent with deconfinement and percolation conditions of QCD phase transition. Some implications of advocating a pseudo-conformal symmetry in dense matter are presented.
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