Charmonium production in heavy-ion collisions is investigated within a kinetic theory framework incorporating in-medium properties of open-and hidden-charm states in line with recent QCD lattice calculations. A continuously decreasing open-charm threshold across the phase boundary of hadronic and quark-gluon matter is found to have important implications for the equilibrium abundance of charmonium states. The survival of J/ψ resonance states above the transition temperature enables their recreation also in the Quark-Gluon Plasma. Including effects of chemical and thermal offequilibrium, we compare our model results to available experimental data at CERN-SPS and BNL-RHIC energies. In particular, earlier found discrepancies in the ψ ′ /ψ ratio can be resolved.The production systematics of heavy-quark bound states in (ultra-) relativistic collisions of heavy nuclei (A-A) is believed to encode valuable information on the hot and dense strong-interaction matter formed in these reactions [1]. Based on the notion that charm quark pairs (cc) are exclusively created in primordial (hard) nucleonnucleon (N -N ) collisions, it has been suggested [2] that a suppression of observed J/ψ mesons in sufficiently central and/or energetic A-A reactions signals the formation of a deconfined medium (Quark-Gluon Plasma=QGP), as tightly bound cc states are conceivably robust in hadronic matter. While theoretical [3] and (indirect) experimental evidence [4] supports N -N collision-scaling of total charm production, it has recently been realized [5,6,7] that coalescence of c andc quarks can induce significant regeneration of charmonium states in later stages of A-A collisions, especially if several pairs are present (e.g., N cc =10-20 in central Au-Au at RHIC). This is a direct consequence of (elastic) c-quark reinteractions, facilitating the backward direction of charmonium dissociation reactions, J/ψ + X 1 ⇋ X 2 + c +c (D +D).Recent lattice computations of Quantum Chromodynamics (QCD) have revealed important information on charm(onium) properties at finite temperature T , most notably: (i) an in-medium reduction of the open-charm threshold which is surprisingly continuous even across the phase transition region [8], and, (ii) the survival of J/ψ and η c states as resonances in the QGP phase [9,10], with essentially unmodified masses. Note that the use of charmonium spectral functions, in connection with appropriate asymptotic states, incorporates both (static) screening and (dynamical) dissociation mechanisms.In this letter, we propose an approach that implements charm properties inferred from lattice QCD as microscopic in-medium effects into a kinetic rate equation. It enables a comprehensive treatment of charmonium dissociation and regeneration across the phase transition, connecting hadronic and QGP phases in a continuous way, not present in previous calculations. E.g., in the kinetic approach of Ref.[6], J/ψ's were only considered in the QGP phase using their vacuum binding energy, whereas recent transport calculations [11,12] do n...

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