Strangeness equilibration at GSI energies

We develop the notion of "broad-band equilibration" in heavy-ion processes involving dense medium. Given density-dependent K--masses we show that the equilibration at GST energies claimed to hold in previous treatments down t o similar to rho (0)/4, can be replaced by a broadband equilibration in whi ch the K--meson and hyperons are produced in an essentially constant ratio independent of density. There are experimental indications that this also h olds for AGS energies. We then proceed to argue that both K+ and K- must ge t Lighter in dense medium at some density rho > rho (0) due to the decoupli ng of the vector mesons. As a consequence, kaon condensation in compact sta rs could take place before chiral restoration since the sum of bare quark m asses in the kaon should lie below mu (e). Another consequence of the decou pling vector interactions is that the quasi-particle picture involving (qua si)quarks, presumably ineffective at low densities, becomes more appropriat e at higher densities as chiral restoration is approached.