The low-temperature phase diagram of bulk Co-Pt is studied with a high-throughput ab-initio method. Global, hcp-, and fcc-restricted convex hulls are constructed to evaluate stable and metastable phases. It is found that fcc-L1 0 is energetically degenerate with hcp-B19. Both structures are unstable with respect to phase decomposition into hcp-D0 19 fcc-β 2 at low temperature. Furthermore, L1 0 is an adaptive structure on the fcc-restricted convex hull which relates to the low energies of antiphase boundaries. Fcc-L1 2 is energetically degenerate with fcc-D0 23 for both Co 3Pt and CoPt 3. L1 2-Co 3Pt and L1 0-CoPt belong to the fcc-restricted convex hull. They might stabilize above the Co hcp/fcc transition and remain kinetically frozen below. L1 2-CoPt 3 is energetically well above the convex hull. Its experimental observation may result from yet unexplained finite-temperature effects. © 2011 American Institute of Physics.