  We perform a critical assessment of the accuracy of DFT-based methods in
predicting stable phases within the Co-Pt binary alloy. Statistical mechanical
analysis applied to zero kelvin DFT predictions yields finite-temperature
results that can be directly compared with experimental measurements. The
predicted temperature-composition phase diagram is qualitatively incompatible
with experimental observations, indicating that the predicted stability of
long-period superstructures as ground states in the Co-Pt binary is incorrect.
We also show that recently suggested methods to better align DFT and experiment
via the hybrid functional HSE06 are unable to resolve the discrepancies in this
system. Our results indicate a need for better verification of DFT based phase
stability predictions, and highlight fundamental flaws in the ability of DFT to
treat late 3$d$-5$d$ binary alloys.
