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Calcium silicate perovskite (CaPv) is the host for many large ion lithophile elements including the heat-producing elements in the lower mantle. Whether, when, and where it forms during the solidification of the magma ocean is fundamental to understanding the geochemical and geodynamical evolution of the early Earth and the trace element distribution in the lower mantle. In this study, we performed first-principles molecular dynamics simulations to investigate the partitioning behavior of Ca (alongside other alkali-earth elements, Sr and Ba) between bridgmanite and molten pyrolite. Our results show that the bridgmanite-melt partition coefficient of Ca remains smaller than 1 along the liquidus across the lower mantle, and decreases further between the magma ocean liquidus and solidus, indicating that Ca is incompatible in bridgmanite at all relevant crystallization conditions in the lower mantle. This results in a progressive enrichment of Ca in the magma ocean as it solidifies, leading unavoidably to the crystallization of CaPv during the final stages of solidification in the deep mantle. Laser-heated diamond anvil cell experiments performed to replicate the crystallization of pyrolitic melt in the same conditions as our simulations confirm the crystallization of CaPv in the last stages of solidification. From Ca to Sr to Ba, the bridgmanite-melt partition coefficients decrease by orders of magnitude, indicating a significant enrichment of these large ion lithophile trace elements in the residual melt. Combined with previous experimental studies at lower P-T conditions, our findings infer that both large ion lithophile elements and their host, CaPv, will be concentrated in the deep mantle at the end of magma ocean solidification.