2026ApJ..1000..147F

The first stars likely formed from pristine clouds, marking a transformative epoch after the dark ages by initiating reionization and synthesising the first heavy elements. Among these, low-mass Population III (Pop III) stars are of particular interest, as their long lifespans raise the possibility that some may survive to the present day in the Milky Way's stellar halo or satellite dwarfs. As the first paper in a series, we present hydrodynamic evolutionary models for 0.7-1 M_⊙ stars evolved up to the white dwarf phase, utilising the MESA software instrument. We systematically vary mass-loss efficiencies, convective transport, and overshooting prescriptions, thereby mapping (i) how uncertain physics influences nucleosynthetic yields; (ii) surface enrichment, including nitrogen-rich post-main-sequence stars arising from convective shell mergers; (iii) remnant properties, such as low-mass helium or carbon-oxygen white dwarfs (M_WD ∼ 0.45-0.55 M_⊙) and transient UV-bright phases; and (iv) potential observational signatures, including neutrino emission during shell mergers and helium flashes. These models establish a predictive framework for identifying surviving Pop III stars and their descendants, providing both evolutionary and observational constraints that were previously unexplored.