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Type Ia supernovae (SNe Ia) play a crucial role as standardizable candles in measurements of the Hubble constant and dark energy. Increasing evidence points towards multiple possible explosion channels as the origin of normal SNe Ia, with possible systematic effects on the determination of cosmological parameters. We present, for the first time, a comprehensive comparison of publicly available SN Ia model nucleosynthetic data with observations of late-time light curve observations of SN Ia events. These models span a wide range of white dwarf (WD) progenitor masses, metallicities, explosion channels, and numerical methodologies. We focus on the influence of 57Ni and its isobaric decay product 57Co in powering the late-time (t > 1000 d) light curves of SNe Ia. 57Ni and 57Co are neutron-rich relative to the more abundant radioisotope 56Ni, and are consequently a sensitive probe of neutronization at the higher densities of near-Chandrashekhar (near-MCh) progenitor WDs. We demonstrate that observations of one SN Ia event, SN 2015F is only consistent with a sub-Chandrasekhar (sub-MCh) WD progenitor. Observations of four other events (SN 2011fe, SN 2012cg, SN 2014J, and SN2013aa) are consistent with both near-MCh and sub-MCh progenitors. Continued observations of late-time light curves of nearby SNe Ia will provide crucial information on the nature of the SN Ia progenitors.