Precise numerical standard solar models (SSMs) now agree with one another and with helioseismological observations in the convective and outer radiative zones. Nevertheless these models obscure how luminosity, neutrino production and g-mode core helioseismology depend on such inputs as opacity and nuclear cross sections. Although the Sun is not homologous, its inner core by itself is chemically evolved and almost homologous, because of its compactness, radiative energy transport, and

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... ed luminosity production. We apply luminosity-fixed homology transformations to the core to estimate theoretical uncertainties in the SSM and to obtain a broad class of non-SSMs, parametrized by central temperature and density and purely radiative energy transport in the core.