  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 ppI-dominated 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.
