  The radiative capture of protons by $^7$Be, which is the source of $^8$B that
$\beta$-decays emitting the majority of solar neutrinos measured on earth, has
not yet been measured at astrophysically relevant energies. The recommended
value for its zero-energy S-factor, $S_{17}$(0) =
20.8$\pm$(0.7)exp$\pm$(1.4)theory eV$\cdot$b, relies on theoretical
extrapolations from higher-energy measurements, a process that leads to
significant uncertainty. We performed a set of first-principle (or, ab initio)
calculations of the $^7$Be($p$, $\gamma$)$^8$B reaction to provide an
independent prediction of the low-energy S-factor with quantified
uncertainties. We demonstrate underlying features in the predicted S-factor
allowing the combination of theoretical calculations and measurements to
produce an evaluated S-factor of $S_{17}$(0) = 19.8$\pm$0.3 eV$\cdot$b. We
expect the calculations and uncertainty quantification process described here
to set a new standard for the evaluation of light-ion astrophysical reactions.
