  Amplitudes derived from scattering data on elementary targets are basic
inputs to neutrino-nucleus cross section predictions. A prominent example is
the isovector axial nucleon form factor, $F_A(q^2)$, which controls charged
current signal processes at accelerator-based neutrino oscillation experiments.
Previous extractions of $F_A$ from neutrino-deuteron scattering data rely on a
dipole shape assumption that introduces an unquantified error. A new analysis
of world data for neutrino-deuteron scattering is performed using a
model-independent, and systematically improvable, representation of $F_A$. A
complete error budget for the nucleon isovector axial radius leads to
$r_A^2=0.46(22) \,{\rm fm}^2$, with a much larger uncertainty than determined
in the original analyses. The quasielastic neutrino-neutron cross section is
determined as $\sigma(\nu_\mu n \to \mu^- p)\big|_{E_\nu =1\,{\rm GeV}} =
10.1(0.9) \times 10^{-39}{\rm cm}^2$. The propagation of nucleon-level
constraints and uncertainties to nuclear cross sections is illustrated using
MINERvA data and the GENIE event generator. These techniques can be readily
extended to other amplitudes and processes.
