  We report the first double-differential neutrino-argon cross section
measurement made simultaneously for final states with and without protons for
the inclusive muon neutrino charged-current interaction channel. The proton
kinematics of this channel are further explored with a differential cross
section measurement as a function of the leading proton's kinetic energy that
extends across the detection threshold. These measurements utilize data
collected using the MicroBooNE detector from 6.4$\times10^{20}$ protons on
target from the Fermilab Booster Neutrino Beam with a mean neutrino energy of
$\sim$0.8 GeV. Extensive data-driven model validation utilizing the conditional
constraint formalism is employed. This motivates enlarging the uncertainties
with an empirical reweighting approach to minimize the possibility of
extracting biased cross section results. The extracted nominal flux-averaged
cross sections are compared to widely used event generator predictions
revealing severe mismodeling of final states without protons for muon neutrino
charged-current interactions, possibly from insufficient treatment of final
state interactions. These measurements provide a wealth of new information
useful for improving event generators which will enhance the sensitivity of
precision measurements in neutrino experiments.
