  A detailed understanding of inclusive muon neutrino charged-current
interactions on argon is crucial to the study of neutrino oscillations in
current and future experiments using liquid argon time projection chambers. To
that end, we report a comprehensive set of differential cross section
measurements for this channel that simultaneously probe the leptonic and
hadronic systems by dividing the channel into final states with and without
protons. Measurements of the proton kinematics and proton multiplicity of the
final state are also presented. For these measurements, we utilize data
collected with the MicroBooNE detector from 6.4$\times10^{20}$ protons on
target from the Fermilab Booster Neutrino Beam at a mean neutrino energy of
approximately 0.8 GeV. We present in detail the cross section extraction
procedure, including the unfolding, and model validation that uses data to
model comparisons and the conditional constraint formalism to detect
mismodeling that may introduce biases to extracted cross sections that are
larger than their uncertainties. The validation exposes insufficiencies in the
overall model, motivating the inclusion of an additional data-driven
reweighting systematic to ensure the accuracy of the unfolding. The extracted
results are compared to a number of event generators and their performance is
discussed with a focus on the regions of phase-space that indicate the greatest
need for modeling improvements.
