  We report the first measurement of the differential cross section
$d^{2}\sigma (E_{\nu})/ d\cos(\theta_{\mu}) dP_{\mu}$ for inclusive
muon-neutrino charged-current scattering on argon. This measurement utilizes
data from 6.4$\times10^{20}$ protons on target of exposure collected using the
MicroBooNE liquid argon time projection chamber located along the Fermilab
Booster Neutrino Beam with a mean neutrino energy of approximately 0.8~GeV. The
mapping from reconstructed kinematics to truth quantities, particularly from
reconstructed to true neutrino energy, is validated by comparing the
distribution of reconstructed hadronic energy in data to that of the model
prediction in different muon scattering angle bins after conditional constraint
from the muon momentum distribution in data. The success of this validation
gives confidence that the missing energy in the MicroBooNE detector is
well-modeled in simulation, enabling the unfolding to a triple-differential
measurement over muon momentum, muon scattering angle, and neutrino energy. The
unfolded measurement covers an extensive phase space, providing a wealth of
information useful for future liquid argon time projection chamber experiments
measuring neutrino oscillations. Comparisons against a number of commonly used
model predictions are included and their performance in different parts of the
available phase-space is discussed.
