  Neutrino oscillation experiments require a precise measurement of the
neutrino energy. However, the kinematic detection of the final-state neutron in
the neutrino interaction is missing in current neutrino oscillation
experiments. The missing neutron kinematic detection results in a feed-down of
the detected neutrino energy compared to the true neutrino energy. A novel
3D\textcolor{black}{-}projection scintillator tracker, which consists of
roughly ten million active cubes covered with an optical reflector, is capable
of measuring the neutron kinetic energy and direction on an event-by-event
basis using the time-of-flight technique thanks to the fast timing, fine
granularity, and high light yield. The $\bar{\nu}_{\mu}$ interactions tend to
produce neutrons in the final state. By inferring the neutron kinetic energy,
the $\bar{\nu}_{\mu}$ energy can be reconstructed better, allowing a tighter
incoming neutrino flux constraint. This paper shows the detector's ability to
reconstruct neutron kinetic energy and the $\bar{\nu}_{\mu}$ flux constraint
achieved by selecting the charged-current interactions without mesons or
protons in the final state.
