4 C. Near-detector event selection A. Data integrity B. Fiducial requirements All of the data accepted for this analysis must pass a series of requirements on the beam and detector perfor- mance. The beam is required to strike within 2 mm of the center of the upstream face of the NuMI target, a segmented rectangular graphite rod measuring 6.4 mm in width, 15 mm in height and 940 mm in length [4]. The full width at half-maximum of the beam at the target is required to be between 0.1 mm and 2.0 mm in the transverse horizontal direction and between 0.1 mm and 1.5 mm in the transverse vertical direction. The minimum allowed beam intensity during a beam spill is 0 . 5 × 10 $^{12}$protons on target. The reconstruction algorithms are designed to han- dle the high rate of interactions occurring in the near- detector during running with typical intensities of 2 . 2 × 10 $^{13}$protons on target per beam spill. At this intensity, an average of 16 neutrino interactions occur in the near- detector for each spill. For the majority of events the algorithms perform very well. However, for certain event subclassess, shortfalls have been identified and quantified using special studies including low intensity beam data and visual scanning. Monte Carlo studies show that 8% of all reconstructed events classified as neutral-current interactions are assigned a value of recontructed energy that is less than half of the actual deposited energy in the detector for the simulated interaction; the remaining energy has been reconstructed as a separate event, re- sulting in an overestimate in the number of reconstructed events. In particular, the number of events with visible energy below 1 GeV that are classified as neutral-current candidates is overestimated by 34%. Therefore, these poorly reconstructed events affect the neutral-current en- ergy spectrum and care has been taken in identifying and removing them from the analysis. For all data used in this analysis, all detector subsys- tems that affect data quality are required to be in normal, stable modes of operation. Checks are made to ensure the coil currents that energize the magnetic fields are at their nominal values in both detectors. The timing between the detectors is synchronized using the Global Positioning System to within 1 µ s to ensure that correct beam extraction timing is provided to the far-detector electronics. The timing synchronization is not affected by the timing resolution of the detectors, which is 18.8 ns and 1.9 ns for the near and far-detectors, respectively. The high voltage supplied to each PMT is required to be at its nominal value. Reconstruction failures are classified into three main categories: (i) split events , (ii) leakage events , and (iii) incomplete events . Split events occur when a single neu- trino interaction results in two or more reconstructed events. Leakage events are due to incorrectly assigned event vertices causing neutrino interactions outside the fiducial volume to be reconstructed within it. The incom- plete event category is a looser classification that refers to further types of failures in shower reconstruction to be described below. In all three categories, the visible energy of a neutrino candidate may be underestimated, resulting in a background to neutral-current events at low energies. As near-detector data are used to predict the expected spectra at the far-detector, reconstruction fail- ures specific to the near-detector must be minimized. A set of selection requirements was developed [26] to reduce the occurrence of these failure modes. After applying the requirements, detailed below, simulations show that the background of poorly reconstructed events having visible energy below 1 GeV has been reduced to 8%. Split events lead to double-counting of neutrino in- teractions and incorrect energy reconstruction. If two reconstructed events are caused by the same neutrino interaction, they are expected to appear close in time and in space. The time for each event has been taken to be the median of the recorded signal arrival times for event strips contained within five planes of the event vertex. To minimize the occurrence of split events, the time separation between an event and the closest other event in time is required to be | Δ t | > 40 ns, as shown in Fig. 1. A requirement that the spatial separation be- tween events along the beam direction | Δ z | > 1 m if 40 ns < | Δ t | < 120 ns is also employed to further elimi- nate split events. Only those events reconstructed in the fiducial volume are included in the analysis. In both detectors the re- constructed event vertex is required to be more than 50 cm from the edges of the instrumented regions and, in the case of the far-detector, more than 45 cm from the center of the magnetic coil that runs through the mid- dle of each detector plane. In addition, a longitudinal veto region comprising either 30 planes at the front of the near-detector or four planes at the front of each of the far-detector supermodules eliminates events that en- ter through the first plane of a detector but may have originated outside the detector volume. To ensure good shower containment, the event vertex is required to be reconstructed more than 1 m from the last plane of each far-detector supermodule and more than 1 m from the last plane in the calorimeter region of the near-detector. The sparsely instrumented spectrometer region of the near-detector is not included in the fiducial volume. The primary vertex of an event is assigned according to the event’s reconstructed track vertex. However, for events without a reconstructed track, the vertex of the hadronic shower is used as the event vertex.