Evaluation of the performance of the event reconstruction algorithms in the JSNS$^2$ experiment using a $^{252}$Cf calibration source

JSNS$^2$ searches for short baseline neutrino oscillations with a baseline of 24~meters and a target of 17~tonnes of the Gd-loaded liquid scintillator. The correct algorithm on the event reconstruction of events, which determines the position and energy of neutrino interactions in the detector, are essential for the physics analysis of the data from the experiment. Therefore, the performance of the event reconstruction is carefully checked with calibrations using $^{252}$Cf source. This manuscript describes the methodology and the performance of the event reconstruction.