The JSNS$^2$ (J-PARC E56) experiment aims to search for a sterile neutrino at the J-PARC Materials and Life Sciences Experimental Facility (MLF). After the submission of a proposal to the J-PARC PAC, Stage-1 approval was granted to the JSNS$^2$ experiment on April 2015.This approval followed a series of background measurements which were performed in 2014. Recently, funding (the grant-in-aid for scientific research (S)) in Japan for building one 25~ton fiducial volume detector module was approved for the experiment. Therefore, we aim to start the experiment with one detector in JFY2018-2019. We are now working to produce precise cost estimates and schedule for construction, noting that most of the detector components can be produced within one year from the date of order. This will be reported at the next PAC meeting. In parallel to the detector construction schedule, JSNS$^2$ will submit a Technical Design report (TDR) to obtain the Stage-2 approval from the J-PARC PAC.The recent progress of the R$&$D efforts towards this TDR are shown in this report. In particular, the R$&$D status of the liquid scintillator, cosmic ray veto system, and software are shown. We have performed a test-experiment using 1.6~L of liquid scintillator at the 3rd floor of the MLF building in order to determine the identities of non-neutrino background particles coming to this detector location during the proton bunch. This is the so-called MLF 2015AU0001 experiment. We briefly show preliminary results from this test-experiment.
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