We present results of a search for unidentified line emission and absorption signals in the 2-12keV energy band of spectra extracted from Perseus Cluster core region observations obtained with the 5eV energy resolution Hitomi Soft X-ray Spectrometer. No significant unidentified line emission or absorption is found. Line flux upper limits (1 sigma per resolution element) vary with photon energy and assumed intrinsic width, decreasing from 100 photons cm$^{-2}$ s$^{-1}$ sr $^{-1}$ at 2keV to $<10$ cm$^{-2}$ s$^{-1}$ sr $^{-1}$ over most of the 5-10 keV energy range for a Gaussian line with Doppler broadening of 640 km/s. Limits for narrower and broader lines have a similar energy dependence and are systematically smaller and larger, respectively. These line flux limits are used to constrain the decay rate of hypothetical dark matter candidates. For the sterile neutrino decay rate, new constraints over the the mass range of 4-24 keV with mass resolution better than any previous X-ray analysis are obtained. Additionally, the accuracy of relevant thermal spectral models and atomic data are evaluated. The Perseus cluster spectra may be described by a composite of multi-temperature thermal and AGN power-law continua. Superposed on these, a few line emission signals possibly originating from unmodeled atomic processes (including Si XIV and Fe XXV) are marginally detected and tabulated. Comparisons with previous X-ray upper limits and future prospects for dark matter searches using high-energy resolution spectroscopy are discussed.
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