Hitomi observations of Perseus with the Soft X-ray Spectrometer (SXS) provide a high-resolution look at the 3.5 keV feature reported by multiple groups in the Perseus cluster. The Hitomi spectrum -which involves the sum of diffuse cluster emission and the point-like central Active Galactic Nucleus (AGN) -does not show any excess at E ∼ 3.5keV, giving an apparent inconsistency with previous observations of excess diffuse emission. We point out that 2009 Chandra data reveals a strong dip in the AGN spectrum at E = (3.54 ± 0.02)keV (cluster frame) -the identical energy to the diffuse excess observed by XMM-Newton. Scaling this dip to the 2016 AGN luminosity and adding it to the diffuse XMM-Newton excess, this predicts an overall dip in the SXS field of view of (−5.9 ± 4.4) × 10 −6 ph cm −2 s −1 at E = 3.54 keV -a precise match to the Hitomi data when broadened by the dark matter virial velocity. We describe models of Fluorescent Dark Matter that can reproduce this physics, in which dark matter absorbs and then re-emits 3.5 keV photons emitted from the central AGN.The nature of dark matter is a question of fundamental importance in particle physics, astrophysics and cosmology. The X-ray spectra around E = 3.5 keV of galaxy clusters and other objects have been intensely studied following the announcement in [1, 2] of an unidentified emission line around this energy. In this respect, the Perseus cluster has been of special interest. For both XMM-Newton and Chandra data, the signal for Perseus found in [1, 2] was much stronger than that inferred from the stacked sample of distant clusters in [1] (in the much studied scenario where the 3.5 keV line arises from dark matter decay to photons). A similar result was found in [3], and also confirmed with Suzaku studies of the Perseus cluster in [4,5] (although see [6] for a contrary view on Suzaku data).The 3.5 keV line has been discussed at length in the literature. Both astrophysical explanations (such as potassium emission [1,3] or sulphur charge exchange [7]) and more exotic ones such as dark matter have been put forward as its origin. There is currently no consensus opinion on the physics behind the line and an overall review of studies of the 3.5 keV line is contained in [8].The CCD technology present on Chandra, XMMNewton and Suzaku has limited energy resolution. The launch of Hitomi, with the microcalorimeters present on its Soft X-ray Spectrometer (SXS), was expected to offer a decisive test of the 3.5 keV line, both in Perseus and in other clusters. Sadly Hitomi was lost around one month after launch, but prior to its loss it performed a deep groundbreaking observation of the centre of the Perseus cluster.The data from the Hitomi observations around E ∼ 3.5 keV were recently reported in [9]. No excess was seen, and it is stated that this is incompatible at more than 3σ with the strong signal from Perseus observed with other telescopes.In this paper, we show that that there is no incompatibility and that the overall observational picture is consistent. While the XMM-...