  As the brightest galaxy cluster in the X-ray sky, Perseus is an excellent
target for studying the Intracluster Medium (ICM), but until recently, its
active galactic nucleus (AGN) made studies of the diffuse emission near its
center nearly impossible to accomplish with NuSTAR due to the extended wings of
NuSTAR's PSF. The development of a new open source software package --
nucrossarf -- now allows the contribution from point and diffuse sources to be
modeled so that scattered light from the AGN can be accounted for. Using this
technique, we present an analysis of diffuse hard X-ray (3-25keV) emission from
the ICM using three archival NuSTAR observations of the Perseus cluster. We
find a ~10% excess of emission beyond 20keV not describable by purely thermal
models. By performing similar analyses of AGN in archival observations, we have
characterized the systematic uncertainty of the modeled AGN contribution to be
3.4%. However, in order to explain the excess, the total scattered AGN emission
would have to be 39% stronger than we have measured. We test physical
explanations for the excess, such as diffuse inverse Compton emission
potentially originating from the radio mini-halo, but we determine that none of
the models are compelling. An upper limit on inverse Compton flux
($\leq1.5\times10^{-11}$erg s$^{-1}$cm$^{-2}$) and a corresponding lower limit
on global magnetic field strength ($\geq 0.35~\mu G$) is derived. We discuss
the potential origin and implications of the excess and present our
characterization of the nucrossarf systematic uncertainty, which should be
useful for future work.
