We present the first sub-arcminute images of the Galactic Center above 10 keV, obtained with NuSTAR. NuSTAR resolves the hard X-ray source IGR J17456-2901 into non-thermal X-ray filaments, molecular clouds, point sources and a previously unknown central component of hard X-ray emission (CHXE). NuSTAR detects four non-thermal X-ray filaments, extending the detection of their power-law spectra with $Gammasim1.3$-$2.3$ up to ~50 keV. A morphological and spectral study of the filaments suggests that their origin may be heterogeneous, where previous studies suggested a common origin in young pulsar wind nebulae (PWNe). NuSTAR detects non-thermal X-ray continuum emission spatially correlated with the 6.4 keV Fe K$alpha$ fluorescence line emission associated with two Sgr A molecular clouds: MC1 and the Bridge. Broad-band X-ray spectral analysis with a Monte-Carlo based X-ray reflection model self-consistently determined their intrinsic column density ($sim10^{23}$ cm$^{-2}$), primary X-ray spectra (power-laws with $Gammasim2$) and set a lower limit of the X-ray luminosity of Sgr A* flare illuminating the Sgr A clouds to $L_X stackrel{>}{sim} 10^{38}$ erg s$^{-1}$. Above ~20 keV, hard X-ray emission in the central 10 pc region around Sgr A* consists of the candidate PWN G359.95-0.04 and the CHXE, possibly resulting from an unresolved population of massive CVs with white dwarf masses $M_{rm WD} sim 0.9 M_{odot}$. Spectral energy distribution analysis suggests that G359.95-0.04 is likely the hard X-ray counterpart of the ultra-high gamma-ray source HESS J1745-290, strongly favoring a leptonic origin of the GC TeV emission.
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