We report on an observation of the Galactic black hole candidate GRS 1739-278 during its 2014 outburst, obtained with NuSTAR. The source was captured at the peak of a rising low/hard state, at a flux of ~0.3 Crab. A broad, skewed iron line and disk reflection spectrum are revealed. Fits to the sensitive NuSTAR spectra with a number of relativistically blurred disk reflection models yield strong geometrical constraints on the disk and hard X-ray corona. Two models that explicitly assume a lamppost corona find its base to have a vertical height above the black hole of h = 5 (+7, -2) GM/c^2 and h = 18 +/-4 GM/c^2 (90% confidence errors); models that do not assume a lamppost return emissivity profiles that are broadly consistent with coronae of this size. Given that X-ray microlensing studies of quasars and reverberation lags in Seyferts find similarly compact coronae, observations may now signal that compact coronae are fundamental across the black hole mass scale. All of the models fit to GRS 1739-278 find that the accretion disk extends very close to the black hole - the least stringent constraint is r = 5 (+3,-4) GM/c^2. Only two of the models deliver meaningful spin constraints, but a = 0.8 +/-0.2 is consistent with all of the fits. Overall, the data provide especially compelling evidence of an association between compact hard X-ray coronae and the base of relativistic radio jets in black holes.
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