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It is well known that, for bright gamma-ray pulsars with high statisticsabove a few GeV, the phase averaged spectral energy distribution (SED) isharder than a simple exponential cutoff above the break. We performphase-resolved spectral analyses of bright gamma-ray pulsars and demonstratethat, even over narrow phase ranges, the SEDs of gamma-ray pulsars above thebreak energy are harder than a simple exponential cutoff. We argue within aradiation-reaction limited curvature framework that this is indicative ofnon-stationary emission or emission from multiple zones. Further, we address acommon problem faced when fitting hard spectral tails with a power-law times asub-exponential function. Namely, that the sub-exponent parameter does notdescribe any parameters of physical models of pulsar emission. We introduce asimple analytical fit function to solve this problem.

On the Spectral Shape of Gamma-ray Pulsars Above the Break Energy