  It is well known that, for bright gamma-ray pulsars with high statistics
above a few GeV, the phase averaged spectral energy distribution (SED) is
harder than a simple exponential cutoff above the break. We perform
phase-resolved spectral analyses of bright gamma-ray pulsars and demonstrate
that, even over narrow phase ranges, the SEDs of gamma-ray pulsars above the
break energy are harder than a simple exponential cutoff. We argue within a
radiation-reaction limited curvature framework that this is indicative of
non-stationary emission or emission from multiple zones. Further, we address a
common problem faced when fitting hard spectral tails with a power-law times a
sub-exponential function. Namely, that the sub-exponent parameter does not
describe any parameters of physical models of pulsar emission. We introduce a
simple analytical fit function to solve this problem.
