  Pulsars are considered to be the leading explanation for the excess in
cosmic-ray positrons detected by PAMELA and AMS-02. A notable feature of
standard pulsar models is the sharp spectral cutoff produced by the
increasingly efficient cooling of very-high-energy electrons by synchrotron and
inverse-Compton processes. This spectral break has been employed to: (1)
constrain the age of pulsars that contribute to the excess, (2) argue that a
large number of pulsars must significantly contribute to the positron flux, and
(3) argue that spectral cutoffs cannot distinguish between dark matter and
pulsar models. We prove that this spectral feature does not exist -- it appears
due to approximations that treat inverse-Compton scattering as a continuous,
instead of as a discrete and catastrophic, energy-loss process. Astrophysical
sources do not produce sharp spectral features via cooling, reopening the
possibility that such a feature would provide incontrovertible evidence for
dark matter.
