  From the hundreds of gamma-ray pulsars known, only a handful show non-thermal
X-ray pulsations. Instead, nine objects pulse in non-thermal X-rays but lack
counterparts at higher energies. Here, we present a physical model for the
non-thermal emission of pulsars above 1 keV. With just four physical
parameters, we fit the spectrum of the gamma/X-ray pulsars along seven orders
of magnitude. We find that all detections can be encompassed in a continuous
variation of the model parameters, and pose that their values could likely
relate to the closure mechanism operating in the accelerating region. The model
explains the appearance of sub-exponential cutoffs at high energies as a
natural consequence of synchro-curvature dominated losses, unveiling that
curvature-only emission may play a relatively minor role --if any-- in the
spectrum of most pulsars. The model also explains the flattening of the X-ray
spectra at soft energies as a result of propagating particles being subject to
synchrotron losses all along their trajectories. Using this model, we show how
observations in gamma-rays can predict the detectability of the pulsar in
X-rays, and viceversa.
