  Dark matter annihilation and other processes may precipitate a flux of
diffuse ultra-high energy $\gamma$-rays. These $\gamma$-rays may be observable
in present day experiments which observe diffuse fluxes at the GeV scale. Yet
the universe is presently opaque to $\gamma$-rays above 10 TeV. It is generally
assumed that cascade radiation is observable at all high energies, however the
disparity in energy from production to observation has important consequences
for theoretical flux limits. We detail the physics of cascade radiation
development and consider the influence of energy and redshift scale on
arbitrary flux limits that result from electromagnetic cascade.
