  The maximum distance bound for ultrahigh energy cosmic rays (UHECR) with
energies above the Greisen-Zatsepin-Kuzmich cutoff $\sim 10^{19} eV$ relaxes
significantly if there is some mechanism that forces UHECR to propagate in
discrete intervals, rather than continuously, through intergalactic space. In
particular, intervals as small as a femtometer relax the bound for protons by
an order of magnitude and potentially account for the observed excess of UHECR
flux.
