2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/108070The 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.3 pagesAstrophysicstext