The Greisen-Zatsepin-Kuzmin Threshold Recomputed with a Density-Bound Correction

The photopion threshold that sets the Greisen-Zatsepin-Kuzmin suppression is recomputed from the Delta(1232) resonance condition and from the direct pion-production threshold, and a density-bound correction drawn from the neutron-branch limit of 9.72e+54 g per cubic centimetre is then applied to the cosmic microwave background photon field. For a mean background photon of 6.34e-04 eV the resonance threshold is 2.514e+20 eV and the direct threshold is 1.110e+20 eV; for a Wien-tail photon of 1.6e-03 eV the resonance threshold falls to 9.960e+19 eV, which is where the observed suppression near 5e19 eV originates. The density-bound correction shifts every threshold by a relative amount of only 4.785e-89, because the mass-equivalent density of the microwave background is smaller than the bound by some eighty-nine orders of magnitude. The negative result is stated plainly: in intergalactic space the frame correction cannot move the cutoff, cannot soften it, and cannot explain any part of the difference between experiments. Whatever distinguishes the measured spectra must lie in energy calibration, composition, or source distribution. This study is simulated and computed from stated assumptions; it is not a measurement.