The Waxman-Bahcall Bound With Computed Source Evolution, Compared With the Measured Diffuse Flux

The Waxman-Bahcall bound converts the energy budget of ultra-high-energy cosmic rays into a ceiling on the diffuse neutrino flux. This paper recomputes the bound with the source-evolution factor evaluated as an explicit integral rather than inserted as a canonical constant. For star-formation-like evolution the integral gives an evolution factor of 9.71, against the canonical value near 3 often quoted, and the corresponding per-flavour bound is 3.569e-08 in E-squared flux units — a factor 1.43 above the measured contained-event level of 2.500e-08. Truncating the source history at redshift 8, as a bounced thermal history would, lowers the evolution factor to 9.2 and the bound by only 5.18 per cent, to 3.384e-08. With the canonical evolution factor of 3 the bound evaluates to 1.103e-08, below the measurement. The bound's verdict on the data therefore depends entirely on which evolution factor is defended — a dependence the integral makes impossible to hide. The study is computed from stated assumptions, not measured.