The Diffuse Astrophysical Neutrino Flux as an Energy Budget: IceCube's Measurement Priced Against the Cosmic-Ray Reservoir

The diffuse astrophysical neutrino flux measured by IceCube is priced against the cosmic-ray reservoir and the Fermi-LAT gamma-ray background using published inputs and a reproducible script. Adopting the IceCube six-year cascade fit (per-flavour normalisation 1.66e-18 GeV-1 cm-2 s-1 sr-1 at 100 TeV, spectral index 2.53, 16 TeV to 2.6 PeV), the all-flavour integrated energy flux is 2.31e-7 GeV cm-2 s-1 sr-1, the energy density is 9.7e-8 eV cm-3, and the volumetric neutrino generation rate is 1.09e44 erg Mpc-3 yr-1 for a source-evolution factor of 3. At 100 TeV the measured per-flavour E2Phi is 0.83 of the Waxman-Bahcall level of 2e-8 GeV cm-2 s-1 sr-1, falling to 0.24 at 1 PeV. Per logarithmic interval the neutrino power is 0.22 of the cosmic-ray generation rate per interval, so a shared origin requires pion-production efficiencies f_pi of about 0.58 (photohadronic) or 0.43 (hadronuclear) under strong evolution, and exceeds unity without evolution. The accompanying cascade gamma-ray power is 5.8-11.6% of the Fermi-LAT isotropic diffuse gamma-ray background power. No source class is identified.