The Running Spectral Index of the Isotropic Background: Where the Spectrum Steepens and What That Excludes

A single power-law index is a poor description of a spectrum with a high-energy cutoff, and the difference matters when components are added or excluded. This paper computes the local, energy-dependent spectral index of the published Fermi Large Area Telescope background spectrum by finite differences, together with the energy-weighted intensity that locates the spectrum's peak contribution. It finds index at 1GeV = 2.32; index at 100GeV = 2.68; E2I peak GeV = 0.3. By a few hundred GeV the local index has steepened far beyond the headline value, so any component proposed for that range must be steeper still or must cut off. The study is simulated and computed, not measured.