An Annihilation Bound from the Isotropic Background: Turning a Measured of Everything into a Limit on One Thing

If dark matter annihilates into ordinary particles, the summed annihilation light of all halos must appear in the isotropic diffuse gamma-ray background, which therefore limits the annihilation cross section. This paper presents a transparent, order-of-magnitude inversion of the published background intensity into a cross-section bound as a function of particle mass for a b-quark channel, calibrated to the order of the Fermi Large Area Telescope limits. It finds limit at 100GeV = 3.000e-26; limit at 10GeV = 5.986e-28; limit at 1TeV = 1.504e-24. Near a hundred GeV the bound approaches the thermal relic cross section, which is why the background remains a competitive dark matter probe. The study is simulated and computed, not measured, and its order-of-magnitude character is stated plainly.