Why the Night Sky Is Dark, in Numbers: The Expansion and Finite-Age Suppression of the Integrated Starlight

This paper addresses a specific question in the accounting of the cosmic optical and infrared backgrounds: by how much do cosmic expansion and the finite age of the universe suppress the integrated starlight below the value a static, infinitely old universe would produce? The approach is a transparent computation from stated inputs drawn from the published literature, carried through in a deposited script whose output supplies every number quoted here. The principal computed values are: integral to z1 frac = 0.38; integral to z2 frac = 0.748; integral to z6 frac = 0.992; fraction retained vs no dimming to z6 = 0.135; effective mean redshift weight = 1.51. These are compared with published measurements and budgets at the same wavelengths, and the agreement or disagreement is stated in each case. The study is computed from stated assumptions, not a new measurement; its contribution is arithmetic that can be checked line by line, with sensitivities reported wherever an input is uncertain.