A Baryon Budget for the Near-Infrared Excess: What a First-Stars Explanation Would Cost

This paper addresses a specific question in the accounting of the cosmic optical and infrared backgrounds: if a stated near-infrared background excess were attributed to the first generations of stars, what fraction of the universe's baryons would that explanation consume? 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: I for fstar 0.001 nW = 0.287; I for fstar 0.01 nW = 2.87; f star needed for 12nW = 0.0419; f star needed frac of baryons pct = 4.19; observed stellar baryon frac today pct = 6. 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.