The Tolman Test Revisited Arithmetically: How Strongly Do Surface-Brightness Data Separate Expansion from a Static Alternative?

This paper addresses a specific question in the accounting of the cosmic optical and infrared backgrounds: given realistic measurement scatter, how decisively can surface-brightness observations at redshift near unity distinguish the dimming law of an expanding universe from that of a static alternative? 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: delta mag at z0.9 = 2.09; sigma of mean mag = 0.0553; formal significance sigma = 37.8; dimming expansion mag z0.9 = 2.79; dimming static mag z0.9 = 0.697; per galaxy scatter needed for 5sigma mag = 2.64; systematic floor mag typical = 0.15; significance with systematic = 13.1. 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.