The Age Test: What the Oldest Stars Allow the Competing Expansion Histories to Claim

Every expansion history implies a total age, and the oldest observed objects set a floor beneath which no history may fall. This paper computes the cosmic age for four histories in the Hubble-tension dispute and grades each against stellar age floors: the Planck standard history gives 13.80 billion years; an evolving-dark-energy variant gives 13.79; the small-ruler combination with the SH0ES expansion rate and Planck physical matter density gives 13.32; and the SH0ES rate imposed on the Planck shape gives 12.73 billion years — below the conservative 13.0-billion-year floor from globular-cluster ages, and 2.17 sigma below the central age of the metal-poor star HD 140283 (14.46 ± 0.8 billion years), whereas the Planck history sits only 0.82 sigma below that star. Inverting the integral, a Planck-shaped history respects a 13.0-billion-year floor only for Hubble constants at or below 71.51 km/s/Mpc, and a 13.5-billion-year floor only at or below 68.86. The computation also settles a side question for bounced cosmologies: replacing the expansion integral above the density-ceiling redshift of 1.05 × 10^22 changes the age by 1.8 × 10^−60 billion years, so the bounce's ceiling buys no meaningful age; whatever time a contracting pre-phase contains is additional to, not a substitute for, the expansion age the stars grade. This study is computed from published values and stated assumptions; it is not a measurement.