An Empirical Constraint on the Hubble Constant from the Relation Ω_γ = α²

Abstract

This is an editorial revision — no change to the physics, the arithmetic, or the predicted H₀ = 68.15 km/s/Mpc. I removed an unused equation for the CMB temperature that duplicated the main result without adding anything, and rewrote the step that derives the Hubble constant so it reads as what it is: a single equation in the single unknown h, with the temperature-fixed left side and α² determining h directly. The earlier version stated an intermediate α²h² value computed from Planck's h, which made the logic look circular; that number is gone. I also tightened the abstract and cut some repetition in the discussion where the "no known mechanism" point was made several times over. The result is a shorter, cleaner note that says the same thing.