The Hubble Tension

The argument makes an unexpected prediction about the Hubble tension. The Hubble tension is the discrepancy between two classes of measurement of H₀: early-universe methods (CMB, Planck: H₀ ≈ 67.4 ± 0.5 km/s/Mpc) and late-universe methods (supernovae, Cepheids: H₀ ≈ 73.0 ± 1.0 km/s/Mpc). These disagree at >4σ. The source of the discrepancy is one of the most important open problems in cosmology.

The argument’s prediction: the floor acceleration a₀ = αcH₀/(2π) with α = 1.0445 must match the observed a₀ = 1.20 × 10⁻¹⁰ m/s². Solving for H₀: H₀ = 2πa₀/(αc) = 2π × 1.20 × 10⁻¹⁰ / (1.0445 × 2.998 × 10⁸) = 74.3 km/s/Mpc. Using a₀ = 1.20 ± 0.02 × 10⁻¹⁰ m/s², this gives H₀ = 74.3 ± 1.2 km/s/Mpc — a parameter-free prediction from the observed a₀ and the derived coefficient α/(2π).

The predicted H₀ = 74.3 is above the SH0ES Cepheid value (≈73.0) and well above the Planck CMB value (≈67.4), placing it in the late-universe bracket. The α correction moves the prediction from H₀ ≈ 78 (the base case cH₀/(2π), above all measurements) to H₀ ≈ 74 (in the empirically contested region). This is structural — a consequence of the S² geometry — not a fit. It is a sharp, testable, parameter-free prediction. If future measurements converge on H₀ ≈ 73–75, this confirms both KS-45 (α = 1.0445) and KS-45.1 (the H₀ prediction). If they converge below 70, the derivation is under pressure; if above 76, the argument overshoots.

The Hubble tension may be telling us that neither measurement is quite right, and that the correct value is determined by the floor: H₀ = 2πa₀/(αc) ≈ 74.