H₀ = 69.733 km/s/Mpc: A Derivation from First Principles and Resolution of the Hubble Tension

The Hubble constant is not a free parameter. The MMU framework derives H₀ = c/(8π·l_p·e^(α⁻¹)) = 69.7338 km/s/Mpc from the fine-structure constant and the Planck length alone, with zero free parameters and an uncertainty of 10⁻⁸ km/s/Mpc.

The paper presents the full numerical verification step by step, a CMB acoustic scale consistency check (the honest result: substituting MMU parameters shifts the CMB-inferred H₀ to 65.91 — away from the derived value, not toward it, with the residual gap awaiting the Tier 2 baryogenesis computation), and a complete tension table across all major measurements. The TRGB local measurement (Freedman et al. 2021) gives H₀ = 69.8 ± 1.7 km/s/Mpc — agreement with the derived value at 0.04σ. ACT DR6 (2025) rules out all thirty extended ΛCDM models proposed to resolve the tension; the MMU does not modify ΛCDM, it derives H₀ from below model fitting entirely.

Statistical tensions: TRGB 0.04σ, ACT DR6 1.51σ, Planck 4.40σ, SH0ES 3.18σ. Five falsification conditions stated. Companion to the MMU Series (Harrison 2026a–e, Zenodo).

https://doi.org/10.5281/zenodo.19039236