Chapter 42: H₀

The Hubble constant H₀ measures the current expansion rate of the universe. For over a decade, two classes of measurement have yielded discrepant values: “early-universe” methods (CMB analysis via Planck planck2020cosmological, BAO calibration) give H₀ ≈ 67.4 ± 0.5 km/s/Mpc, while “late-universe” methods (Cepheid-calibrated Type Ia supernovae riess1998observational via SH0ES and related programmes) give H₀ ≈ 73.0 ± 1.0 km/s/Mpc. The discrepancy exceeds 5σ and has resisted resolution within the ΛCDM framework for nearly a decade.

This chapter presents the τ-resolution. In Category τ, the Hubble parameter is not a single number. It is an orbit-depth-dependent readout : the progression rate on the base τ¹ varies with the depth n of the refinement tower, and “early” and “late” measurements probe different depths. The early-universe measurement reads the progression rate at large depth (high redshift, z ∼ 1100), while the late-universe measurement reads it at shallow depth (low redshift, z ≲ 0.1). There is no tension: both measurements are correct. They measure different things.

The second half of the chapter re-reads ΛCDM as a whole. The model has correct parameters (Ω_m, Ω_Λ, H₀, n_s, σ₈) but wrong ontology (dark matter as particle, dark energy as field, spacetime as manifold). The parameters are readout projections of the τ-structure. The chapter closes with the final word on the dark sector: after the relevant chapter (dark energy artifact), the relevant chapter (rotation curves), the relevant chapter (Bullet Cluster), and the relevant chapter (Sector Exhaustion), the case is closed.