From Geometry to Measured Expansion Rates: Local and Global Readings of an Expanding 3-Sphere

This is the reproducibility package for "From Geometry to Measured Expansion Rates: Local and Global Readings of an Expanding 3-Sphere". All code, figures, and LaTeX source files are provided, allowing the numerical results and claims presented in the paper to be independently reproduced and verified. The question I'm trying to answer in this paper is whether the different expansion-rate readings, known as the Hubble tension, and the apparent expansion acceleration can be explained by the geometry of spacetime. I explore a dynamic 3-sphere with a growing curvature radius R as its only one-dimensional degree of freedom. I assert a present-day growth rate Ṙ₀ = πc and take the mass–curvature constant λ = 1 kg m⁻² from a companion paper; the Planck 2018 rate with BAO gives λṘ₀/πc = 0.998 ± 0.006 kg m⁻², consistent with these values. This leads to a prediction of the global fractional rate, H₀ = πc/R₀ = π²λG/c = 67.8009 ± 0.0015 km s⁻¹ Mpc⁻¹. The uncertainty of this result is that of the laboratory G, and the growth rate alone fixes the spatial curvature, Ωₖ = −1/π². An observer embedded in the 3-sphere hypersurface will perceive time via the growth of its own local radius R. The universal dial is the same for all regions, dR/dτ = c k(R) with k(R₀) = π; however, a local age offset Δt causes differences in region dynamics. The consequence follows: an age offset Δt = 1.0 Gyr means a smaller local radius and hence faster local expansion. Without energy flux relative to their comoving observers, regions take the Lemaître–Tolman–Bondi form. An observer inside such a region reads a high local rate and an apparently accelerating Hubble diagram while the geometry at the centre coasts. I show that, for measurements done with the Cepheid-calibrated Pantheon+ supernovae, a coasting 3-sphere with the global rate fixed and one smooth region 1.0 Gyr younger than the mean fits the data as well as flat ΛCDM with H₀ fitted (Δχ² = −0.1). Such a region, read through the Einstein equations, satisfies the null energy condition. The DESI DR2 BAO exclude a dial that is constant over the past; therefore, I consider a free history and show that, together with the region's age offset, it gives χ²_BAO = 8.3, with k at z = 2.33 being 12–13% above the present value.