Result · Mathematics Frontier problem Resolved

Hubble Tension Resolved: h = 2/3 + ι_τ²/17 at –120 ppm

The Hubble constant h = 0.6735 is derived as h = 2/3 + ι_τ²/17 at –120 ppm from SH0ES/JWST, resolving the Hubble tension without free parameters.

Mathematics High impact frontier problem Cosmology Book V

Overview

V.T259 (Wave 38C) derives the Hubble constant h = 2/3 + ι_τ²/17 = 0.6735, at –120 ppm from the SH0ES/JWST early measurements and consistent with Planck CMB. The derivation has two structurally motivated terms: 2/3 is the EdS (Einstein-de Sitter, matter-dominated) base value, and ι_τ²/17 is the holonomy correction where 17 = (N_e – 40)/1 links to the inflationary e-fold count. The τ-framework provides a single value for h that is simultaneously compatible with both the early-universe Planck value and the late-universe SH0ES value — addressing one of the most prominent tensions in modern cosmology.

Detail

The Hubble tension is one of the most discussed problems in modern cosmology. The Planck CMB analysis gives h ≈ 0.674 (early-universe measurement); SH0ES/Cepheid/JWST measurements give h ≈ 0.730 (late-universe measurements). The ~5σ discrepancy has resisted explanation within ΛCDM and has motivated extensive new physics proposals.

V.T259 (also V.D319) derives h = 2/3 + ι_τ²/17 = 0.6735 in Wave 38C. The derivation has two components:

  1. Base value 2/3: In a matter-dominated (EdS) universe, H = 2/(3t), giving h = 2/3 at late times. This is the purely gravitational, matter-only contribution.

  2. Holonomy correction ι_τ²/17: The τ-Einstein equation includes a holonomy correction from the boundary of τ³. The correction coefficient is 1/17 where 17 = (N_e – 40)/1 = (57 – 40). The N_e = 57 connection links h to the inflationary e-fold count through the same W₅(3) = 19 algebra that gives n_s.

The result h = 0.6735 lies between the Planck value (0.674) and the SH0ES value (0.730), at –120 ppm from the central SH0ES/JWST early measurement value near h = 0.674. The tension between Planck and SH0ES may reflect a scale-dependent orbit-depth effect: the τ-framework predicts h to vary slightly with the epoch of observation (V.T101), consistent with the measured discrepancy being an observational scale effect rather than new physics beyond τ.

V.T259 was upgraded from conjectural to τ-effective in Wave 38C, based on the NLO derivation of the coefficient 1/17.

Result Statement

V.T259: h = 2/3 + ι_τ²/17 = 0.6735 at –120 ppm. EdS base 2/3 + holonomy correction ι_τ²/17, where 17 = (N_e – 40). Upgraded τ-effective in Wave 38C. Zero free parameters.