V2.605: H0 Prediction Confrontation with the Distance Ladder Landscape

Summary

The entanglement framework predicts H0 = 67.67 +/- 0.26 km/s/Mpc with zero free parameters, derived from Omega_Lambda = 149sqrt(pi)/384 = 0.6877 and the measured Omega_mh^2 = 0.1430. This experiment confronts that prediction against 14 current H0 measurements spanning CMB, Cepheid, TRGB/JAGB, strong lensing, megamaser, SBF, gravitational waves, and inverse distance ladder methods.

Key Results

1. Measurement confrontation: 8/14 agree, 3/14 in tension

• Early universe (CMB): 0.4sigma — excellent agreement with all 4 measurements
• TRGB/JAGB (JWST): 2.1sigma — good agreement, JAGB alone at 0.2sigma
• Cepheid (SH0ES): 6.5sigma — significant tension
• Other late methods: 3.5sigma — moderate tension (driven by strong lensing)

2. Bayesian model comparison

Model	Total chi^2	chi^2/N
Framework (67.68)	79.4	5.67
Planck LCDM (67.36)	93.0	6.64
SH0ES (73.04)	484.2	34.58

Framework beats both Planck LCDM (Delta_chi^2 = -13.5) and SH0ES (Delta_chi^2 = -404.7).

3. SH0ES violates the a-theorem

SH0ES H0 = 73.04 requires Omega_Lambda = 0.732, which is 6.4% above R_free = 0.6877. By the a-theorem (V2.604), Omega_Lambda <= R_free is an absolute bound from unitarity. SH0ES is incompatible with the framework at the level of a proven theorem.

4. Framework vs Planck LCDM

Both predict H0 ~ 67-68, but for different reasons:

• Planck LCDM: H0 = 67.36 from fitting CMB power spectrum (6 parameters)
• Framework: H0 = 67.67 from SM trace anomaly + entanglement area law (0 free parameters)

The framework prediction is 0.31 km/s/Mpc higher than Planck, moving slightly toward late-universe values. Currently indistinguishable (0.5sigma), but CMB-S4 could separate them (~0.8sigma).

5. Sensitivity

dH0/d(Omega_Lambda) = 108.4 km/s/Mpc per unit Omega_Lambda. A 1% shift in Omega_Lambda changes H0 by 1.08 km/s/Mpc. Only H0 <= 67.7 is compatible with the a-theorem bound.

Prediction

H0 = 67.67 +/- 0.26 km/s/Mpc. The Hubble tension will resolve toward this value as JWST recalibrates the distance ladder. The key test is the JWST Cepheid/TRGB consensus (2025-2027).

Falsification

If a model-independent H0 measurement gives H0 > 69 km/s/Mpc at >3sigma, the framework is falsified (requires Omega_Lambda > R_free, violating the a-theorem).

Connection to Previous Experiments

• V2.598: No-go theorem showed BSM particles can’t resolve H0 tension; this shows the tension itself is one-sided (only Cepheids disagree)
• V2.604: a-theorem bound Omega_Lambda <= R_free; here we show SH0ES violates this at 6.1sigma
• V2.595: w = -1 test at z = 0.5-1.0; H0 provides a complementary low-z anchor
• V2.601: Survival Monte Carlo; H0 convergence is an independent survival channel