An Independent Test Against Carnegie-Chicago Hubble Program Tip of the Red Giant Branch Measurements via Entropy Mechanics

The Hubble tension — the persistent disagreement between H0 measured at the cosmic microwave background (∼ 67 km/s/Mpc) and H0 measured locally via the distance ladder (∼ 73 km/s/Mpc) — has resisted resolution within standard ΛCDM, which treats H0 as a single global parameter that should give the same value at any scale. We present an independent test of the H-ΛCDM (Holographic ΛCDM) framework, an extension of the standard cosmological model in which cosmological structure emerges from holographicinformation processing on the cosmic-horizon causal diamond. The framework’s projection formula reduces to the parameter-free linear form Hlocal/HCMB = 1 + (γ/H) · ln(dCMB/dlocal), with γ/H = 1/281.7 derived from the modular structure of the cosmic-horizon algebra of observables and dCMB = 13869.7 Mpc derived from the same modular foundation. No free parameters and no assumptions enter the projection. The framework predicts Hlocal = 70.36 ± 0.56 km/s/Mpc at the LMC anchor and Hlocal = 69.15 ± 0.56 km/s/Mpc at the NGC 4258 anchor; both predictions are perturbatively valid across the full local-distance-ladder regime. We test these predictions by independently reproducing the Carnegie-Chicago Hubble Program TRGB methodology across four supernova photometric systems and three calibrator sample variants, validated against an Uddin 2024 positive-control test (∆ = −0.027 km/s/Mpc) and against published CCHP values. The framework prediction matches all four JWST-only TRGB+JAGB chains at NGC 4258 within 1σ and matches the CSP-II 24-SN augmented chain at 0.05σ. At the LMC anchor, the framework prediction matches three of four pipeline reproductions within 1σ. The framework’s prediction sits in the conservative-TRGB regime of the active TRGB H0 debate and ∼ 3.3σ below SH0ES Cepheid measurements, which would place the SH0ES-vs-CMB gap in the Cepheid distance-ladder calibration; recent JWST-anchored TRGB analyses are consistent with that attribution but do not establish it. The framework’s parameter-free algebraic structure means its predictions are fixed by the cosmological inputs and cannot be adjusted to accommodate future data; observational convergence asTRGB precision improves provides a clean falsification test.