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RCA Ω 2027 — Phase VIII: Three Falsifiable Predictions from mu-Sigma Separation and Boltzmann Validation

RCA Ω 2027 — Phase VIII: Three Falsifiable Predictions from mu-Sigma Separation and Boltzmann Validation

Abstract

Phase VIII of the Relativistic Coupling Ansatz (RCA) separates the two couplings beta (expansion geometry) and delta (gravitational slip) into independent physical channels. Delta is now the EFT-of-dark-energy gravitational-slip amplitude mu(z) = 1 + delta × gate(z), the same "mu" constrained by Planck 2018 and DESI 2024 modified-gravity analyses. This release archives three falsifiable predictions not present in Phase VII: [1] Growth-without-lensing: mu(z) > 1 while Sigma(z) ~ 1 at z=[0.16,0.40]. Confirmed in CLASS Boltzmann code Stage B: 6.32% Weyl-power separation, 0.00% growth spread (commit 49c209b). Survey target: DESI Y3 + Rubin LSST. [2] fsigma8 deficit at z=[0.10,0.40] if delta > 0. Current data miss this window entirely (chi2 monotone, Δchi2=-0.016). DESI Year 3 (2027-2029) will fill the gap with 3 points at z=0.15, 0.25, 0.35. Detection threshold: delta ~ 0.30 at TPR=50%. [3] fsigma8 sign-flip at z ~ 0.58. The deviation changes sign due to beta-delta competition — unique to two-channel models. No single-channel model produces this pattern. Phase XVIII MCMC (96 walkers, 15,000 steps, tau_max=123, converged): corr(beta,delta) = -0.052 (degeneracy broken from -1.000 in Phase VII) Omega_m = 0.294 ± 0.006 H0 = 69.30 +0.37/-0.22 km/s/Mpc delta 95% upper bound: < 0.716 (prior-dominated; not a detection)

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