RLMT:RLMT and the Hubble Tension: Primordial and Late-Time $\Omega$-Layer Tests against Planck, DESI DR2 and Pantheon+ with Methodological Corrections

This paper tests whether R-layer Mode Theory (RLMT), in any form implemented so far, can move the cosmologically inferred Hubble constant H0 toward the locally measured values (SH0ES, CCHP, SN H0pe). ΛCDM is used as the comparison baseline, not as a model to be refuted. Primordial route. RLMT-lite, the primordial-spectrum model of the parent paper, fits Planck 2018 and Pantheon+SH0ES as well as ΛCDM (Δχ² = +0.9, +1.3). It is disfavoured only by the penalty for its seven extra parameters (ΔAIC = +14.9, +15.3), and it cannot shift H0, because its parameters never enter the background expansion. Late-time route. Five phenomenological Ω-layer dark-energy models, built from the provisional TH-021 layer eigenvalues and implemented as a CAMB PPF fluid, improve χ² by 9–12 on Planck + DESI DR2 BAO + Pantheon+SH0ES. A standard w0waCDM run does equally well, so the improvement is that of evolving dark energy in general, not something specific to RLMT. Decisive test. With SH0ES removed from the likelihood, no model moves H0 appreciably toward the local values. The largest shift is +0.19 km/s/Mpc, and two variants lower H0 as w0waCDM does. A test of the TH-021 eigenvalue position is uninformative. Methodological corrections. An earlier, unpublished draft of this paper, and version 1 of the parent paper, read the best-fit χ² as 2 min(−ln P), which includes the prior (ERR-001). This and two further errors (ERR-002, ERR-003) are documented in a dedicated section, and all affected runs were repeated with multiple chains. The answer to the paper's question is negative for every RLMT implementation tested so far, and the paper states why. Files: English PDF The cobaya yaml files of all 16 reported runs, with proposal covariance matrices The theory classes: RLMTCAMB v6, and the Ω-layer dark-energy classes The analysis scripts: chi2_from_txt.py, compare_models_aic_bic.py, h0_tension_metrics.py, rminus1_by_param.py, plot_r_posterior.py, covmat_from_chains.py, make_noshoes_yaml.py, make_w0wa_yaml.py, and the figure scripts YAML_LIST.md, describing every run The MCMC chains are available on request. Related records: Parent paper: doi:10.51094/jxiv.5386 Technical foundation X-II v1.2: doi:10.5281/zenodo.23130084