α-EFC III: Momentum-Exchange Holographic Drag and the S8 Tension Falsification of the Homogeneous Drag Limit and the First Boltzmann-Level Implementation of Baryon–Entropy-Field Momentum Transfer in hi class

Converged Cobaya MCMC chains and configuration files accompanying the paper "α-EFC III: Momentum-Exchange Holographic Drag and the S₈ Tension" (Ciobanu J.A., 2026). This dataset contains the three Markov chains underlying the model comparison of Paper III, in which an entropy field exchanges momentum with the baryon fluid (pure momentum-exchange class, following Pourtsidou & Tram 2016), implemented natively in a custom-modified hi_class and tested with Cobaya against Planck NPIPE + Planck Lensing + BAO SDSS DR12 + a KiDS-1000 S₈ Gaussian prior (S₈ = 0.759 ± 0.024). The SH0ES distance-ladder prior is deliberately excluded. Chains (all converged, Gelman–Rubin R−1 ≤ 0.02): Run 26 — α-EFC + drag, Γ_drag prior [0,3] (132k samples) Run 27 — ΛCDM mirror with free neutrino mass (72k samples) Run 28 — α-EFC + drag, wide prior Γ_drag [0,8] (161k samples) Each archive includes the chain, covariance matrix, checkpoint and progress files, and the input/updated YAML. The three Cobaya configuration files and the custom KiDS-1000 S₈ likelihood (s8_kids_prior.py) are included for full reproducibility. Main results. The drag suppresses late-time clustering, yielding S₈ = 0.790 ± 0.013 (midway between Planck-ΛCDM and KiDS) and H₀ = 72.92 ± 0.68 with no local distance information in the fit. The drag amplitude is constrained as a lower limit, Γ_drag > 1.48 (95% CL); the suppression saturates (σ₈ flattens beyond Γ_drag ≈ 4), so no central value is meaningful, as Run 28 confirms. The drag is statistically orthogonal to the neutrino mass (r = −0.066). In the model comparison against the ΛCDM mirror, the best-fit improvement is Δχ² = −2.86, located entirely in the KiDS S₈ prior (−2.06) and the CMB lensing amplitude (−2.04); however, ΛCDM remains favoured by the Bayesian information criterion on every parameter accounting (ΔBIC = +24.7 for the full three-parameter model). This corresponds to a ~1.7σ indication, not a detection, and is reported as such. Software: CLASS v3.3.4 / hi_class (custom-modified, patches at the GitHub repository below), Cobaya, GetDist. Related resources: Paper I: doi:10.5281/zenodo.20429926 Paper II: doi:10.5281/zenodo.20610734 Code and hi_class patches: https://github.com/Domosensei/alpha_efc