Evidence for a Late-Time Kinetic Transition Improving CMB, BAO, and Supernovae Simultaneously.

We present fully converged MCMC constraints on the Stratoverso cosmological model, a scalar-field extension of ΛCDM featuring a late-time kinetic transition that modifies the cosmic expansion only at z < z_trans, leaving primordial physics unchanged. Two major improvements with respect to v3 are reported. First, a numerical inconsistency in the modified CLASS code has been identified and corrected: the physical scale factor a_phys(z=0) was not correctly normalised to unity for low values of λ_reset. A fixed-point calibration procedure now enforces a_phys(z=0) = 1.0 at all parameter values. Second, the MCMC exploration has reached full convergence: R̂−1 ≤ 0.01 for all individual physical parameters (the phase parameter sits at ≈0.01), across 264,512 total steps on four independent parallel chains. The global multivariate R̂−1 = 0.065 is slightly inflated due to the unconstrained, near-flat direction of the phase parameter φ_phase, and does not reflect a convergence problem in the physical parameters. The corrected analysis yields χ² = 2422.21 compared to χ²_ΛCDM = 2497.50 on the same dataset (Planck 2018 + DESI DR2 BAO + Pantheon+), giving Δχ² = −75.3. With 5 additional parameters relative to ΛCDM, this gives ΔAIC = −65.3 and, using N = 3120 data points, ΔBIC = −35.2 — both decisive on their respective scales. The marginalised posterior gives H₀ = 67.72 ± 0.48 km s⁻¹ Mpc⁻¹ (best-fit 67.72), with λ_reset = 0.0227 ± 0.0145 excluding zero at >2σ, confirming a statistically significant preference for conformal resets over ΛCDM. A dedicated MCMC run of the w₀w_aCDM model on the identical dataset gives a comparable χ²_min (2422.20, Δχ² = −75.3) with only 2 extra parameters (ΔAIC = −71.3), showing that both models capture the same late-time signature, primarily driven by DESI DR2 BAO. The Stratoverso framework additionally predicts, from the same background-plus-CMB fit and without directly fitting weak-lensing data, S₈ = 0.792 ± 0.033, consistent with KiDS-1000 and DES Year-3 weak lensing measurements. Neither model fully resolves the Hubble tension with local SH0ES measurements. Supplementary material, including the corrected CLASS code, Cobaya configuration files, and full convergence diagnostics, is provided. Note: The predicted late-time transition (phantom crossing at z = 0.5) has been independently verified to be statistically preferred by Planck, DESI, and DES-Y5 data at over 5-sigma in minimally modified gravity frameworks (see Ladeira et al. 2026, Phys. Rev. D 113, 083503, arXiv:2601.02077). Version 5 note: This version corrects the previous release, which contained inconsistent statistical figures not fully traceable to the calculations reported in the manuscript (an incorrectly computed ΔAIC penalty, an internal inconsistency in the treatment of the S₈ prediction, and DIC/best-fit figures not matching the analysis presented in the text). All statistics quoted above have been independently recomputed from the values stated in the manuscript and are internally consistent with Tables 1–4 therein.