Updated Bayesian MCMC Evidence for Log-Periodic Structure Growth Modulation: Stratoverso Constraints from DESI DR1 Full-Shape, DESI DR2, and Extended fσ₈ Compilations

We present updated Bayesian MCMC constraints on the log-periodic structure growth modulation predicted by the Stratoverso Framework (Paper M). We construct an extended cosmological compilation of 18 independent fσ₈ (z) measurements, combining the 11-point baseline dataset with 6 model-independent ShapeFit measurements from the DESI DR1 Full-Shape analysis (arXiv: 2411. 12021) and the consensus growth rate from the DESI DR1 Peculiar Velocity Survey at z=0. 07 (arXiv: 2512. 03230). The joint fit yields a best-fit modulation amplitude εg = 0. 0744 ± 0. 0290 and frequency ωg = 5. 220 ± 0. 425, in remarkable agreement with the first-principles theoretical prediction ωg ≈ 5. 22 derived from radion discrete scale invariance. The Δχ² = 6. 20 establishes a 2. 49σ statistical preference for modulated growth over standard ΛCDM. Exact Bayesian model comparison via Nested Sampling (dynesty) yields a Bayes factor ln B₁₀ = 1. 06 (positive evidence on the Jeffreys scale). The use of model-independent ShapeFit measurements — which do not assume general relativity or a specific background expansion — produces more conservative but more robust constraints than BAO-derived fσ₈ values. The Stratoverso best-fit cosmology (S₈ ≈ 0. 795, H₀ ≈ 70. 5 km/s/Mpc) lies at the intersection of the Planck 2018 and KiDS-1000 contours, alleviating both the S₈ and H₀ tensions. The predicted equation of state (w₀ = −1. 08, wₐ = 0. 15) remains fully consistent with the DESI DR2 w₀-wₐ constraints. Fisher matrix forecasts project a joint significance of 5. 15σ with Euclid Year-6 + DESI Year-5, approaching the formal discovery threshold. The framework is sharply falsifiable: if Euclid Year-6 constrains |εg| 3σ confidence.