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 ε_g = 0.0744 ± 0.0290 and frequency ω_g = 5.220 ± 0.425, in remarkable agreement with the first-principles theoretical prediction ω_g ≈ 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, w_a = 0.15) remains fully consistent with the DESI DR2 w₀-w_a 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 |ε_g| < 0.02 at 2σ, the Stratoverso is excluded at >3σ confidence.