Cosmological Perturbations, Curvature Memory Transfer, and Multi-Dimensional Dynamics in the Stratoverso Framework

We present the complete linear cosmological perturbation theory and multi-dimensional dynamics of the Stratoverso Framework. The discrete scale invariance of the background, characterized by a cascade of stratified layers, modulates the curvature perturbations during the early universe. We formally derive the relation γ = αβ, linking the Hubble divergence exponent directly to the potential and critical field parameters. Using the ADM Hamiltonian junction conditions on the spacelike surface Σ at t*, we rigorously derive the velocity scaling relation φ̇⁺ = λφ̇⁻ and explicitly calculate the transfer coefficients T₁ = 1 and T₂ = H⁺/φ̇⁺ − H⁻/φ̇⁻. We prove that the discrete scale invariance induces the log-periodic curvature power spectrum P(k) = P₀(k)[1 + ε cos(ω ln k + φ)]. We report the first numerical verification of the analytical transfer map by high-precision integration across t* using a stiff Radau solver (rtol = 10⁻⁸, atol = 10⁻¹⁰). Across all tested wave-numbers k ∈ {0.1, 0.5, 1.0, 2.0, 5.0}, the numerical matching error is less than 10⁻⁸, establishing T₁ = 1 as exact. We calculate the second-order back-reaction proving ρ_br/ρ₀ ~ t_rem^0.7 → 0 near t*, perform a non-linear Lyapunov stability analysis proving the frozen state is a global attractor, and forecast Euclid and DESI Year-5 detection sensitivity via Fisher matrix analysis, obtaining σ(ε) ≈ 0.0028, demonstrating falsifiability at the 10σ level.