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Version 3. 7 of The S-Layer Cosmology presents a compact, falsifiable, and analytically derived alternative to particle dark matter. The model introduces a thin, non-dynamical spectral layer embedded in spacetime, which modifies the effective gravitational response of baryonic matter via a universal saturation law with exponent δ ≃ 0. 5. This single mechanism reproduces the baryonic Tully–Fisher relation (n = 4), flat galactic rotation curves, cored central densities, and cluster-scale gravitational lensing through a geometric amplification factor F (b). Because AS is negligible at early times, the S-layer preserves the standard cosmological expansion history, the CMB acoustic peaks, and BAO scales, while predicting measurable deviations in P (k), σ₈, void dynamics, and CMB lensing. Version 3. 7 contains refined abstract and conclusion sections, with no changes to the mathematical framework. This release is considered the stable reference version for evaluation, comparison, and citation. This work is licensed under a Creative Commons Attribution 4. 0 International License (CC BY 4. 0). The author retains full copyright.