The Stratoverso Framework: Data-Driven Constraints and Statistical Tests of Log-Periodic Cosmological Signatures

This work presents a data-driven analysis of the Stratoverso framework, a hierarchical cosmological model based on discrete scale invariance and isoentropic evolution. The study tests the presence of log-periodic modulations in cosmological observables by comparing the model predictions with current observational constraints. In this framework, corrections to the primordial power spectrum are expressed as: P (k) = Aₛ k^ (nₛ − 1) 1 + ε cos (ω ln k + φ) These oscillatory terms arise from the discrete scaling properties of the model and are directly comparable with observational search templates used in cosmology. Constraints from Planck measurements, baryon acoustic oscillations (BAO), and recent large-scale structure surveys (including DESI) are considered. Current data require any modulation to remain subdominant, while not excluding the presence of small-amplitude oscillatory features. No statistically significant preference over the standard ΛCDM model is observed. However, the results show that the predicted signatures remain compatible with existing data and lie within the sensitivity range of current and near-future surveys. The framework is therefore empirically testable. Future high-precision observations, particularly from Euclid and upcoming DESI releases, will provide stronger constraints on the presence of log-periodic structures. This work is part of a structured research series developing the Stratoverso framework across theoretical, dynamical, and observational levels.