The Stratoverso Framework: Log-Periodic Signatures and Discrete Scale Invariance in Cosmology

This work presents a testable extension of the Stratoverso framework, a hierarchical cosmological model based on discrete scale invariance and isoentropic evolution. The study introduces log-periodic modulations in cosmological observables as a natural consequence of the underlying stratified structure. In particular, corrections to the primordial power spectrum are expressed in the form: P (k) = Aₛ k^ (nₛ − 1) 1 + ε cos (ω ln k + φ) Such features are not introduced phenomenologically, but arise from the discrete scaling properties of the framework. The predicted signatures are directly comparable with current observational probes, including cosmic microwave background measurements and large-scale structure surveys. Existing data constrain the amplitude of possible modulations to remain small, while still allowing for the presence of oscillatory structures. Recent analyses of primordial feature models explicitly search for logarithmic oscillations of this type, showing that the functional form proposed here is aligned with current observational methodologies. No statistically significant detection has been established so far. However, the framework provides clear falsifiability criteria: the absence of log-periodic signatures in future high-precision data would rule out the model. This work is part of a structured research series developing the Stratoverso framework across theoretical, dynamical, and observational levels.