The Stratoverso Hierarchy: A Discrete Multi-Layer Cosmological Structure from Non-Perturbative Scalar Field Dynamics

This paper presents the complete mathematical architecture of the Stratoverso Hierarchy — the discrete, 140-layer cosmological structure that underlies the Stratoverso Framework introduced in Berti (2026a). The Stratoverso Framework established that the loss of Lipschitz continuity of scalar field equations of motion at a finite-time critical point generates a discrete family of post-critical solution branches, endowing the cosmological phase space with a toroidal topology S¹×S¹. This paper shows that this branch structure encodes a complete hierarchical cosmological architecture whose global parameters are fully determined by the best-fit observational parameters of the parent framework. Key results: (i) derivation of N=140±3 discrete cosmological layers from three independent routes using only parameters fixed by observational data; (ii) formalization of the primordial genesis as a spontaneous Z₂ symmetry breaking in the null manifold V×S×T=0, with explicit derivation of the initial phase φ₀=+π/4; (iii) identification of the toroidal topology as the result of the attraction between the imprinting and outprinting poles of the primordial sphere, with explicit interpolating metric S³→T²; (iv) introduction of the Holographic Spherical Membranes (MSO) as cosmic backup surfaces grounded in the Bousso (1999) covariant entropy bound; (v) the BH→WH information transfer mechanism anchored to Haggard-Rovelli (2014); (vi) formal analogy with a Stirling thermodynamic engine; (vii) perturbative stability analysis showing all 140 layers are linearly stable with inter-layer transition threshold of 70% field amplitude; (viii) the Universal Train formalized as a Hamiltonian flow on T². Global parameters derived from first principles: T_cycle ≃ 2000 Gyr (from N × H₀⁻¹) and D_eq ≃ 800 Gly (from the sinusoidal radial profile), in excellent agreement with the speculative estimates of Berti (2026c). The framework is sharply falsifiable by DESI Year-5, Euclid, and CMB-S4 within 2027–2033, offering a unified interpretation of the Hubble tension, the DESI w<−1 anomaly, and the JWST black-hole excess as simultaneous observational signatures of the compression phase of Layer 137. Third paper in the Stratoverso series: Paper A (framework): https://doi.org/10.5281/zenodo.20266625 Paper B (predictions): https://doi.org/10.5281/zenodo.20267494 Paper C (this work): the Stratoverso Hierarchy