We present a rigorous mathematical and physical unification of the two primary representations of the Stratoverso cosmology: the holographic scale-space representation (Berti 2026, doi: 10. 5281/zenodo. 18979384) and the temporal scalar field dynamical representation (Berti 2026, doi: 10. 5281/zenodo. 20514118). By deriving the exact physical mapping between the logarithmic scale coordinate χ and cosmic time τ ≡ t* − t, we show that χ = L + (γ/2) ln (τ/τ₁₃₇), where L ≈ 140 is the total scale-space length. We demonstrate that the physical spacing of the Holographic Spherical Membranes (MSO) is δχ = ln (1/λ) ≈ 1. 204, and that the observed temporal scaling factor λ ≈ 0. 30 is reproduced by the effective critical exponent γₑff = 1. 661, incorporating one-loop Coleman-Weinberg corrections and gravitational backreaction, via the relation ln (1/λ) = 2/γₑff. This yields the log-periodic frequency ωg = π γₑff ≈ 5. 22. We establish the generating function Zs as the Mellin transform of the discrete MSO density, resolving the pole structure at Im (s) = n ωg. We derive the scalar field freezing limit φ_∞ ≈ 1. 500 MPl from the Klein-Gordon slow-roll condition and map it to the equatorial radius of the toroidal topological transition S³ → S¹ × S². A unified parameter table and a figure of the scale-time mapping complete the mathematical dictionary of the Stratoverso, establishing it as a highly predictive and falsifiable paradigm for cyclic cosmology.
Fabio Berti (Fri,) studied this question.