We develop a rigorous effective thermodynamic formulation of the Stratoversal cosmological framework, in which the radion — the inter-brane distance in a warped 5D Anti-de Sitter bulk — acts as a physical thermodynamic variable. Starting from the 5D Einstein-Hilbert action, we derive the warp factor W (r) = e^−A (r), construct the Goldberger-Wise equation of state P (T, r), and demonstrate that the Stratoversal cosmological cycle maps onto a closed Stirling-like thermodynamic engine with a geometric efficiency of exactly 25%, dynamically fixed by the warp factor ratio WIR/WUV = 0. 75. The scalar field freezing phenomenon is proved via two independent, fully ansatz-free Lyapunov arguments: for the friction-dominated regime (γ ≥ 2), Grönwall's inequality establishes φ̇ → 0 through the divergence of the Hubble integral; for the inertia-dominated regime (γ < 2, physical Stratoverso case with γₑff = 1. 661), LaSalle's invariance principle applied to the Coleman-Weinberg corrected potential identifies the frozen state as the unique dynamical attractor. A new section introduces the intrinsic toroidal breathing of the MSO membranes: the brane area expands isothermally from φ_∞ = 1. 500 MPl to φₑquatore = 2. 000 MPl and contracts back, with the warp factor e^−A = 0. 75 acting as the coefficient of thermal contraction of the toroidal membrane. This provides a unified geometric interpretation of the Stirling efficiency, the frozen field value, and the layer transition mechanism. All key parameters (WIR = 0. 75, λ = 0. 300, η = 25%) are derived from the 5D bulk action without free parameters. The framework resolves the H₀ tension (H₀ = 72. 4 ± 1. 2 km/s/Mpc) and S₈ tension (S₈ = 0. 778 ± 0. 015). This is Paper P of the Stratoverso series.
Fabio Berti (Sun,) studied this question.