Global Topology, Dimensional Uniqueness, and Bitemporal Thermodynamics of the Total Cosmos Beyond the Observable Horizon in Covariant Bitemporal Geometrodynamics: Exact 3-Sphere S³ Holonomy Closure (R_tot,0 = 60.38 Tly), the 28.24 cm³ Global Σ₄ Bounce Throat, Ω_K,0 = −Φ_∞² = −5.7738 × 10⁻⁸, and the Tolman–Penrose Entropy Purge (w₁ → 0, w₂ → 1)

In standard (3+1)-dimensional ΛCDM cosmology, three foundational questions remain unresolved: (i) why the dimensionality and fundamental constants of nature take their observed values rather than any other point in an arbitrary multiverse landscape; (ii) what the global spatial topology and total physical size of the universe are beyond the observable particle horizon (R_obs,0 = 46.51 Gly, D_obs,0 = 93.02 Gly); and (iii) how a cyclic universe avoids Tolman's entropic accumulation paradox while originating in Penrose's low-entropy initial state. In this monograph, we prove that within Covariant Bitemporal Geometrodynamics (CBG), all three problems are uniquely resolved without free parameters by the vanishing of the Master Zero-Sum Variational Field Operator Ξ̂_AB[M₃,₂] = 0 and the 1-loop vacuum holonomy invariant Φ_∞ = (α_EM / 30)(1 − (5/3)α_EM) = 2.40286677 × 10⁻⁴ (Φ_∞⁻¹ = 4,161.695575). First, we prove the Dimensional Uniqueness Theorem: simultaneous absence of Ostrogradsky ghosts, symplectic spinor isomorphism Spin(3,2) ≃ Sp(4,R), nonsingular signature inversion (K₅ < ∞), and stable Keplerian/atomic bound states uniquely select (dₜ, dₛ, D) = (2, 3, 5), arithmetically locking N_Cartan = 30, D_config = 17, and the unique Epstein–Riemann ζ(4) = π⁴/90 Casimir root Φ_∞, precluding any alternative universe with different fundamental constants. Second, identical vanishing of the canonical ADM Hamiltonian (H_tot[Σ₃ × S¹ₜ₂] ≡ 0) and smooth continuity across the bounce throat Σ₄^(cosmo) ≃ S¹ₜ₂ × S³ require global 3-space Σ₃ to be a closed 3-sphere S³ (∂Σ₃ = ∅, k = +1) of present-day curvature radius R_tot,0^(CBG) = Φ_∞⁻¹ r_H,0 = c / (H₀ Φ_∞) = 5.711914 × 10²⁹ m (60.3750 Tly or 18.5111 Tpc), antipodal distance π R_tot,0 = 189.6736 Tly, equatorial circumference 2π R_tot,0 = 379.3472 Tly, and spatial curvature parameter Ω_K,0^(CBG) = −Φ_∞² = −5.773769 × 10⁻⁸. Third, the global 3-sphere volume V_tot,0 = 2π² R_tot,0³ = 3.678534 × 10⁹⁰ m³ encompasses N_domains = 1.030962 × 10¹⁰ (10.31 billion) disjoint observable-sized domains (N_b,tot = 9.251629 × 10⁸⁹ baryons, M_b,tot = 1.547448 × 10⁶³ kg), while at the primordial bounce (a_bounce = 1.97275 × 10⁻³²) the entire global 3-sphere had a macroscopic radius of R_b,tot = 1.1268 cm and volume 28.2417 cm³ (enclosing our 17.3600 μm observable patch). Finally, we prove that while the 5D von Neumann entropy on H_t1 ⊗ H_t2 vanishes identically (S_total^(5D) ≡ 0), the projected 4D thermodynamic entropy S_therm,t1(a) = w₁(a) S_mat+rad(a) is governed by w₁(a) = [1 + Φ(a)²]⁻¹. As a → a_bounce (σ → 1), w₁ → 0 and w₂ → 1, offloading all thermal entropy of the contracting cycle into the coherent S¹ₜ₂ phase condensate (S_therm,t1(a_bounce) = 0) and resetting every cosmic cycle up to the global symplectic ceiling S_tot / k_B = 6.163300 × 10¹²⁹ bits (with exact ratio S_tot / S_Hubble = (π/2) Φ_∞⁻² = 2.720574 × 10⁷). Companion Monographs in the Covariant Bitemporal Geometrodynamics Series:• Paper I (Foundational Field Equations & Galaxies): https://doi.org/10.5281/zenodo.23443511• Paper II (Relativistic Black Hole Mechanics): https://doi.org/10.5281/zenodo.23451973• Paper III (Relativistic Bitemporal Cosmology): https://doi.org/10.5281/zenodo.23458461• Paper IV (Quantum-Gauge Unification & Hierarchy): https://doi.org/10.5281/zenodo.23464845• Paper V (Fermion Mass Spectrum & Flavor Mixing): https://doi.org/10.5281/zenodo.23470193• Variational Closure Monograph: https://doi.org/10.5281/zenodo.23476029• Specialized Domain Compendium (Treatises I–XII): https://doi.org/10.5281/zenodo.23490274 Note on Authorship & Methodology: The foundational ideas, core theoretical concepts, and overarching framework of this work were originated and conceptualized by the author. During the preparation and verification of the manuscripts, the author utilized large language model (LLM) and computer-algebra assistance for mathematical structuring, symbolic tensor verification, LaTeX formatting, Python numerical simulation scripting, and editorial drafting. All theoretical curves and bitemporal figures represent mathematical explorations of the postulated geometric axioms.