Closed Temporal Topology on S³: Brans–Dicke Embedding with Zero Free Parameters and Five Parameter-Free Cosmological Predictions

We present the 4D Clockwork Universe (4DCU) — a framework built on one geometric choice: the temporal topology on the three-sphere S³ is closed rather than open. This requires no new fields, no new postulates, and no modification to Einstein's equations. The defining constraint Ti² + Ci² = 1 is simply Einstein's energy–momentum identity E² = (mc²)² + (pc)² divided by E² — a relation already in every textbook. From this single boundary condition, six previously independent physical constants (c, G, ℏ, σ_SB, H₀, Ω_Λ) emerge as geometric projections of one algebraic number — the tetranacci constant Φ₄ = 1.92756…, the real root of x⁴ = x³ + x² + x + 1. Five parameter-free cosmological predictions match observation simultaneously: Hubble tension ratio H₀^local / H₀^CMB = 1/(Φ₄−1) = 1.0781 (0.3σ, verified via 8 independent channels) DESI dark-energy equation of state w₀ = −0.838 (0.18σ) Bullet Cluster collisionless fraction f = 0.8353 (0.18σ) Primordial spectral index n_s = 1 − 2/61 = 0.96721 (0.55σ) Cosmological constant Ω_Λ = 5π²/72 = 0.6854 (0.09σ) and Ω_Λ = 11/16 = 0.6875 (0.38σ) The gravity sector embeds exactly in the Brans–Dicke / Horndeski / Khoury–Weltman lineage with zero free parameters (Theorem D1). The SPARC galaxy rotation curves (175 galaxies) are reproduced with 3.5% scatter and zero free parameters via a Beer–Lambert temporal absorption law. The framework proposes a falsification table with seven specific numerical thresholds. This is a comprehensive reference document (~200 pages) from which topical journal papers are extracted. It is not a journal submission itself, but a living theoretical compendium. Version S77 adds Theorem N1 — a universal n-nacci algebraic identity generalizing the core geometric result to all dimensions — and resolves a potential equivalence-principle ambiguity via domain separation of three Ti registers. Keywords: cosmology, Hubble tension, dark energy, foundations of physics, S^3 geometry, tetranacci constant, arrow of time, 600-cell, Coxeter symmetry, Past Hypothesis. Author: Miroslav Ivanov YosifovIndependent Researcher, Plovdiv, BulgariaORCID: 0009-0007-1842-656XContact: YosifovSpace@gmail.com