A scalar-tensor extension of general relativity with closed temporal topology: zero-parameter resolution of the Hubble tension"

The 4D Clockwork Universe (4DCU) framework derives a wide range of 
cosmological observables from a single geometric postulate on the 
three-sphere S³: the unit four-vector constraint Tᵢ² + Cᵢ² = 1, where 
Tᵢ (temporal phase) and Cᵢ (spatial phase) are dimensionless fields. 
From this constraint and a dissipative leakage equation 
dTᵢ/dt = -α·Tᵢ²·Cᵢ² with α = √3/2 (a geometric constant fixed by 
the H₄ Coxeter symmetry of the 600-cell), the framework produces 
fourteen quantitative parameter-free predictions ("Monuments") and 
resolves jointly seven foundational tensions of Lambda-CDM cosmology:

1. The Hubble tension (5σ → 0.4σ structural prediction, with 
   H₀^local ∈ [72.28, 72.66] km/s/Mpc derived from the Planck CMB 
   anchor and tetranacci algebra alone, no SH0ES input required; 
   compatible within 1.5σ with all 2024-2026 late-universe 
   measurements);
   
2. Dark energy fine-tuning (Omega_Lambda derived structurally 
   without 10^120 cancellation);
   
3. Galaxy rotation curves (175 SPARC galaxies fit by Tᵢ-gradient 
   force with single coupling α_SPARC = 0.866 ± 0.038 matching 
   geometric prediction √3/2);
   
4. The fine-structure constant (α_EM = Tᵢ_orbital at the Bohr 
   orbit, exact);
   
5. The G scatter (200 ppm inter-laboratory variation explained 
   by G_local = G_geom · Tᵢ²);
   
6. The Past Hypothesis (low-entropy initial state and arrow of 
   time forced by the logical necessity Tᵢ(0) = 1 together with 
   the gradient-flow structure of the leakage ODE — a geometric 
   theorem, not an external boundary postulate);
   
7. The Big Bang singularity (replaced by a smooth boundary point 
   on S³ where all observables remain finite).

The framework includes honest treatment of open problems and 
working frontiers, including the algebraic conjecture 
Tᵢ_0 = Φ₄ - 1 (where Φ₄ is the tetranacci constant), the 
LLR bound on Newton-G time variation, the fine-structure constant 
cosmological drift, and the BAO sound-horizon target.

This is Skeleton 62, the comprehensive reference document. 
Topical papers will follow.

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 Yosifov
Independent Researcher, Plovdiv, Bulgaria
ORCID: 0009-0007-1842-656X
Contact: YosifovSpace@gmail.com