What question did this study set out to answer?

The study aims to derive cosmological observables from a single geometric postulate on S³ and address critical tensions in Lambda-CDM cosmology.

May 1, 2026Open Access

4D Clockwork Universe: A Geometric Framework on S³ Resolving Seven Foundational Tensions of Standard Cosmology from a Single Postulate

Puntos clave

The study aims to derive cosmological observables from a single geometric postulate on S³ and address critical tensions in Lambda-CDM cosmology.
Developed a geometric framework based on the four-vector constraint on S³.
Utilized a dissipative leakage equation to generate parameter-free predictions.
Analyzed seven fundamental tensions of standard cosmology with comprehensive geometric approaches.
Resolved the Hubble tension with a structural prediction of H₀^local within 1.5σ of late-universe measurements.
Derived dark energy density without substantial fine-tuning (Omega_Lambda no 10^120 cancellation).
Explained 200 ppm G scatter with local variations derived from geometric factors.

Resumen

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 H₀ˡocal ∈ 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 (OmegaLambda derived structurally without 10¹20 cancellation) ; 3. Galaxy rotation curves (175 SPARC galaxies fit by Tᵢ-gradient force with single coupling αSPARC = 0. 866 ± 0. 038 matching geometric prediction √3/2) ; 4. The fine-structure constant (αEM = Tᵢₒrbital at the Bohr orbit, exact) ; 5. The G scatter (200 ppm inter-laboratory variation explained by Gₗocal = Ggeom · 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 Tᵢ₀ = 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, S³ 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

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