Resolving the Hubble Tension in the Theory of Hyperbolic Unity (THUI): Cubic Curvature Correction R³ and Vacuum Duality as the Key to the Evolution of the Universe

The Hubble tension — the persistent discrepancy between the Hubble constant H₀ measured from early-universe data (CMB, Planck: 67–68 km/s/Mpc) and late-universe observations (supernovae, JWST: ~73 km/s/Mpc) — remains one of the most significant puzzles in modern cosmology, exceeding 5σ significance and suggesting the need for new physics beyond the standard ΛCDM model. In the Theory of Hyperbolic Unity (THUI), the vacuum is modeled as a dual structure: a local cubic layer at the Planck scale and a nonlocal hyperbolic layer {5,3,3}. The cubic curvature correction R³ to the Einstein–Hilbert action ensures finite loop integrals and eliminates singularities, while the resonant number 1729 balances the transition between layers. The global Hubble constant is geometrically derived as H₀ = (1729)^{1/3} × c / (ℓ_Pl × 10^{17}) ≈ 67.74 km/s/Mpc, matching early-universe measurements. The higher late-universe value (73 km/s/Mpc) emerges naturally as an effect of vacuum “unfolding” in the low-curvature regime, where the nonlocal layer dominates and induces an apparent 5–8% increase in expansion rate. This mechanism explains the tension without additional fields, particles, or parameter tuning — as a direct consequence of vacuum dynamics. THUI also resolves the cosmological constant problem via resonant suppression, derives 39 fundamental constants and Standard Model particle masses from five base entities (ℓ_Pl, ϕ, π, e, 1729), and predicts testable signatures, including a vacuum resonance at 1729 Hz and finite black-hole entropy scaling as 1729 × 10^{77} k_B. The theory offers a unified geometric framework for cosmology, particle physics, and quantum gravity, awaiting experimental verification in the coming years.