The Hubble Tension as Geometric Signature of Dimensional Transition: A Parameter-Free Prediction from Ferreyra Dimensional Mechanics

The Hubble tension—a 5σ discrepancy between early-universe (CMB-based) and late-universe (distance-ladder) measurements of H₀—remains unresolved within ΛCDM cosmology. We show that this tension emerges naturally in Ferreyra Dimensional Mechanics (FDM), where the effective spatial dimensionality varies from Dₑff ≈ 3 at high density (CMB epoch) to Dₑff → 2 at low density (local universe). The fundamental constant ΦF = √2 - 1 ≈ 0. 414, which governs this transition, predicts Hₗocal/Hglobal = 1/√ (1-ΦF²) = 1. 0987 with zero adjustable parameters. Using Planck's Hglobal = 67. 4 km/s/Mpc, FDM predicts Hₗocal = 74. 05 km/s/Mpc, consistent with Riess+ (73. 04±1. 04), Pesce+ (73. 9±3. 0), and H0LiCOW (73. 3±1. 8). χ² analysis across 6 independent local measurements yields χ²ᵣed = 1. 73, indicating excellent agreement. Critically, this same constant ΦF simultaneously predicts cosmic energy densities (ΩΛ=0. 707, Ωm=0. 293) and the Tully-Fisher relation (M∝V⁴), demonstrating unprecedented unification. The framework makes specific falsifiable predictions about redshift-dependent systematics and environmental variations in H₀ measurements.