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 D_eff ≈ 3 at high density (CMB epoch) to D_eff → 2 at low density (local universe). The fundamental constant ΦF = √2 - 1 ≈ 0.414, which governs this transition, predicts H_local/H_global = 1/√(1-ΦF²) = 1.0987 with zero adjustable parameters. Using Planck's H_global = 67.4 km/s/Mpc, FDM predicts H_local = 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 χ²_red = 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.