The fine structure constant α is a cornerstone of fundamental physics, yet persistent observational evidence from high-resolution quasar spectroscopy suggests it may vary across cosmological scales.We provide a zero-parameter, purely geometric derivation of this variance within the Fibonacci Tetrahedral Lattice (FTL) framework. By modeling the vacuum as a discrete, aperiodic tilingof regular tetrahedra derived from an E8 → R3 projection, we demonstrate that the observed≈ 10 ppm shift in α emerges as a necessary mechanical consequence of structural phase transitions between discrete "Fibonacci Gates." Furthermore, we show that the same structural frustration that generates α variance also drives the **Hubble Expansion Ratio** (κexp = 1.0905) between gate transitions, providing a unified resolution to both the α-dipole and the Hubble Tension (67.4 × 1.0905 ≈ 73.5 km/s/Mpc). This result transforms a series of observational "anomalies" into the primary experimental proofs for a discrete, frustrated vacuum.