The Holographic Axion: Inertial Freezing and the Geometric Origin of Dark Energy

We present a novel dark energy framework based on the 5D Holographic Axion, where the cosmic acceleration emerges from a geometric phase transition in the bulk. Contrary to standard thawing quintessence, our numerical simulations reveal a three-phase "Inertial Freezing" dynamics: a high-redshift stiff regime (w=1) that protects Big Bang Nucleosynthesis (BBN), a holographic trigger at z_c ≈ 3500 where the potential activates, and a late-time capture phase. Our model yields H₀ ≈ 72.1 ± 0.8 km/s/Mpc and w₀ ≈ -0.967, effectively resolving the H₀ and S₈ tensions. The scale of dark energy is naturally explained by a geometric seesaw mechanism, confirmed by a calibration factor λ_cal ≈ 0.615 which eliminates the 120-orders-of-magnitude fine-tuning problem.