Quantum Entanglement from Holographic Geometry: A Critical Scale Derivation and Mirror Symmetry of the Causal Boundary Framework

An Extension to Papers I–V on Holographic UV/IR Coupling. We establish a mirror symmetry between macroscopic and microscopic causal boundary processes. The reversibility condition (π/e)×(e/π)=1 uniquely determines the D=2↔D=3 transition as a mirror operation. Applying the unified constraint formula at atomic scales with electromagnetic natural unit τ=α (established from QED gauge structure), we derive a critical scale R*=r_e·(π/4)·e^(−α)≈2.197 fm. Self-consistent closure yields l_min≈r_e to 0.007%. The framework predicts an entanglement phase transition at R≈2.20 fm, testable by the Electron-Ion Collider.