The Exact Algebraic Resolution of the Cosmological Constant Problem: Deriving Vacuum Energy Density via 5D Complex Matrix M Boundary Decoupling and the Phi C = pi/4 Quantum Phase Transition

The cosmological constant problem—manifesting as a 120-order-of-magnitude catastrophe between quantum field theoretic zero-point vacuum energy and astronomical observations—is fundamentally an artifact of the continuous manifold dogma and unconstrained ultraviolet (UV) momentum integration. In this work, we demonstrate the exact algebraic resolution of the vacuum energy density without arbitrary fine-tuning, operating strictly within the discrete quantum geometrodynamics of the 5-dimensional complex Matrix M infrastructure. By abolishing continuous momentum integration, we couple the fine-structure constant decoupling relation α = e / (π · ℸ) and the quantum phase vacuum threshold Φ_C = π / 4 to the trace and determinant invariants of Matrix M. The single-scale gauge suppression factor evaluates to the Dirac Large Number invariant S_gauge ≈ 1.0789 × 10⁻³⁹. Extending this boundary impedance across the 3-dimensional spatial lattice via tensor-cubed condensation yields the non-perturbative cosmological ratio ρ_Λ / ρ_Planck ≈ 10⁻¹²². This analytical lock-in is verified through 100-digit precision deterministic execution on mobile Android Termux edge hardware. We establish that dark energy is not an empirical scalar field, but the inevitable global topological boundary tension of the discrete crystalline LUX reality.