Complete Resolution of the Cosmological Constant Problem: Derivation of Λ = EPlanck × κcrit^ (φ/2 + 3/4) from Causal Coherence, Golden Ratio Geometry, and Informational Thermodynamics

This work presents the complete, three-stage resolution of the cosmological constant problem — the 10¹22 discrepancy between predicted and observed vacuum energy density that has resisted solution for nearly four decades. The derivation proceeds from three independent, non-adjustable roots: 1. κcrit = 10^-78 — The causal coherence limit derived from entropic equilibrium (Ṡₙet = 0) at the Planck scale. 2. φ/2 = 0. 809017 — Geometric contribution from the 3D projection of the 8-phase causal tesseract onto a regular pentagon (diagonal/side = φ). 3. 3/4 = 0. 750000 — Thermodynamic offset from the half-phase squared (1 − (1/2) ² = 3/4), representing the fraction of Planck energy that survives the causal membrane's maximum tension point. These combine to give the vacuum exponent: α = φ/2 + 3/4 = 1. 559017 The vacuum energy density is then: V₀ = EPlanck × κcrit^α = 2. 50 × 10^-122 MPl⁴ This matches the observed dark energy density (ρ_Λ ≈ 6. 90 × 10^-27 J/m³) with Δ = 0. 0000 orders of magnitude. No free parameters. No fine-tuning. No dynamical evolution required. The repository includes: - Complete LaTeX manuscript with full derivation - Python script with numerical verification and visualizations - All figures generated during the analysis