1. Executive Summary This document derives the Klein-Gordon equation from ArXe first principles, extending the quantum mechanical framework to relativistic field theory. What We Derive: ✅ Klein-Gordon equation: (□ + μ²)φ = 0 where: □ = (1/c²)∂²/∂t² – ∇² (d'Alembertian operator) μ = mc/ℏ (Compton wave number) ✅ From Einstein’s relation: E² = (pc)² + (mc²)² ✅ Field interpretation: φ…