The Geometric Standard Model: A Zero-Parameter Unified Theory from Binary Logic

We present a complete derivation of the Standard Model and General Relativity from a single axiom: the existence of logical distinction {0,1}. Through a rigorous six-level Lagrangian hierarchy, we demonstrate that all fundamental interactions arise as necessary consequences of compositional logic. The framework eliminates all 19 free parameters of modern physics. We derive the fine structure constant α⁻¹ = 137.036011 (0.09 ppm precision vs CODATA 2024), all fermion mass ratios (50-66 ppm), and Newton's constant from Mersenne saturation at computational level 127. The topological origin of exactly three fermion generations emerges from pentagon symmetry (Chern number = 3), and the gauge structure SU(2)×SU(3)×U(1) arises from non-commutative compositions at level 5. Each Lagrangian is rigorously derived with verified Euler-Lagrange equations. We provide five falsifiable predictions testable within 2025-2030. The universe emerges as the unique stable fixed point of binary self-reference.