Gap Channel Theory: Fundamental Constants, Wave Dynamics, and Electromagnetism from a Single Geometric Axiom

We present Gap Channel Theory (GCT), a geometric framework that derives all three Standard Model gauge couplings, five particle masses, and quantum correlations from a single axiom: the Dimension Selection Principle. This principle identifies d = 3 as the unique spatial dimension in which regular simplex packing produces a non-zero angular deficit whose gap fraction matches the order of the corresponding symmetry group. From d = 3 alone, we derive: the exact identities sin² (δ/2) = 3⁻⁵, cos δ = 241/3⁵; the electromagnetic coupling αEM = Tδ/ ( (S₂−S₁) π), giving 1/α = 137. 029 (0. 005%) ; the strong coupling αₛ = Tδ/ (√d π) = 0. 11797 (0. 03σ) ; the weak mixing angle sin²θW = 3/13 (0. 19%) ; five particle masses (electron, muon, tau, proton, neutron) all within single-digit ppm with zero free parameters; the Koide ratio 2/3; the Cabibbo angle arcsin (9/40) (0. 04σ) ; the CHSH bound 2√2; Ngen = 3; and three algebraic identities linking all constants into an over-determined system. The Hessian of the discrete Regge action on the five- 1Gap Channel Theory — The Complete Framework Kahramanlar 2026 tetrahedron ring provides wave propagation (index-1 saddle, five transverse modes at λ = 1/3). Maxwell’s equations are derived on the 600-cell via discrete exterior calculus. The 120 vertices of the 600-cell encode the periodic table’s electron structure. The theory has one axiom and zero free parameters.