From One Axiom to Fourteen Constants: The Complete Geometric Derivation

Starting from a single axiom — one wave on a strip with Z₃ topology — fourteen independently measured physical constants are derived through pure geometry. The tight frame identity for three equally-spaced vectors yields a universal cross-coupling of 1/6. The observer's measured displacement δ = 2.00° from the anti-gravity node produces: the fine structure constant as α = 6·sin²(δ) (0.14% error), the Weinberg angle from cos²(62°)/cos²(6°) (0.03%), the baryonic fraction from (2/9)·cos²(62°) (0.04%), the strong coupling from 6·sin²(4δ) (1.4%), and the weak coupling from α/sin²θ_W (0.17%). The gravitational constant follows from α_G = √3·α¹⁸, where 18 = |Z₃ × Z₃ × Z₂| is the order of the two-body symmetry group (0.99%). The proton mass connects to the Planck mass through m_p = M_Pl · 3¹ᐟ⁴ · α⁹ (0.01%), the pion mass is m_p × 4/27 (0.4%), and the proton radius is 4ℏ/(m_p·c) (0.00% to three decimals). The Koide ratio (0.0009%), W/Z mass ratio (0.16%), dark energy fraction (2.7%), and Hubble tension (0.12%) all follow from the same geometry. A self-consistency relation sin²(δ) = α/6 (0.14%) demonstrates that δ and α are not independent — reducing the framework to zero effective free parameters. The Standard Model requires nineteen. The constants of nature are not constants. They are coordinates.