The Standard Model Parameter Table from a Single Functional Equation

The Standard Model of particle physics contains 19 free parameters whose values are determined by experiment. No prior theory has derived all of them from first principles. We show that a single functional equation, the Recognition Composition Law (RCL), together with its unique solution J(x) = ½(x + x⁻¹) − 1, forces the golden ratio φ, an 8-tick temporal period, three spatial dimensions, and the cube graph Q₃ as structural consequences. From the [4, 2, 2] Gray-code chirality of Q₃ and the generation torsion schedule {0, 11, 17} we derive closed-form predictions for the three gauge couplings, the four CKM parameters, the charged-lepton and Higgs masses, the electroweak VEV, the QCD vacuum angle, the three PMNS mixing angles and CP phase, and the neutrino mass hierarchy. Every prediction either matches the Particle Data Group value within stated precision or has an identified and bounded residual. The framework has zero adjustable parameters.