We present a phenomenological framework expressing all 19 free parameters of the Standard Model (SM), along with additional observables, as closed-form functions of pi, the golden ratio phi = (1+sqrt (5) ) /2, and integer topological invariants of the five Platonic solids (faces F, vertices V, edges E). The master formula mᵢ = mPlanck x alphaN x Gᵢ, with alpha inverse = 137 + (pi/88) (1 + phi/190) and Gᵢ constructed from phi, pi, and Platonic numbers, reproduces 56 observables with median deviation 0. 18% using zero free parameters. The framework yields 11 exact algebraic identities and 10 falsifiable predictions, including dark matter mass mDM = 123 GeV, sum of neutrino masses 61 meV, and proton lifetime approximately 10³7 years. Running of alphaₛ = 10 x alpha x phi from MZ to the GUT scale yields alpha₃ inverse approaching 45, consistent with alphaGUT = 1/45. No dynamical mechanism is proposed; the work is presented as a phenomenological observation requiring theoretical explanation, potentially through modular Gamma (5) isomorphic to A₅ flavor symmetry at the special point tau = i x phi.
Yuriy S. Vinogradov (Wed,) studied this question.