Zero-Parameter Derivation of the Standard Model Free Parameters within Array Cosmology: From the Planck Scale to the Electroweak Sector

Abstract

The Standard Model of particle physics requires 19 free parameters inserted from
experiment, with no theoretical justification for their values. This paper demonstrates that the five-axiom framework of Array Cosmology, {12, π, γ1, ln 2, φ}, derives these quantities from first principles with zero free parameters—including the
proton mass itself. We first resolve the Hierarchy Problem: mp = 144×13/2+ (20+ π)Znoise = 938.271 MeV (error 0.00008%). With mp fully derived, we then obtain the electroweak mixing angle (sin2^θW = ln 2/3, error 0.021%), the W boson mass (error
0.006%), the Z boson mass (error 0.002%), the Higgs dump energy (mH ≈ 125.247 GeV, error 0.002%), the complete CKM matrix including Wolfenstein parameters (ρ¯error 0.28%, η¯ error 0.032%), the Jarlskog invariant (error 2.9%), and the pion mass
spectrum (π0 error 0.001%). No free parameters, no fine-tuning, no supersymmetry required.