Closing Gaps with SymC: Physical Inheritance from Stabilized Substrates in Dynamical Systems
Christensen, Nate
Abstract
Version 2 upgrades a central element of the SymC program by replacing its last phenomenological postulation with an explicit derivation, yielding the first rigorous demonstration that the substrate-induced parameter relations arise internally from the model’s structure. This work proposes that effective parameters of low-energy physics emerge from interactions with a hierarchy of χ-stabilized substrate modes formed during successive symmetry-breaking stages of the early universe. The central condition χ = Γ/(2Ω) = 1 defines an adaptive stability boundary that appears in quantum transitions, in cosmological structure growth, and in the formation of collective substrates at the electroweak and QCD scales. A minimal effective Hamiltonian is constructed that incorporates QCD condensate, Higgs fluctuation, and proto-lepton modes, and the physical electron is shown to arise as the lowest eigenmode of this coupled system. Its mass satisfies m_e = ε_e Λ_QCD, where ε_e is the overlap of the electron mode with the QCD substrate. Using Λ_QCD ≈ 200 MeV, the observed electron mass yields ε_e ≈ 2.6 × 10⁻³, and the corresponding Yukawa coupling y_e = ε_e (√2 Λ_QCD / v) reproduces the Standard Model value y_e ≈ 2.9 × 10⁻⁶ without free tuning. The mechanism generalizes to all fermions, with mass hierarchies reflecting overlap amplitudes with stabilized substrates. The model leads to testable predictions spanning lattice QCD, quantum dynamical systems, and cosmological structure growth, providing multiple independent channels for empirical evaluation.