The Extended Periodic System of Elementary Particles: Quantum Indices, Dynamical Transformation Laws, and the Four Predicted Topological Solitons

The standard classification of elementary particles is systematically reinterpreted through the physics of the non-linear continuous plenum, transforming abstract quantum numbers into tangible geometric invariants of vortex knots and elastic shear waves. A comprehensive pedagogical and rigorous treatise is presented detailing: (1) the architecture of the 17 Standard Model particles across three fermionic generations; (2) the exact physical meaning of quantum numbers—intrinsic spin (J), fractional electric charge (Q), color charge (C), weak isospin (T3), weak hypercharge (Y_W), and baryon/lepton conservation numbers (B, L); (3) the dynamical laws governing particle transmutation, including weak beta decay, Cabibbo-Kobayashi-Maskawa (CKM) quark mixing, Pontecorvo-Maki-Nakagawa-Sakata (PMNS) neutrino oscillations, and space-time reflection symmetries (C, P, T, CPT). Crucially, this work identifies the five structural deficiencies of the Standard Model and formulates the Extended Periodic System incorporating the Four Predicted Topological Solitons: the Eka-Neutrino (nu_s, 7.100 keV, warm dark matter), the Axion Soliton (a_0, 100 micro-eV, strong CP and cold dark matter), the Leptoquark Soliton (LQ, 1.80 TeV, quark-lepton hybrid), and the Fourth-Generation Eka-Top Quark (t', 2.40 TeV, n=4 radial breathing mode). The specific reaction channels, monochromatic spectral lines, and collider signatures for their experimental verification are quantitatively established.