Cosmic Topology: Geometric Unification of Spatial Overlap, Matter, and Interactions (Version 4.0 — Rigorous Derivation of the Complete Particle Periodic Table, Photon Masslessness, and Geometric Quantum Numbers)

We present a complete geometric theory (SGCU) in which three-dimensional space can undergo multi-layer overlap. From this single postulate and only two fundamental parameters (κ,φ₀), we derive the entire spectrum of known elementary particles and predict twelve new ones. The theory is built on rigorous mathematics: we define spatial overlap, prove global overlap number conservation, construct a 3+1-dimensional action, and show the existence of topological soliton solutions identified as particles. Fermion generations arise from interlayer knotting with a maximum winding number Wₘₐₓ≈2.1 that forbids a fourth generation. The cosmic energy budget emerges as a 3-7-11 layer structure in precise agreement with Planck 2018 data. The electroweak scale and Higgs mechanism are derived as a collective phase transition of the knotting network, reducing the number of fundamental parameters. Crucially, the photon is exactly massless because it occupies $N=1$ (no overlap). Five geometric quantum numbers $(N,L,W,C,Q)$ classify every particle, explaining spin, charge, confinement, stability, and generation. We provide a complete particle periodic table in the style of Mendeleev, with empty slots for predicted particles and forbidden zones. All derivations are presented with full mathematical rigor, and the theory is falsifiable through multiple experimental tests.