Cosmic Topology: Geometric Unification of Spatial Overlap, Material Structure, and Gravity (Version 3.1 — Final)

This paper establishes Cosmic Topology (Spatial Geometry of Cosmic Unification, SGCU) with full mathematical rigor. The central postulate is: three-dimensional space may undergo multi-layer overlap within the same region, and this overlap itself constitutes the common geometric origin of mass, energy, and interactions. We provide a strict axiomatic definition of spatial overlap, construct a 3+1-dimensional field-theoretic model, prove the existence of soliton solutions, and derive the discrete mass spectrum. Within a unified framework, we derive the cosmic composition structure (the 3-7-11 structure) and present a geometric interpretation of the four fundamental interactions. The theory yields two testable predictions: (1) the existence of a neutral scalar boson with a mass of approximately 47 MeV (the quantum of the φ-field); (2) the photon possesses a non-zero rest mass (qualitatively inevitable, quantitatively pending). Both predictions are accompanied by clear experimental falsification conditions.