Topological Ontology of Three-Dimensional Space · Polar Structure and Global Connectivity Rules

Project: W≡0 Universal Topological Unified Field TheoryStage Affiliation: Phase Three · Sub-paper 1 (Paper 3.2) Abstract Since the establishment of classical physics, three-dimensional space has long been regarded as an a priori existence that requires no further interpretation. Classical mechanics defines space as a passive container for material motion, while relativity further upgrades it into a geometric manifold interacting with matter. Nevertheless, neither theory has addressed three core fundamental issues: the ontological origin of space, its intrinsic microscopic structure, and the topological inevitability of spatial dimensionality. This essential ontological deficiency not only prevents classical and modern physics from revealing the physical essence of fundamental spatial properties such as spatial homogeneity and isotropy, but also constitutes an underlying root cause for the paradigm conflicts between relativity and quantum mechanics, as well as the failure to unify the four fundamental interactions. Based solely on the universal topological polarity conservation axiom as the first principle, this paper systematically constructs the ontological framework of three-dimensional space by adopting axiomatic deduction, algebraic topological analysis, continuous group theory and variational extremum method without introducing any empirical parameters or artificial hypotheses. This study proves that three-dimensional space is not an a priori entity independent of matter and fields, but a macroscopically emergent steady-state structure formed by spontaneous symmetry breaking of the universal polarity field under the system. Each orthogonal dimension of three-dimensional space inherently possesses a strict dual structure of positive and negative topological polarities, and spatial dimensions are essentially orthogonal propagation directions of polarity gradients. The global connectivity of space is uniquely constrained by the universal topological polarity conservation law, and all local spatial properties are rigidly restricted by the global topological structure. Further verified via abstract stability functional extremum analysis and topological invariant classification, the three-dimensional orthogonal decomposition stands for the minimal non-trivial stable topological solution within the orthogonal decomposition system of polarity gradient fields. It serves as the naturally optimal configuration with the lowest energy, most stable structure and full compliance with global conservation constraints in the self-consistent theoretical system. This research fundamentally overturns the a priori presuppositions of classical absolute space view and relativistic geometric space view, and realizes the axiomatic reconstruction of three-dimensional spatial ontology. It clarifies the physical essence and topological attributes of space, and lays an unshakable underlying theoretical foundation for subsequent researches including the construction of four-dimensional topological spacetime, derivation of spacetime coupling mechanisms and first-principle calculation of fundamental physical constants. Keywords: Topological Ontology of Space; Polar Structure; Topological Connectivity; Origin of Dimension; Spontaneous Symmetry Breaking; Theory