Integral Modeling and Mathematical Formalization of XYZ+T Four-Dimensional Topological Spacetime

Project: W≡0 Global Topological Unified Field TheoryStage Affiliation: Phase III · Sub-thesis 3 Abstract Research Background: Previous studies have established the ontological theories of three-dimensional space (XYZ) topology (Phase III Sub-thesis 1) and one-dimensional time (T) topology (Phase III Sub-thesis 2), clarifying that space originates from orthogonal decomposition of polarity gradients and time derives from the propagation direction of polarity gradients. Meanwhile, the meta-stability and ultimate simplicity verification of the W≡0 axiom have been completed (Phase III Sub-thesis 4), laying a solid meta-theoretical and fundamental topological foundation for unified spacetime modeling. It is urgent to integrate three-dimensional spatial topology and one-dimensional temporal topology into a unified four-dimensional spacetime model, and verify its compatibility with classical physics, relativity and other existing physical theories to solve the core difficulties in spacetime unification. Research Objectives: To construct the exclusive XYZ+T four-dimensional topological spacetime mathematical model for the W≡0 theory, and define its topological structure, basic invariants and evolution laws; to prove that the model can be strictly degraded into all verified existing spacetime theories under different approximate conditions; to realize seamless connection with previous sub-theses and improve the spacetime ontological foundation of the W≡0 theory. Research Methods: Adopt pure topological mathematical methods including point-set topology and algebraic topology to construct the overall spacetime structure, and combine measure theory to define spacetime topological correlation and evolution measures. Apply limit deduction to simulate approximate processes under various physical conditions and complete strict mathematical verification of degradation of existing theories. Error analysis is adopted to ensure deduction rigor. All researches abide by phase boundary constraints without introducing advanced tools such as differential geometry and metrics. Core Conclusions: The XYZ+T four-dimensional topological spacetime is the uniquely self-consistent original spacetime model deduced from the W≡0 axiom, which is organically integrated by three-dimensional spatial polarity topology and one-dimensional temporal gradient topology without any external geometric presuppositions. Classical absolute spacetime, Minkowski spacetime of special relativity and weak-field solutions of general relativity are all equivalent forms of this model under corresponding physical approximation conditions, with logical consistent degradation processes and controllable errors. This spacetime model completes the construction of spacetime ontology in Phase III, and provides a standard spacetime framework for the derivation of fundamental physical constants in Phase IV and researches on strong gravitational field subjects in Phase V. Keywords Four-dimensional topological spacetime; Mathematical formalization; Degradation verification of existing theories; Topological correlation structure; W≡0 theory; Polarity gradient; Spacetime topological invariant