Mathematical Principles and Physical Interpretation of Spacetime Birth and Evolution Based on Taiji Philosophy

The origin and evolution of spacetime is a core issue of common concern in physics and philosophy. For a long time, physics has faced the dilemma of integrating general relativity and quantum mechanics, especially the "spacetime-free" confusion at the Planck scale, while Taiji philosophy, with its naive dialectical thought of "Yin-Yang coexistence, interdependence and all things born from three", has provided a holistic and intuitive framework for the evolution of the universe. Based on the core framework of Taiji philosophy, this paper constructs a "philosophy-mathematics-physics" triple unified spacetime evolution model by combining the topological constraints of Brouwer Fixed Point Theorem, the entanglement principle of quantum field theory, and the energy conservation law of the Zeroing Equation. The results show that the origin of spacetime is a zero-dimensional dual fixed point (Taiji origin), which exists as a coordinate singularity in the 6-dimensional joint field space composed of spin wave field and matter wave field, and only possesses the intrinsic dual correlation between spin waves (carrying temporal information) and matter waves (carrying spatial information), without any dimensional characteristics. Through the progressive logic of "topological extension + symmetry breaking", this zero-dimensional fixed point sequentially completes the dimensional evolution process from 0D to 1D, 1D to 2D, and 2D to 3D driven by quantum fluctuations and energy changes, and finally generates the classical spacetime structure of "1D time + 3D space" that conforms to human observational experience. Among them, the 1D evolution dominated by spin waves corresponds to the "Yang fish eye" of Taiji, which is the origin of time, with active, rhythmic and irreversible characteristics; the 3D evolution dominated by matter waves corresponds to the "Yin fish eye" of Taiji, which is the origin of space, with static, extensive and isotropic characteristics. These two evolution paths are closely bound by the residual balance of the Zeroing Equation, which effectively avoids spacetime separation or annihilation and ensures the stability of classical spacetime. This model not only verifies the mathematical feasibility of dimensional evolution through the topological invariants of Brouwer's theorem, but also clearly explains the physical mechanism of spacetime generation through quantum entanglement and three times of symmetry breaking, and forms a precise and in-depth echo with Taiji's philosophical logic of "Tao generates one, one generates two, two generates three, three generates all things". As an interdisciplinary exploration, it not only provides a new theoretical paradigm for the study of spacetime essence, but also offers a precise mathematical and physical basis for the modern scientific interpretation of Taiji philosophy, bridging the gap between Eastern traditional philosophy and Western modern physics.