The Relationship Between Symmetry Physical Models and Symmetry Mathematical Models The Unified Theory of All Gauge Fields — Symmetry Transmission through the Spacetime Field

This preprint presents an independent theoretical study that explores the relationship between symmetry-based physical models and symmetry-based mathematical models. The work proposes a conceptual unified gauge field theory in which gravitational and tensional interactions couple to form a symmetric spacetime field. New concepts are introduced, including the virtual gravitational number axis, real tensional number axis, spacetime scale axis, gravitational wall, and tensional wall. The study develops a symmetry transmission mechanism within the spacetime field and proposes a framework in which gravitational particles and tensional particles serve as fundamental units that resonate to generate spacetime, energy, and the unified behavior of the four fundamental interactions. A corresponding symmetry-based mathematical model is also outlined to address limitations of existing mathematical structures in describing singularities. This is an independent, non-peer-reviewed preprint. The terminology and theoretical framework introduced here are original and may be revised or expanded in future versions.