The Spatial Emergence Significance of the Squared Distance R²: A Geometric Derivation and Interpretation Based on the Virtual Particle Spacetime Symbiosis Theory

English:This paper derives the fundamental relation R² = t² from the spiral equations of the Virtual Particle Spacetime Symbiosis Theory, and provides a rigorous geometric and philosophical interpretation. We demonstrate that the squared distance R² is a measure of the "emergence" intensity of the virtual particle's motion on the substantialization projection plane, isomorphic to the definition of variance in statistical mechanics. This result provides a purely geometric, zero-free-parameter explanation for the flatness of galaxy rotation curves and the inverse square law of gravity, eliminating the need for the dark matter hypothesis. This manuscript is published under the CC BY 4.0 license, allowing for free distribution and adaptation, provided the original author is credited. 中文:本文从虚粒子时空共生理论的螺旋方程出发,严格推导出 R² = t² 的基本关系式,并提供了严谨的几何与哲学诠释。我们证明了距离的平方 R² 是虚粒子运动在“实质化投影”平面上的“涌现”强度度量,与统计力学中方差的定义同构。这一结果为星系旋转曲线的平坦性和引力的平方反比律提供了一个纯粹的、零自由参数的几何化解释,从而消除了对暗物质假说的需求。 本手稿根据 CC BY 4.0 许可证发布,允许自由分发和改编,但须注明原作者。