T₃代数下的光路涌现几何与动力学时空生成 Light‑Path Emergent Geometry and Dynamical Spacetime Generation under the T₃‑Algebra

摘要 本报告基于T₃三维数代数 ,提出一种全新的光路涌现几何框架。本理论彻底摒弃“预设黎曼流形背景”,主张物理时空的度规、测地线、曲率乃至拓扑结构,均是由T₃本源场中信号涡旋(光路)的解集 内部关联所涌现的产物。 通过严格定义T₃内部的点、距离、夹角与曲率原语,并建立本源场动力学方程,证明了欧氏几何仅仅是稳态、弱场条件下的退化特解。本报告进一步解出了椭圆螺旋(周期性时空)与双曲螺旋(暴胀/膨胀时空)的曲率解析式,并揭示出T₃代数特有的零因子锥 正是局部几何破裂(奇点)的拓扑根源。本理论为非结合代数与时空涌现动力学提供了第一性框架。 Abstract Based on the T₃ three‑dimensional‑number algebra , this report proposes a novel framework of light‑path emergent geometry. Completely abandoning the presumption of a pre‑existing Riemannian manifold background, the theory argues that the metric, geodesics, curvature and even topological structure of physical spacetime are emergent products of internal correlations among solution sets of signal vortices (light paths) within the T₃ primordial field. By rigorously defining primitive geometric entities including point, distance, angle and curvature inside T₃, and establishing dynamical equations for the primordial field, we prove that Euclidean geometry is merely a degenerate special solution under steady‑state and weak‑field conditions. We further derive analytical curvature expressions for elliptic spirals (periodic spacetime) and hyperbolic spirals (inflationary/expanding spacetime). It is revealed that the T₃‑specific zero‑divisor cone constitutes the topological origin of local geometric breakdown (singularities). This report provides a first‑principle framework for non‑associative algebra and emergent spacetime dynamics.