An Algebraic Solution to Galaxy Dynamics: The Kinematic Field Geometry Constant (KG.P.) in Dynamic Field Geometry (KFG)

This manuscript proposes the Kinematic Field Geometry (KFG) as a first-principles approach to describing galactic dynamics, thus algebraically solving the Dark Matter problem. KFG posits that a galaxy is not a system of point masses but a Vortex Field (VF) characterized by a **Geometric Field Constant (𝑲𝑮.𝑷). Orbital velocity (𝒗′) is regulated by smooth geometric modulation, not by a diminishing gravitational potential. Using this method, we derive a single formula that accurately models both the velocity rise in the galactic core and the constant velocity (Plateau) in the outer disk, using only one global constant and simple trigonometry.

本研究提出运动场几何学（Kinematic Field Geometry, KFG）作为描述星系动力学的第一性原理方法，以此代数求解暗物质问题。KFG认为，星系并非质点系统，而是以**几何场常数（Geometric Field Constant, KG.P）**为特征的涡旋场（Vortex Field, VF）。轨道速度（v′）由平滑的几何调制作用调控，而非依赖递减的引力势。借助该方法，我们推导出单一公式，仅需一个全局常数与简单三角学知识，即可精准模拟银核内的速度上升现象与星系外盘的恒定速度（速度平台）特征。