The Galactic Dynamics of the Fundamental Speed Theory: Numerical Solution of the Spherically Symmetric Field Equation and Comparison with SPARC Galaxy Data

This work presents the numerical solution to the core field equation of the Fundamental Speed Theory (FST) in a static, spherically symmetric configuration. The equation governing the spatial profile of the vector field V^\mu is solved numerically using Python, yielding the field behavior V(r) and its induced acceleration a_V(r) . The results demonstrate a characteristic screening mechanism where the field is suppressed in high-density regions while contributing significantly to the dynamics in galactic outskirts. The model accurately reproduces the rotation curves of galaxies from the SPARC database (e.g., NGC 2403 and UGC 128) without invoking dark matter. Furthermore, a testable prediction for gravitational lensing in dwarf galaxies is proposed, with a detectable correction \varepsilon_V \approx 2.3 \times 10^{-5} . This study establishes a direct link between the galactic dynamics of FST and its cosmological implications, using consistent parameters ( m_V = 3.2 \times 10^{-30} eV, \( \lambda = 10^{-4} \)) across scales.本研究针对静态球对称构型下的基本速度理论（Fundamental Speed Theory, FST）核心场方程，给出其数值解。研究通过Python对控制矢量场V^μ空间分布的场方程完成数值求解，得到了场的分布行为V(r)及其诱导加速度a_V(r)。结果揭示了一种典型的屏蔽机制：场在高密度区域受到抑制，而在星系外围则对动力学过程产生显著贡献。该模型无需引入暗物质，即可精准复现SPARC数据库中星系的旋转曲线（例如NGC 2403与UGC 128）。此外，本研究针对矮星系的引力透镜效应提出一项可检验的理论预言，其可探测修正量ε_V ≈ 2.3 × 10^{-5}。本研究采用跨尺度统一的参数（m_V = 3.2 × 10^{-30} eV，λ = 10^{-4}），建立了FST星系动力学与其宇宙学效应之间的直接关联。