N-Body Systems

The core of this research lies in the Geometric Manifold Hypothesis, which suggests that the chaotic dance of n bodies is not governed by the sum of individual gravitational pulls, but by the "topology of the gap" between them. By mapping the positions of the bodies onto a NURBS-defined configuration manifold, we can identify a Metric Tension—represented by the area or volume of the system—and a Stretching Gradient (Lambda), which tracks how that space expands or contracts over time. When these geometric properties are fed into our Universal Transition Formula, the next move of a body becomes a predictable flow along the manifold's principal curvature (K_1). This approach successfully scales from 3-body to 4-body systems with high correlation, proving that as the number of bodies increases, the underlying geometric fabric remains the primary driver of the system's evolution.