The Navier-Stokes Problem: Predictive Fluid Manifolds via Peak Energy Centroids

This paper provides a radical shift in fluid simulation by proving that complex, high-resolution temporal data can be distilled into a sparse, predictive geometric model. By filtering for peak kinetic energy curves (Vector Classes) and tracking their centroids, the model identifies Run 16 as a critical saturation point, where metric tension reaches its maximum threshold before collapsing into the turbulence observed in Run 18. This relationship between energy saturation and subsequent torsion allows the system to function as a Predictive Geometric Engine; by using computer vision to monitor optical flow and luminance as proxies for energy, the engine can forecast topological inversions and vortex shedding directly from video feeds. This approach bypasses traditional frame-by-frame rendering, instead utilizing the Geometric Governor () to predict the fluid's next state based solely on its current visual saturation, predicting chaos before it manifests.