Spectral Energy Retention and Stability Analysis of the Electro-Atomic Rupture (EAR) Model in Multidimensional Flows

Summary of Version 7.0: This version marks the transition from conceptual 1D/2D models to fully realized 3D turbulence analysis. Key Discoveries in v7.0: 3D Vortex Dynamics: Using Taylor-Green and ABC flows, we show that the EAR model increases enstrophy by 8% and energy retention by nearly 4x at micro-scales compared to classical N-S solvers. Intermittency: The model exhibits a 15% increase in "Flatness," aligning more closely with the intermittent nature of real-world turbulence. Self-Contained Theory: A complete explanation of the "Rupture Operator" is included, making this the definitive standalone reference for the EAR Theory. Numerical Honesty: We document the physical limits of the model, including its transition to singularities under extreme conditions.