Three Operating Zones of a Gaussian-Windowed Spectral Kernel: Structure of the Stability Manifold from 24,903 Validated Runs
Abstract
A dense parameter sweep of a Gaussian-windowed spectral kernel (24,903 runs, zero errors) reveals three distinct operating zones defined by the Gaussian bandwidth relative to active Fourier modes. The kernel is confirmed exactly linear with perfect amplitude-squared drift scaling. Drive frequency is orthogonal to energy conservation. The critical coupling boundary is amplitude-dependent and piecewise. Active dynamics requiring physics-like behavior exist only in the wide-bandwidth regime. All results are reproducible from pure Python on consumer hardware.
Fields of Study & Subjects
Nonlinear Dynamics and Pattern Formation
Model Reduction and Neural Networks
Numerical Solvers for Ordinary Differential Equations
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 4 March 2026
- Language
- EN
- Document type
- Preprint