# Эксперимент: Hill-Floquet Regularization for Periodic RNNs (#430)

{
  "worked": false,
  "confidence": 9,
  "verdict": "Built a self-contained Fourier Hill-matrix MVP with independent monodromy integration and a toy regularization comparison. The exact offset-scaling prediction passed with slope 1.0, and true Floquet modes had Hill residuals below 6e-8, but the raw truncated Hill maximum produced a persistent spurious positive exponent and shifted the stability boundary by about 0.00816. Therefore the proposed practical largest-real-eigenvalue penalty was not reliable in this test and is not counted as a win.",
  "metrics": {
    "baseline": "At gamma=0.2: raw Hill mu_max=0.205914, rho=3.647; task-only baseline remains at the unstable target.",
    "idea": "Penalty optimization moved gamma to 0.062724, raw Hill mu_max=0.068638, rho=1.539, but true stability was not established; exact boundary gamma=0.002251 versus raw Hill boundary gamma=-0.005914."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 hill_floquet_experiment.py",
  "files": [
    "hill_floquet_experiment.py",
    "results.json",
    "REPORT.md"
  ],
  "limitations": "This is a 2D smooth linear toy rather than a trained GRU/SSM on sine prediction. Singular descriptor matrices, autodiff Jacobians, periodic-orbit shooting, GPU execution, and robust physical-mode continuation or structure-preserving Hill discretization were not tested."
}