# Эксперимент: Floquet-Stabilized Periodic Training Dynamics (#909)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built an exact 2x2 piecewise-periodic Floquet MVP with matrix-exponential propagators, damping and period sweeps, adiabatic estimates, commutator measurement, and a matched constant-mean baseline. The math checks succeeded: damping shifted gamma by 2.000000 with maximum error below 2e-14; the long-period stability boundary converged to the adiabatic prediction 1.568305, reaching 1.568421 at T=100; and a noncommuting rescue regime was found where both instantaneous edges were positive (0.203 and 0.134), yet periodic gamma=-2.809 while the constant-mean baseline was unstable at +0.0683. This is a clear mechanism-level win, though it is not evidence of improved neural-network training.",
  "metrics": {
    "baseline": "Constant-mean matrix at damping 1.4, T=1.0: gamma=+0.0683; norm after 20 periods=2.4362",
    "idea": "Periodic noncommuting matrix at damping 1.4, T=1.0: gamma=-2.8086; norm after 20 periods=1.47e-24; instantaneous phase edges remain positive"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 floquet_mvp.py",
  "files": [
    "floquet_mvp.py",
    "floquet_results.json",
    "run_output.txt",
    "search_pairs.py"
  ],
  "limitations": "Only the core linearized dynamics were tested; no residual MLP, RNN, CIFAR-10 training, optimizer schedule, validation accuracy, FLOPs, or runtime comparison was performed. The rescue matrices were selected by a seeded random search, and the piecewise-constant two-phase forcing is an idealized toy setting."
}