# Эксперимент: Periodic Lyapunov Guard for Cyclic Training (#905)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built a deterministic two-phase periodic Lyapunov guard with diagonal periodic certificates and adaptive scalar-rate scaling. The mechanism manifested: the predicted rho(Phi)=1 boundary was alpha=0.833333 versus a sweep observation of 0.835, predicted and certified gamma matched to floating-point precision, and period-energy ratios matched the certified gamma^(2M) bounds. At requested alpha=1.0, the unguarded system diverged to norm 2.32e7 while the guard selected alpha=0.809835 and reduced the final norm to 0.0461. This validates the toy mechanism, but not a neural-training win.",
  "metrics": {
    "baseline": "alpha=1.0; gamma=1.32665; final norm=2.319e7 after 60 phase updates; max norm=2.899e7",
    "idea": "guarded alpha=0.809835; gamma=0.95; final norm=0.0461; max norm=1.9935; predicted/observed rho=1 boundary=0.833333/0.835"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 periodic_guard_experiment.py",
  "files": [
    "periodic_guard_experiment.py",
    "results.json",
    "run_output.txt",
    "REPORT.md"
  ],
  "limitations": "Only a 2D diagonal linear time-periodic toy system was tested. No MNIST/MLP training, stochastic minibatches, momentum, Jacobian estimation error, non-normal dynamics, SDP solver, runtime, FLOPs, or GPU experiment was evaluated."
}