# Эксперимент: Pullback random-attractor monitor (#1104)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a pullback random-attractor monitor with shared-noise replay, Euler and semi-implicit oscillator updates, Lyapunov/spectral-radius checks, stability sweeps, and an independent-noise control. The mechanism manifested: Euler changed from contraction to divergence at the analytically predicted h≈0.20 boundary, measured pullback slopes closely matched log(rho)/h, and shared noise contracted to 0.0076 versus 0.5724 with independent noise. The 10%-diameter time prediction was accurate for stronger damping, though weaker cases were limited by finite horizon and transients.",
  "metrics": {
    "baseline": "Euler measured slopes at h=0.10, 0.18, 0.20, 0.22, 0.40 were -0.05058, -0.01002, -0.00009, +0.01004, +0.09618; it diverged above the predicted h=0.20 boundary. Independent-noise final diameter was 0.5724.",
    "idea": "Semi-implicit remained contracting with slopes -0.09906, -0.09825, -0.09805, -0.09786, -0.09621 across the same step sizes. Shared-noise final diameter was 0.00759. For Euler damping 0.10, 0.20, 0.40, 0.80, measured pullback slopes were -0.02515, -0.07576, -0.17854, -0.39185 versus predicted -0.02503, -0.07528, -0.17655, -0.38221."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 pullback_monitor.py",
  "files": [
    "pullback_monitor.py",
    "results.json",
    "REPORT.md",
    "run_output.txt",
    "run_output2.txt",
    "run_output3.txt"
  ],
  "limitations": "Only a two-dimensional linear noisy oscillator was tested, not a learned stochastic RNN, SSM, world model, or training regularizer. The semi-implicit update is oscillator-specific; attractor-set geometry and long-run generalization were not evaluated."
}