# Эксперимент: Self-Correcting Euler Horizon Rule (#376)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built a reproducible scalar contracting-ODE MVP with Euler error sweeps, stability-boundary verification, peak-time scaling, decay-rate fitting, and a contraction-aware controller. The three mechanism predictions manifested: the stability transition was observed at lambda*h=2.00, peak time scaled as 1/lambda with 9.7% deviation from the analytic estimate, and post-peak log-error slopes matched -lambda within 0.91%. The controller used 33 versus 40 steps but had worse terminal error (3.26e-4 versus 2.03e-4), so this is evidence for the mechanism, not an end-to-end accuracy or speed win.",
  "metrics": {
    "baseline": "Fixed Euler, lambda=1, T=8, h=0.2: 40 steps, terminal absolute error 2.0254e-4.",
    "idea": "Contraction-capped two-half-step controller, alpha=1.8: 33 steps, terminal absolute error 3.2625e-4; stability boundary observed z=2.00, peak lambda*t=0.9278 versus predicted 0.8456, decay slope relative error 0.57%-0.91%."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json",
    "REPORT.md"
  ],
  "limitations": "Only the scalar linear contracting surrogate was tested; no nonlinear MLP neural ODE, CIFAR-10 latent diffusion, Jacobian/secant-rate estimation, wall-clock benchmark, adaptive horizon extension, or GPU experiment was performed."
}