# Эксперимент: Reachable-Set Risk Head for Early-Warning Rollouts (#566)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built and numerically verified the reachable-set risk head for Gaussian linearized dynamics. The predicted monotone margin response, q=0.5 transition at zero margin, stable-versus-unstable covariance behavior, and increasing horizon union risk all matched quantitatively. In the 2-D rollout experiment, reachable risk had recall 0.710 versus 0.733 for a fair endpoint baseline at 5% false-warning rate, but its ECE was 0.117 versus 0.081; therefore the mechanism manifested, but no overall warning-quality win was observed.",
  "metrics": {
    "baseline": "Fixed-variance endpoint Gaussian warning: recall@5% FPR=0.733, ECE=0.0812",
    "idea": "Reachable-set Gaussian union risk: recall@5% FPR=0.710, ECE=0.1169; mechanism checks: q(m=0)=0.5 observed, stable covariance limit error=3.9e-14, horizon-5 union risk=0.40951 observed"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py",
  "files": [
    "reachable_risk.py",
    "run_experiment.py",
    "results.json",
    "REPORT.md"
  ],
  "limitations": "No learned GRU, calibration loss, deep ensemble, nonlinear dynamics, multiple half-spaces, or held-out calibration procedure was tested. The toy dynamics were linear and the reachable score used known covariance and independent half-space/horizon risk multiplication."
}