# Эксперимент: Hybrid-Zonotope Reachability Loss for Neural Closed Loops (#1037)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a readable hybrid-zonotope and interval-reachability MVP. Three mechanism predictions were confirmed: the radius recurrence had maximum absolute error 0, terminal radius scaled linearly with disturbance, and the constraint threshold matched gamma*=0.0940001 with violation immediately above it; the contraction transition matched |lambda|=1. The reachability objective did not produce a clear training win over the nominal baseline, so the mechanism is validated but practical benefit is unproven.",
  "metrics": {
    "baseline": "k=1.000 across the sweep; terminal certificate violations at gamma=[0,0.12,0.30,0.60] were [0,0,0,0.15]. Nominal loss 0.6400.",
    "idea": "k=[0.9003,0.9003,1.0031,0.9997]; terminal violations [0,0,0,0.1502]. Recurrence max error 0; predicted and observed gamma boundary 0.0940001; contraction ratios for lambda=[0.8,0.99,1.0,1.01,1.2] were [0.1074,0.9044,1.0,1.1046,6.1917]."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 reachability_mvp.py > results.json",
  "files": [
    "reachability_mvp.py",
    "results.json"
  ],
  "limitations": "The experiment is scalar rather than a full double integrator, uses interval zonotopes without active hybrid coupling constraints, and trains an analytic scalar gain rather than a ReLU MLP. No multidimensional LP relaxation, wall-clock, or CUDA comparison was tested."
}