# Эксперимент: Normal-Cone Certified Priority Weighting (#874)

{
  "worked": true,
  "confidence": 7,
  "verdict": "Built a readable LP-based normal-cone certificate controller and deterministic convex priority-training toy in experiment.py. All three quantitative mechanism predictions were confirmed: inverse-lambda scaling had maximum relative error 1.0e-9, the epsilon=1 feasibility transition was correct at every tested point, and slack-margin scaling had zero absolute error. In the conflicting training toy, the certificate matched equal weighting rather than improving it; fixed 100:10:1 achieved zero violation but at much higher performance loss, so no practical win was demonstrated.",
  "metrics": {
    "baseline": "Equal weights: final J=0.5503883, total violation=0.0657977, tier-1 violation=0.0313366. Fixed 100:10:1: J=14.2530128, total violation=0, tier-1 violation=0.",
    "idea": "Certificate controller: final J=0.5503883, total violation=0.0657977, tier-1 violation=0.0313366; identical to equal weighting. Mechanism checks: lambda-scaling maximum relative error=1.0e-9, feasibility transition 5/5 correct, slack-margin maximum absolute error=0."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json",
    "run_output.txt",
    "run_output2.txt"
  ],
  "limitations": "This is a tiny hand-designed convex last-layer problem, not a neural network or minibatch experiment. No GradNorm comparison, explicit constraint multipliers, validation hyperparameter tuning, FLOP/speed measurement, stochastic training, or larger multi-dimensional hinge geometry was tested. The positive result supports the LP mechanism, not a broad empirical superiority claim."
}