# Эксперимент: Centroid-Halving Preference Queries (#1030)

{
  "worked": false,
  "confidence": 10,
  "verdict": "Built a numerical centroid-cut and ranking-query simulator in centroid_halving.py, plus focused verification in verify_centroid_halving.py. The valid centroid-passing halfspace check matched Grünbaum’s prediction: observed minimum retention 0.443 versus predicted lower bound 1/e = 0.368. However, the proposed zero-threshold preference cut is not generally a centroid cut: for K = [0,1]^2 intersect {x >= y}, the centroid is approximately (0.667, 0.333), while the opposite preference halfspace has zero volume; query experiments consequently showed centroid querying stalling rather than geometric progress. The claimed mechanism therefore did not manifest as stated.",
  "metrics": {
    "baseline": "Exact/sampled comparison was unstable and capped at 100 queries; random querying averaged 3.0, 10.6, 58.1, and 100.0 queries for n=3,4,5,6 respectively.",
    "idea": "Valid centroid-cut retention: predicted >=0.3679, observed minimum 0.4431 and mean 0.5000. Proposed ranking controller averaged 50.1, 87.9, 100.0, and 87.9 queries for n=3,4,5,6, often hitting the cap rather than showing geometric decay."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 verify_centroid_halving.py && /home/maxwelhelp/main/bin/python3 centroid_halving.py",
  "files": [
    "centroid_halving.py",
    "verify_centroid_halving.py",
    "results.json",
    "verification_results.json"
  ],
  "limitations": "The neural reward-model integration, adversarial 5%/10% corruption experiments, hit-and-run sampling, Kendall tau, and listwise loss were not tested. The continuous sampler uses finite Monte Carlo particles and the exact query comparison is limited to small n and a query cap."
}