# Эксперимент: Pisot-Orbit Deterministic JL Layer (#882)

{
  "worked": false,
  "confidence": 9,
  "verdict": "Built a deterministic Pisot-orbit JL layer using the golden-ratio beta transformation, empirical centering/scaling, scalar norm calibration, seed/gap search, reproducibility hashing, and Gaussian-JL comparison. Correlations decayed strongly after a short transient and calibration search improved worst pairwise distortion from 1.891 to 0.522, but the global correlation fit was non-decaying (rho≈1.0001) and norm-estimator variance scaled with slope -0.72 rather than the predicted -1.0. Under the required mechanism criterion, this is not a validated win.",
  "metrics": {
    "baseline": "Gaussian JL, d=24,m=16: max pairwise distortion 2.021, mean 0.288.",
    "idea": "Fixed Pisot orbit: max pairwise distortion 1.891, mean 0.396; searched seed/gap: max 0.522, mean 0.189 at gap=2; global correlation fit rho=1.0001, post-transient rho=0.898; variance-vs-m slope=-0.724."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 compare.py",
  "files": [
    "experiment.py",
    "compare.py",
    "results.json"
  ],
  "limitations": "Only a small synthetic Gaussian-vector experiment was tested; no CIFAR, retrieval, classifier, router, learned post-scale, sparse-JL comparison, GPU benchmark, exact finite-field implementation, or proof of the stated spectral-gap bounds was performed. The calibration search uses the same small calibration set for selection and evaluation, so its distortion improvement may overfit."
}