# Эксперимент: Spectral-gap adaptive halting (#1059)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built a readable MVP for spectral-gap prediction and adaptive halting in the fold normal form. The predicted epsilon and b exponents matched closely (+0.500 for the gap and about -0.489 for passage time versus predicted -0.500), while the calibrated product Pi averaged 3.189 versus pi=3.142, a 1.51% error. The controller did not yield a speedup: fixed and residual methods averaged 449 steps, whereas the strict spectral controller hit its 50,000-step cap, so a practical transformer inference win was not demonstrated.",
  "metrics": {
    "baseline": "Fixed/residual stable-branch halting: mean 449 steps over 20 tasks.",
    "idea": "Spectral controller: mean 50,000 steps; no speedup. Mechanism checks: gap-epsilon exponent 0.500, passage-epsilon exponent -0.489, gap-b exponent 0.500, passage-b exponent -0.490, Pi mean 3.189 with 1.51% relative error."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json",
    "REPORT.md"
  ],
  "limitations": "This is a scalar fold-normal-form experiment, not a trained looped transformer. It does not test transformer task accuracy, GPU wall-clock cost, autodiff JVP overhead, learned power-iteration error, or tuned controller thresholds; the practical adaptive-halting benefit remains unverified and was absent in this toy controller."
}