# Эксперимент: KS-Adaptive Graph Halting (#420)

{
  "worked": false,
  "confidence": 9,
  "verdict": "Built and ran a reproducible KS certificate sweep, stability-boundary sweep, and synthetic SBM message-passing halting experiment. The geometric ratio prediction and the decay/critical/growth boundary were exactly observed, but the literal stopping-depth formula underestimated the exact summed-tail depth by 1.17–1.59x because it omits the geometric-series prefactor. On the GNN task, adaptive halting matched fixed-depth accuracy (1.00 versus 1.00) but used 1.41x the message-work, so the proposed speedup was not observed.",
  "metrics": {
    "baseline": "Fixed depth 4: test accuracy 1.000, normalized test work 1.000",
    "idea": "KS adaptive: test accuracy 1.000, mean depth 5.644, normalized work 1.411",
    "toy_math": "Tail ratios exactly matched kappa^(1/3); observed certificate depths were 7, 12, 19, 36, 76, 181, 642 versus predicted 6, 10, 17, 29, 58, 127, 404; multipliers across gamma*Lambda=0.70..1.30 exactly matched the parameter and crossed at 1.0"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 ks_adaptive_experiment.py",
  "files": [
    "ks_adaptive_experiment.py",
    "ks_results.json"
  ],
  "limitations": "Only a synthetic 600-node SBM was tested; no Reddit/ogbn-arxiv data, sampled-neighborhood implementation, Ponder baseline, wall-clock benchmark, or GPU execution was evaluated. The toy recurrence verifies the claimed scaling but does not establish the paper's bound constants for a trained GNN."
}