# Эксперимент: Capacity-Preserving Transient Message Passing (#539)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Implemented distance-weighted Markov diffusion, residual message passing utilities, exact shell Dirichlet-capacity solves, and a synthetic comparison in run_experiment.py. The mechanism manifested: 1D capacity fit was -1.000 versus the predicted -1, 2D capacity was strongly affine in 1/log(R) (R²=0.985), 3D capacity remained nonzero (late/early=0.878), and influence norm decayed with exponent -0.249 versus the predicted -0.25. The weighted layer gave a small fixed-readout accuracy improvement (0.911 vs 0.906), but this is not evidence of a robust trained-GNN win.",
  "metrics": {
    "baseline": "Unweighted residual diffusion: best accuracy 0.9056 at depth 7; depth-20 accuracy 0.9000; variance 0.4231.",
    "idea": "Distance-weighted residual diffusion: best accuracy 0.9111 at depth 7; depth-20 accuracy 0.9000; variance 0.4536. Math checks: 1D exponent -1.000, 2D capacity-vs-1/log(R) R² 0.9845, 3D late/early capacity 0.8776, influence exponent -0.2486."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py",
  "files": [
    "run_experiment.py",
    "capacity_diffusion.py",
    "results.json",
    "run_output.txt"
  ],
  "limitations": "The task comparison uses a fixed coordinate readout rather than training matched-parameter GNNs. Capacity was evaluated on regular lattice shells with unit edge distances, not hyperbolic Delaunay graphs; no citation or molecular benchmark, GPU/CPU speed study, learned capacity regularizer, curvature sweep, or statistical repeats were run."
}