# Эксперимент: Detailed-Balance Graph Transport Layer (#1069)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a NumPy detailed-balance master-equation transport implementation and a learnable PyTorch transport layer. The mechanism manifested: mass conservation error stayed below 4.4e-16, transport remained nonnegative at 0.99x and 1.01x the sufficient bound and became negative at 100x, while the finite-difference dissipation estimate matched the predicted value within 0.053% at the smallest tested step. Conductance scaling was exact across 0.25x–4x; the tiny classification test tied the baseline at 100% accuracy, so no accuracy win was observed.",
  "metrics": {
    "baseline": "Unconstrained residual graph update: 100.0% classification accuracy; minimum activation 0.0401 under the tested large residual multiplier.",
    "idea": "Detailed-balance transport: 100.0% classification accuracy; minimum mass 0.00375 using 0.9x the positivity bound; total-mass error <4.4e-16; dissipation relative error 0.000525 at dt=1e-5 and 0.0514 at dt=1e-3; conductance-scaling relative error 0.0."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py",
  "files": [
    "db_transport.py",
    "run_experiment.py",
    "results.json"
  ],
  "limitations": "Only a synthetic 80-node classification utility test was run, with no training, Cora benchmark, implicit solver, FLOP or parameter matching, calibration, or multi-seed statistical evaluation. The positivity sweep sampled factors up to 1000 and established failure at 100x, but did not bracket the exact first-failure threshold."
}