# Эксперимент: Fundamental-Cycle Compatibility Basis (#1147)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a spanning-forest fundamental-cycle basis for bipartite support graphs, with correctly oriented signed cycle coefficients, cycle-rank verification, exhaustive simple-cycle comparison, and compatible/perturbed edge-field checks. Compatible node-potential fields produced near-zero residuals for both basis and exhaustive cycles (maximum about 2e-15), while the basis used exactly the cycle rank and was 68x–2520x faster than exhaustive evaluation in the tested graphs. This validates the mathematical and computational claim, but not downstream neural-network training gains.",
  "metrics": {
    "baseline": "Exhaustive simple-cycle evaluation: 110–5000 cycles; wall time 0.00290–0.24937 sec per 10 evaluations; perturbed-field 95th-percentile residual 0.472–0.706.",
    "idea": "Fundamental basis: 10–41 constraints equal to |E|-|V|+C; wall time 0.000043–0.000175 sec per 10 evaluations; speedups 68x–2520x; compatible-field maximum residual 2.2e-16–5.6e-16."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py"
  ],
  "limitations": "No neural conditional models, optimization, held-out data, GPU execution, Huber loss, or task-loss comparison was tested. Exhaustive cycle enumeration is capped at 5000 cycles for dense supports, and timing is a small NumPy regularizer-cost proxy rather than an end-to-end training benchmark."
}