# Эксперимент: Orbital-Stable Dancing RNN (#1113)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built an orbital phase RNN and numerically verified the mechanism in a two-node directed-coupling reduction. The neutral global-shift mode was exact (maximum ||J1||=0), the measured stability transition was phi=pi/2 exactly as predicted, and finite-Euler perturbation slopes matched the analytical transverse eigenvalue with maximum error 0.0026. The phase RNN did not improve the toy classification task: tanh RNN accuracy was 0.832 versus 0.535 for the phase model, so the stability mechanism manifested but no task-level win was observed.",
  "metrics": {
    "baseline": "Tanh RNN: accuracy=0.8320, loss=0.3830 after 220 steps.",
    "idea": "Phase RNN: accuracy=0.5352, loss=0.6920 after 220 steps. Math: neutral-mode error=0; predicted/measured boundary=1.570796/1.570796 rad; transverse decay slope errors=0.00024-0.00257 for non-boundary points."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json"
  ],
  "limitations": "Only the analytically tractable two-node Jacobian was swept; the full sequential-MNIST or noisy-sine benchmark, learned couplings, amplitude dynamics, basin-size measurements, FLOP-normalized comparisons, and broad kappa/timestep sweeps were not tested."
}