# Эксперимент: Harmonic Global Latent Channels (#1193)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a weighted discrete harmonic decomposition and a four-layer ring message-passing model with an explicit harmonic latent head. The numerical check verified the harmonic constraints, weighted orthonormality, gauge projection, reconstruction, and period consistency to approximately 1e-16. On the toy global-circulation task, the harmonic head improved field RMSE, period RMSE, and far-edge RMSE, though it used more parameters and the task favors global circulation.",
  "metrics": {
    "baseline": "field RMSE 0.18425; period RMSE 0.87976; far-edge RMSE 0.20344; 2497 parameters",
    "idea": "field RMSE 0.02108; period RMSE 0.10729; far-edge RMSE 0.01881; 3122 parameters",
    "math_check": "closed residual 0.0; coclosed residual 1.04e-16; weighted orthonormality 1.0; gauge residual 6.66e-16; reconstruction residual 2.22e-16; period-basis residual 0.0"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json"
  ],
  "limitations": "Only a 24-edge weighted cycle with one harmonic mode was tested. No 2D mesh, mesh-refinement transfer, equal-parameter matching, FLOP or speed measurement, period-supervised loss, or multiple random seeds were tested. The harmonic model has 3122 parameters versus 2497 for the baseline."
}