# Эксперимент: Reciprocal-Lattice Gauge-Covariant Bloch Network (#910)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built a reciprocal-lattice gauge-aware Bloch MLP wrapper and numerical verification suite. For shifts m=-3..3, phase reconstruction error was 3.43e-16 and operator covariance residual was 6.60e-15, matching machine-precision predictions; the naive untransformed alias mismatch was exactly 1.4142 as predicted. In the toy MLP, mean nonzero-shift RMSE fell from 0.8810 for raw-q conditioning to 0.02344 with canonicalization plus the exact gauge phase, demonstrating the promised mechanism.",
  "metrics": {
    "baseline": "Raw-q MLP: nonzero reciprocal-shift mean RMSE 0.88098; m=0 RMSE 0.02692.",
    "idea": "Canonicalized q with exact gauge transformation: nonzero reciprocal-shift mean RMSE 0.02344; identical 0.02344 RMSE across m=-3..3.",
    "math_check": "Maximum phase identity error 3.43e-16; maximum operator covariance relative error 6.60e-15; predicted naive alias RMS sqrt(2)=1.41421, observed 1.41421."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json"
  ],
  "limitations": "This is a small synthetic 1D experiment with a hand-designed periodic target and an MLP, not a full material-profile dataset or Fourier neural operator. It tests canonicalization and exact gauge wrapping, but not the stronger covariance-loss training variant, physical band-structure accuracy, FLOPs, or large-scale generalization."
}