# Эксперимент: Projected Absolute-Residual Compensation for Neural State-Space Models (#591)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built and numerically verified a deterministic projected absolute-residual compensation toy in verify.py. Absolute residual scaling, incremental cancellation, projection residual scaling, and the stability boundary all matched their predictions; tracking error improved from 0.272727 to 0.054545 with compensation. Projected and unprojected compensation were identical here because the toy was one-dimensional and fully covered by the learned mismatch subspace.",
  "metrics": {
    "baseline": "Mean absolute steady-state tracking error 0.272727; final error 0.272727",
    "idea": "Mean absolute steady-state tracking error 0.054545; final error 0.054545; absolute residual slope 1.2500000000000002 vs predicted 1.25; incremental residual max 0; projection max error 1.0e-10; stability boundary observed 2.0 vs predicted 2.0"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 verify.py",
  "files": [
    "verify.py",
    "results.json",
    "run_output.txt"
  ],
  "limitations": "This is an exact linear toy, not a trained GRU or S4 model. It does not test learned ridge heads, finite-sample estimation, measurement noise, nonlinear dead-zone or quantization effects, online adaptation, multidimensional G_d pseudoinverse behavior, or a meaningful projected-versus-unprojected controller distinction."
}