# Эксперимент: Quadratic center-manifold bottleneck (#988)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built an explicit ordered-Kronecker quadratic manifold decoder with analytic tangent evaluation and reproducible numerical checks. The mechanism manifested: central differences of the quadratic map were exact to floating-point error, the quadratic tangent contribution scaled with coefficient slope 1.00, invariance residual scaled as epsilon^2 with observed slope 2.00, and linear-decoder curvature error scaled as curvature^2 with observed slope 2.00. On translated Gaussian-profile data, the quadratic decoder reduced test MSE from 0.0443181 to 0.0229951, although it used more parameters.",
  "metrics": {
    "baseline": "Linear decoder: test MSE 0.0443181, train MSE 0.0434609, 96 parameters",
    "idea": "Quadratic decoder: test MSE 0.0229951, train MSE 0.0229754, 224 parameters; exact analytic invariance residual 0.0"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json",
    "results_final.json",
    "run.txt"
  ],
  "limitations": "The experiment used fixed known latent coordinates and closed-form regression rather than training an encoder, latent dynamics, or full invariance-regularized autoencoder. It did not test long-horizon rollouts, controls, held-out forcing frequencies, equal-parameter comparisons, or a learned full-state vector field."
}