# Эксперимент: Entropy-Symmetrized Neural Flux (#129)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Implemented the entropy-symmetrized flux MVP in experiment.py using symmetric S, Cholesky-parameterized H=LL^T+epsilon I, and Gauss-Legendre path integration. The similarity identity held numerically with zero observed imaginary eigenvalue parts through condition number 1e12, while antisymmetric contamination produced complex spectra at rates close to analytic predictions. The constrained model also achieved lower toy held-out flux MSE than the direct MLP, but no PDE rollout or long-horizon stability win was established.",
  "metrics": {
    "baseline": "Direct MLP: 722 parameters, held-out flux MSE 9.2103e-5, max sampled Jacobian imaginary part 0.0",
    "idea": "Entropy-symmetrized flux: 585 parameters, held-out flux MSE 3.2301e-5, max sampled Jacobian imaginary part 0.0; similarity eigenvalue error 1.6e-15 at condition 1 and 9.3e-6 at 1e12"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json",
    "REPORT.md"
  ],
  "limitations": "Only a small two-state flux-regression experiment was tested. Finite-volume integration, long-horizon rollouts, CFL behavior, Riemann problems, multidimensional directions, and repeated-seed statistical significance were not evaluated."
}