# Эксперимент: Response-from-Hessian Regularizer (#890)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built and ran a differentiable Response-from-Hessian Regularizer MVP with autodiff Hessian-vector products, curvature penalties, susceptibility sweeps, and stability checks. The mechanism manifested clearly: HVP error was 1.1e-16, susceptibility followed the predicted 1/lambda law with log-log slope -1.000 and zero relative error, and explicit-Euler instability began at the predicted gamma=2 boundary. Regularization moved a fitted negative curvature from -0.20 to -0.021 while leaving a deliberately soft positive mode at 0.020 unchanged, indicating selective stabilization rather than indiscriminate stiffening.",
  "metrics": {
    "baseline": "Negative-curvature fit: final curvature -0.200000, MSE 4.0e-16; soft-mode fit: 0.0200001.",
    "idea": "Negative-curvature fit: final curvature -0.021333, MSE 0.0319; soft-mode fit: 0.0200007. Inverse-curvature sweep observed [50,25,12.5,6.25,3.125,1.5625] for lambda [0.02,0.04,0.08,0.16,0.32,0.64], exactly matching 1/lambda."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 response_hessian_experiment.py",
  "files": [
    "response_hessian_experiment.py",
    "results.json"
  ],
  "limitations": "This is a small synthetic diagonal/quartic functional rather than a learned 16^3 or 32^3 cDFT model. It does not test full approximate minimization, conserved-number projection, Lanczos extremal eigenvalue estimation, response re-minimization, wall-clock overhead, or generalization across external potentials."
}