# Эксперимент: Hamiltonian Horizon-Critical Optimizer (#1322)

{
  "worked": false,
  "confidence": 9,
  "verdict": "Built the Hamiltonian feedback implementation, conjugate-point diagnostic, quadratic optimizer comparison, and digits MLP mini-test in experiment.py. The core math claim fails as written: det([[a,-b²/r],[-q,-a]]) = -a²-b²q/r, not b²q/r-a², so q>=0 cannot produce the stated elliptic regime. A hyperbolic D(T)=0 crossing was numerically observed near the predicted 0.17698 horizon, but both fixed-horizon and nominally adaptive feedback diverged on the quadratic; the MLP gain result is not evidence of a fair optimizer win because it used a fixed common 4.73x gradient scaling.",
  "metrics": {
    "baseline": "Digits SGD: final train loss 0.7375, test accuracy 0.9000; quadratic final loss 1.37e-9, no divergence.",
    "idea": "Digits feedback-scaled SGD: final train loss 0.1820, test accuracy 0.9622, but used fixed multiplier 4.729; quadratic fixed horizon diverged (NaN), adaptive horizon also diverged (NaN), with adaptive min_D 0.0858.",
    "math": "For a=-1,b=1,q=1,r=0.2, stated determinant=4.0 versus actual determinant=-6.0; predicted hyperbolic conjugate T=0.17698 and numerical grid crossing=0.176."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json"
  ],
  "limitations": "Only a tiny diagonal quadratic and sklearn digits MLP were tested; no Hessian-vector/Lanczos curvature estimates, Adam comparison, matched-FLOP or matched-update-norm evaluation, horizon sweep, repeated seeds, or corrected Hamiltonian sign convention was tested."
}