# Эксперимент: Decision-Oriented Optimum Preservation (#1029)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a differentiable surrogate with unrolled projected inner optimization and decision loss, plus fixed-seed math sweeps. The quadratic inner-loop stability boundary was confirmed at rho=2/H: predicted 0.5405, with contraction at 0.50 and divergence at 0.55. Objective perturbations produced extra minima as epsilon increased, and decision-aware training reduced optimum displacement from 0.40495 to 0.01505 (96.3%) with nearly unchanged data MSE. The mechanism manifested, but the stronger claim about removing extra minima was not established because the simple multistart gradient-flow count produced flat-region artifacts.",
  "metrics": {
    "baseline": "MSE-only: optimum u=0.160, displacement=0.40495, objective=0.01587, data MSE=0.07961, grid minima=1; multistart endpoint count=19 but unreliable.",
    "idea": "Decision-aware: optimum u=0.580, displacement=0.01505, objective=0.01005, data MSE=0.08007, grid minima=1; multistart endpoint count=14 but unreliable. Stability: predicted boundary rho=0.54054, observed transition between 0.50 stable and 0.55 divergent. Perturbation sweep: 1 minimum through epsilon=0.01, 2 at 0.02, 3 at 0.04."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json",
    "REPORT.md"
  ],
  "limitations": "Only a one-dimensional synthetic steady-state surrogate was tested; no neural ODE, constraints beyond box projection, noisy trajectories, multiple decision dimensions, computational/FLOP comparison, or robust Hessian-filtered/local-root basin counting was performed. The simple multistart gradient-flow endpoint counts should not be interpreted as distinct local-minimum counts."
}