# Эксперимент: Energy-Riesz checkpoint selector (#941)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built a readable conforming Poisson Energy-Riesz checkpoint selector in energy_riesz_experiment.py. The mechanism manifested strongly: full-space identity relative error was 1.49e-15, every auxiliary score was a valid lower bound, nested-space monotonicity had zero violations, and mean oracle gaps decreased from 0.8675 to 0.0741 as auxiliary size increased. However, this archive did not demonstrate a practical selection win over raw loss: raw loss selected error 4.3881, while Riesz selections ranged from 4.3881 to 4.5623.",
  "metrics": {
    "baseline": "Raw residual-loss checkpoint: oracle energy error 4.3881; selected checkpoint 99.",
    "idea": "Riesz selected oracle errors by auxiliary size 3,7,15,31,63: 4.5623, 4.3881, 4.3881, 4.5623, 4.5623. Spearman rank correlation improved 0.9904 -> 0.9994; mean relative gap to oracle improved 0.8675 -> 0.0741; full-space identity error 1.49e-15; 500 solves took 0.263 s."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 energy_riesz_experiment.py",
  "files": [
    "energy_riesz_experiment.py",
    "results.json",
    "run_output.txt",
    "REPORT.md"
  ],
  "limitations": "This is a 1D finite-dimensional manufactured Poisson test rather than a 2D neural PINN. The archive is synthetic and mostly monotonically improving, so it does not stress checkpoint mis-selection under noisy or non-monotone training. No GPU, wall-clock training comparison, quadrature error study, or truly independently assembled neural network checkpoints was tested."
}