# Стенд-проверка (stage-2) · промт оператора:

(универсальный)

Ответ агента:

{
  "worked": false,
  "confidence": 9,
  "verdict": "Implemented the harmonic-coordinate neural PDE ansatz and evaluated it on a structurally matched custom Poisson/harmonic-square track with 8 paired seeds. The idea was significantly worse: baseline MSE 0.00103270 versus idea MSE 0.00344777, paired delta +0.00241507, permutation p=0.03935, with only 1 of 8 paired wins. The trained-model mechanism measurements were finite but did not yield a useful transfer benefit.",
  "metrics": {
    "baseline": "best lr=0.01; 8-seed test MSE mean 0.0010326977680961136, std 0.0006915660191288916",
    "idea": "best shared lr=0.01; 8-seed test MSE mean 0.0034477697263355367, std 0.003057254396847933",
    "paired_delta_mean": 0.002415071958239423,
    "permutation_p_value": 0.03935,
    "idea_wins": 1,
    "n_pairs": 8
  },
  "bench_report": {
    "bench_version": 1,
    "track": "poisson_harmonic_square",
    "model": "mlp_tiny",
    "metric_direction": "lower is better",
    "n_seeds": 8,
    "baseline": {
      "best_cfg": {
        "lr": 0.01
      },
      "sweep": [
        {
          "cfg": {
            "lr": 0.001
          },
          "mean": 0.11668895371258259
        },
        {
          "cfg": {
            "lr": 0.003
          },
          "mean": 0.003221849736291915
        },
        {
          "cfg": {
            "lr": 0.01
          },
          "mean": 0.0012928899232065305
        }
      ],
      "full": {
        "mean": 0.0010326977680961136,
        "std": 0.0006915660191288916,
        "per_seed": [
          0.000628755777142942,
          0.002497267909348011,
          0.0017118228133767843,
          0.00033371319295838475,
          0.00040585428359918296,
          0.0008253304404206574,
          0.0006939232698641717,
          0.0011649144580587745
        ],
        "n": 8
      }
    },
    "idea": {
      "mean": 0.0034477697263355367,
      "std": 0.003057254396847933,
      "per_seed": [
        0.0011874843621626496,
        0.009428461082279682,
        0.0006923572509549558,
        0.002130375476554036,
        0.0021641517523676157,
        0.007692142855376005,
        0.003011035965755582,
        0.001276149065233767
      ],
      "n": 8
    },
    "comparison": {
      "delta_mean": 0.002415071958239423,
      "idea_wins": 1,
      "n_pairs": 8,
      "per_seed_diffs": [
        0.0005587285850197077,
        0.006931193172931671,
        -0.0010194655624218285,
        0.0017966622835956514,
        0.0017582974687684327,
        0.006866812414955348,
        0.00231711269589141,
        0.00011123460717499256
      ],
      "p_value": 0.03935,
      "mde": 0.002480160072007651,
      "mde_rel_pct": 240.1632063735439,
      "verdict": "idea worse (significant)",
      "system_worked": false
    },
    "mechanism_signature": {
      "trained_model": true,
      "idea_q_constraint_rms": 0.1779780387878418,
      "idea_observed_mean_abs_laplacian": 0.0778733491897583,
      "prediction": "lower coordinate defect should accompany lower Laplacian residual",
      "baseline_observed_model": true,
      "confirmed": true
    },
    "idea_sweep": [
      {
        "cfg": {
          "lr": 0.001
        },
        "result": {
          "mean": 0.1455571036785841,
          "std": 0.007538120960623546
        }
      },
      {
        "cfg": {
          "lr": 0.003
        },
        "result": {
          "mean": 0.0774294026196003,
          "std": 0.013261691418440134
        }
      },
      {
        "cfg": {
          "lr": 0.01
        },
        "result": {
          "mean": 0.0034477697263355367,
          "std": 0.003057254396847933
        }
      }
    ],
    "custom_track": {
      "name": "poisson_harmonic_square",
      "file": "custom_pde_track.py",
      "domain": "pde"
    }
  },
  "how_to_run": "cd /home/maxwelhelp/all/math2nn/experiments/exp892_harmonic-coordinate-neural-pde-ansatz && /home/maxwelhelp/main/bin/python3 stage2_bench.py",
  "files": [
    "custom_pde_track.py",
    "stage2_bench.py",
    "bench_report.json"
  ],
  "limitations": "Only one custom manufactured harmonic PDE family was tested; no disk geometry, nonzero Poisson forcing, Fourier-feature baseline, q pretraining/freezing, larger collocation budgets, or equal-FLOP parameter-normalized study was run.",
  "system_verdict": "partial",
  "practical_verdict": "harms",
  "mechanism_ok": 1,
  "system_judged": true
}