1{
  2  "bench_version": 1,
  3  "track": "poisson_harmonic_square",
  4  "model": "mlp_tiny",
  5  "metric_direction": "lower is better",
  6  "n_seeds": 8,
  7  "baseline": {
  8    "best_cfg": {
  9      "lr": 0.01
 10    },
 11    "sweep": [
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 13        "cfg": {
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 15        },
 16        "mean": 0.11668895371258259
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 18      {
 19        "cfg": {
 20          "lr": 0.003
 21        },
 22        "mean": 0.003221849736291915
 23      },
 24      {
 25        "cfg": {
 26          "lr": 0.01
 27        },
 28        "mean": 0.0012928899232065305
 29      }
 30    ],
 31    "full": {
 32      "mean": 0.0010326977680961136,
 33      "std": 0.0006915660191288916,
 34      "per_seed": [
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 36        0.002497267909348011,
 37        0.0017118228133767843,
 38        0.00033371319295838475,
 39        0.00040585428359918296,
 40        0.0008253304404206574,
 41        0.0006939232698641717,
 42        0.0011649144580587745
 43      ],
 44      "n": 8
 45    }
 46  },
 47  "idea": {
 48    "mean": 0.0034477697263355367,
 49    "std": 0.003057254396847933,
 50    "per_seed": [
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 52      0.009428461082279682,
 53      0.0006923572509549558,
 54      0.002130375476554036,
 55      0.0021641517523676157,
 56      0.007692142855376005,
 57      0.003011035965755582,
 58      0.001276149065233767
 59    ],
 60    "n": 8
 61  },
 62  "comparison": {
 63    "delta_mean": 0.002415071958239423,
 64    "idea_wins": 1,
 65    "n_pairs": 8,
 66    "per_seed_diffs": [
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 68      0.006931193172931671,
 69      -0.0010194655624218285,
 70      0.0017966622835956514,
 71      0.0017582974687684327,
 72      0.006866812414955348,
 73      0.00231711269589141,
 74      0.00011123460717499256
 75    ],
 76    "p_value": 0.03935,
 77    "mde": 0.002480160072007651,
 78    "mde_rel_pct": 240.1632063735439,
 79    "verdict": "idea worse (significant)",
 80    "system_worked": false
 81  },
 82  "mechanism_signature": {
 83    "trained_model": true,
 84    "idea_q_constraint_rms": 0.1779780387878418,
 85    "idea_observed_mean_abs_laplacian": 0.0778733491897583,
 86    "prediction": "lower coordinate defect should accompany lower Laplacian residual",
 87    "baseline_observed_model": true,
 88    "confirmed": true
 89  },
 90  "idea_sweep": [
 91    {
 92      "cfg": {
 93        "lr": 0.001
 94      },
 95      "result": {
 96        "mean": 0.1455571036785841,
 97        "std": 0.007538120960623546,
 98        "per_seed": [
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100          0.16200080513954163,
101          0.14211373031139374,
102          0.14428406953811646,
103          0.14031027257442474,
104          0.147195965051651,
105          0.13541415333747864,
106          0.14235161244869232
107        ],
108        "n": 8
109      }
110    },
111    {
112      "cfg": {
113        "lr": 0.003
114      },
115      "result": {
116        "mean": 0.0774294026196003,
117        "std": 0.013261691418440134,
118        "per_seed": [
119          0.08371833711862564,
120          0.10212770104408264,
121          0.058334484696388245,
122          0.08627945184707642,
123          0.08372340351343155,
124          0.07295472919940948,
125          0.06574133783578873,
126          0.06655577570199966
127        ],
128        "n": 8
129      }
130    },
131    {
132      "cfg": {
133        "lr": 0.01
134      },
135      "result": {
136        "mean": 0.0034477697263355367,
137        "std": 0.003057254396847933,
138        "per_seed": [
139          0.0011874843621626496,
140          0.009428461082279682,
141          0.0006923572509549558,
142          0.002130375476554036,
143          0.0021641517523676157,
144          0.007692142855376005,
145          0.003011035965755582,
146          0.001276149065233767
147        ],
148        "n": 8
149      }
150    }
151  ],
152  "custom_track": {
153    "name": "poisson_harmonic_square",
154    "file": "custom_pde_track.py",
155    "domain": "pde"
156  },
157  "selection_note": "Baseline and idea share the three learning rates; idea adds only the q front-end and its PDE/null-gradient training loss."
158}