1{
  2  "bench_version": 1,
  3  "track": "symmetric_periodic_poisson",
  4  "model": "matched_mlp_implicit_poisson",
  5  "metric_direction": "lower is better",
  6  "n_seeds": 8,
  7  "baseline": {
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 24      {
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103          0.15940041840076447,
104          0.1558334082365036,
105          0.16848696768283844,
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107          0.15929055213928223
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109        "n": 8
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111    ],
112    "cfg": {
113      "lr": 0.01,
114      "nearby_tested": [
115        0.001,
116        0.003,
117        0.01
118      ]
119    }
120  },
121  "comparison": {
122    "delta_mean": -1542.8096787557006,
123    "idea_wins": 8,
124    "n_pairs": 8,
125    "per_seed_diffs": [
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127      -1715.362874493003,
128      -1606.6729110181332,
129      -3546.3623280972242,
130      -896.577687099576,
131      -1585.3755804151297,
132      -690.0688900053501,
133      -1750.4232289791107
134    ],
135    "p_value": 0.0081,
136    "mde": 788.2054458068113,
137    "mde_rel_pct": 51.08352522860764,
138    "verdict": "idea better (significant)",
139    "system_worked": true
140  },
141  "mechanism_signature": {
142    "prediction": "symmetry-basis implicit solve preserves the discretized solution and commutes with translations",
143    "trained_model_observed_max_relative_solve_residual": 0.0692358985543251,
144    "trained_model_observed_max_translation_equivariance_error": 0.4862891137599945,
145    "operator_commutator_frobenius": 8.0,
146    "predicted_residual_and_equivariance": 0.0,
147    "confirmed": false,
148    "note": "signature is measured from the trained idea model on held-out benchmark inputs"
149  },
150  "custom_track": {
151    "name": "symmetric_periodic_poisson",
152    "file": "poisson_symmetry_track.py",
153    "domain": "pde"
154  },
155  "stage2_config": {
156    "epochs": 16,
157    "batch": 64,
158    "seeds": [
159      0,
160      1,
161      2,
162      3,
163      4,
164      5,
165      6,
166      7
167    ],
168    "lr_union": [
169      0.001,
170      0.003,
171      0.01
172    ],
173    "track_reason": "PDE inverse problem with periodic Poisson operator; no built-in track had this structure"
174  }
175}