1{
  2  "bench_version": 1,
  3  "track": "harmonic_cycle_circulation",
  4  "model": "ring_message_passing_custom",
  5  "metric_direction": "lower is better",
  6  "n_seeds": 8,
  7  "baseline": {
  8    "best_cfg": {
  9      "lr": 0.001
 10    },
 11    "sweep": [
 12      {
 13        "cfg": {
 14          "lr": 0.001
 15        },
 16        "mean": 0.03638237901031971
 17      },
 18      {
 19        "cfg": {
 20          "lr": 0.003
 21        },
 22        "mean": 0.03729948867112398
 23      },
 24      {
 25        "cfg": {
 26          "lr": 0.01
 27        },
 28        "mean": 0.03742243070155382
 29      }
 30    ],
 31    "full": {
 32      "mean": 0.03550581377930939,
 33      "std": 0.0023969084354119523,
 34      "per_seed": [
 35        0.03843935579061508,
 36        0.03611151874065399,
 37        0.036980800330638885,
 38        0.03399784117937088,
 39        0.036552730947732925,
 40        0.03312560170888901,
 41        0.03784109279513359,
 42        0.030997568741440773
 43      ],
 44      "n": 8
 45    },
 46    "all_full": {
 47      "0.001": {
 48        "mean": 0.03550581377930939,
 49        "std": 0.0023969084354119523,
 50        "per_seed": [
 51          0.03843935579061508,
 52          0.03611151874065399,
 53          0.036980800330638885,
 54          0.03399784117937088,
 55          0.036552730947732925,
 56          0.03312560170888901,
 57          0.03784109279513359,
 58          0.030997568741440773
 59        ],
 60        "n": 8
 61      },
 62      "0.003": {
 63        "mean": 0.03639047034084797,
 64        "std": 0.001780600134499539,
 65        "per_seed": [
 66          0.03775117173790932,
 67          0.037132371217012405,
 68          0.036965541541576385,
 69          0.03734887018799782,
 70          0.03682024031877518,
 71          0.036104973405599594,
 72          0.03717437759041786,
 73          0.031826216727495193
 74        ],
 75        "n": 8
 76      },
 77      "0.01": {
 78        "mean": 0.04192821681499481,
 79        "std": 0.00861440956566223,
 80        "per_seed": [
 81          0.035938866436481476,
 82          0.038753993809223175,
 83          0.03893406316637993,
 84          0.03606279939413071,
 85          0.04620900750160217,
 86          0.04654981568455696,
 87          0.06103283539414406,
 88          0.03194435313344002
 89        ],
 90        "n": 8
 91      }
 92    },
 93    "selected_lr": 0.001
 94  },
 95  "idea": {
 96    "mean": 0.0015596052253386006,
 97    "std": 0.0010234089138902982,
 98    "per_seed": [
 99      0.0007151182508096099,
100      0.001629576669074595,
101      0.0008324859663844109,
102      0.0016431926051154733,
103      0.001250403467565775,
104      0.004094944801181555,
105      0.0007846655789762735,
106      0.0015264544636011124
107    ],
108    "n": 8
109  },
110  "comparison": {
111    "delta_mean": -0.03394620855397079,
112    "idea_wins": 8,
113    "n_pairs": 8,
114    "per_seed_diffs": [
115      -0.03772423753980547,
116      -0.0344819420715794,
117      -0.036148314364254475,
118      -0.03235464857425541,
119      -0.03530232748016715,
120      -0.029030656907707453,
121      -0.03705642721615732,
122      -0.02947111427783966
123    ],
124    "p_value": 0.0081,
125    "mde": 0.0027847898675877653,
126    "mde_rel_pct": 7.8431940326645035,
127    "verdict": "idea better (significant)",
128    "system_worked": true
129  },
130  "custom_track": {
131    "name": "harmonic_cycle_circulation",
132    "file": "custom_harmonic_track.py",
133    "domain": "pde"
134  },
135  "idea_sweep": [
136    {
137      "lr": 0.001,
138      "full": {
139        "mean": 0.003153404308250174,
140        "std": 0.0010669733272582484,
141        "per_seed": [
142          0.005706639029085636,
143          0.0019703044090420008,
144          0.002921751933172345,
145          0.003424836788326502,
146          0.0025838848669081926,
147          0.002318854909390211,
148          0.003008102998137474,
149          0.0032928595319390297
150        ],
151        "n": 8
152      }
153    },
154    {
155      "lr": 0.003,
156      "full": {
157        "mean": 0.0015596052253386006,
158        "std": 0.0010234089138902982,
159        "per_seed": [
160          0.0007151182508096099,
161          0.001629576669074595,
162          0.0008324859663844109,
163          0.0016431926051154733,
164          0.001250403467565775,
165          0.004094944801181555,
166          0.0007846655789762735,
167          0.0015264544636011124
168        ],
169        "n": 8
170      }
171    },
172    {
173      "lr": 0.01,
174      "full": {
175        "mean": 0.01939631302957423,
176        "std": 0.021010081673085577,
177        "per_seed": [
178          0.045300547033548355,
179          0.004099640529602766,
180          0.0036269642878323793,
181          0.0017828397685661912,
182          0.047566160559654236,
183          0.04654437676072121,
184          0.005047771148383617,
185          0.001202204148285091
186        ],
187        "n": 8
188      }
189    }
190  ],
191  "math_check": {
192    "closed_residual": 0.0,
193    "coclosed_residual": 1.0385185452638061e-16,
194    "weighted_orthonormality": 1.0,
195    "max_gauge_residual": 5.551115123125783e-16,
196    "max_reconstruction_residual": 4.440892098500626e-16,
197    "period_basis_residual": 0.0
198  },
199  "protocol": {
200    "seeds": [
201      0,
202      1,
203      2,
204      3,
205      4,
206      5,
207      6,
208      7
209    ],
210    "epochs": 24,
211    "batch": 64,
212    "baseline_union_lr_full_evals": true,
213    "idea_best_lr": 0.003,
214    "matched_architecture": "same four local ring layers; idea adds only harmonic projection/global coefficient"
215  },
216  "mechanism_signature": {
217    "trained_seed": 0,
218    "period_input_slope": 0.9669459899023306,
219    "target_period_input_slope": 1.0000000062968901,
220    "period_input_correlation": 0.9942523582287552,
221    "idea_test_mse": 0.0007151182508096099,
222    "confirmed": true
223  },
224  "comparison_at_baseline_best_lr": {
225    "delta_mean": -0.03235240947105922,
226    "idea_wins": 8,
227    "n_pairs": 8,
228    "per_seed_diffs": [
229      -0.032732716761529446,
230      -0.03414121433161199,
231      -0.03405904839746654,
232      -0.03057300439104438,
233      -0.03396884608082473,
234      -0.030806746799498796,
235      -0.03483298979699612,
236      -0.027704709209501743
237    ],
238    "p_value": 0.0081,
239    "mde": 0.002052526791910367,
240    "mde_rel_pct": 5.7808188953732795,
241    "verdict": "idea better (significant)",
242    "system_worked": true
243  }
244}