1{
  2  "bench_version": 1,
  3  "track": "anisotropic_oblique_bvp",
  4  "model": "mlp_tiny",
  5  "metric_direction": "lower is better",
  6  "n_seeds": 8,
  7  "baseline": {
  8    "best_cfg": {
  9      "lr": 0.003,
 10      "weight_decay": 0.0
 11    },
 12    "sweep": [
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 23          "weight_decay": 0.0
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 25        "mean": 0.00010377542184869526
 26      },
 27      {
 28        "cfg": {
 29          "lr": 0.006,
 30          "weight_decay": 0.0
 31        },
 32        "mean": 0.00011149384499731241
 33      }
 34    ],
 35    "full": {
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 37      "std": 2.4013090964758765e-05,
 38      "per_seed": [
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 43        8.006240386748686e-05,
 44        9.653119195718318e-05,
 45        9.42463957471773e-05,
 46        6.891691737109795e-05
 47      ],
 48      "n": 8
 49    }
 50  },
 51  "idea": {
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 53    "std": 3.095430559427717e-05,
 54    "per_seed": [
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 57      6.513581320177764e-05,
 58      9.932620014296845e-05,
 59      0.00011056653602281585,
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 62      8.550836355425417e-05
 63    ],
 64    "n": 8,
 65    "cfg": {
 66      "lr": 0.003,
 67      "weight_decay": 0.0,
 68      "bc_weight": 0.1
 69    },
 70    "selected_cfg": {
 71      "lr": 0.003,
 72      "weight_decay": 0.0,
 73      "bc_weight": 0.1
 74    }
 75  },
 76  "comparison": {
 77    "delta_mean": 2.2641099803877296e-05,
 78    "idea_wins": 1,
 79    "n_pairs": 8,
 80    "per_seed_diffs": [
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 82      1.523268292658031e-05,
 83      9.003782906802371e-06,
 84      -4.550536687020212e-06,
 85      3.050413215532899e-05,
 86      3.974868741352111e-05,
 87      3.534421557560563e-05,
 88      1.6591446183156222e-05
 89    ],
 90    "p_value": 0.0152,
 91    "mde": 1.3440697763296005e-05,
 92    "mde_rel_pct": 14.244466795243426,
 93    "verdict": "idea worse (significant)",
 94    "system_worked": false
 95  },
 96  "mechanism_signature": {
 97    "mechanism_signature": {
 98      "prediction": "boundary-aware PDE training reduces measured oblique/no-flux residuals",
 99      "mean_baseline_oblique_residual": 0.02720322646200657,
100      "mean_idea_oblique_residual": 0.01003198220860213,
101      "mean_baseline_normal_residual": 0.04276570677757263,
102      "mean_idea_normal_residual": 0.008119827311020344,
103      "per_seed": [
104        {
105          "seed": 0,
106          "baseline_oblique_abs_derivative": 0.03964276611804962,
107          "idea_oblique_abs_derivative": 0.01283207256346941,
108          "baseline_normal_abs_derivative": 0.03705023229122162,
109          "idea_normal_abs_derivative": 0.009148340672254562
110        },
111        {
112          "seed": 1,
113          "baseline_oblique_abs_derivative": 0.020765259861946106,
114          "idea_oblique_abs_derivative": 0.008115937002003193,
115          "baseline_normal_abs_derivative": 0.04100044071674347,
116          "idea_normal_abs_derivative": 0.010081736370921135
117        },
118        {
119          "seed": 2,
120          "baseline_oblique_abs_derivative": 0.020734591409564018,
121          "idea_oblique_abs_derivative": 0.009465154260396957,
122          "baseline_normal_abs_derivative": 0.06341361999511719,
123          "idea_normal_abs_derivative": 0.01047296728938818
124        },
125        {
126          "seed": 3,
127          "baseline_oblique_abs_derivative": 0.023547939956188202,
128          "idea_oblique_abs_derivative": 0.009573541581630707,
129          "baseline_normal_abs_derivative": 0.027527321130037308,
130          "idea_normal_abs_derivative": 0.00741744227707386
131        },
132        {
133          "seed": 4,
134          "baseline_oblique_abs_derivative": 0.02001587674021721,
135          "idea_oblique_abs_derivative": 0.009027393534779549,
136          "baseline_normal_abs_derivative": 0.04191877692937851,
137          "idea_normal_abs_derivative": 0.008082550019025803
138        },
139        {
140          "seed": 5,
141          "baseline_oblique_abs_derivative": 0.026504037901759148,
142          "idea_oblique_abs_derivative": 0.007130592130124569,
143          "baseline_normal_abs_derivative": 0.031208854168653488,
144          "idea_normal_abs_derivative": 0.007085439749062061
145        },
146        {
147          "seed": 6,
148          "baseline_oblique_abs_derivative": 0.0324188694357872,
149          "idea_oblique_abs_derivative": 0.016259243711829185,
150          "baseline_normal_abs_derivative": 0.03935849666595459,
151          "idea_normal_abs_derivative": 0.007526469882577658
152        },
153        {
154          "seed": 7,
155          "baseline_oblique_abs_derivative": 0.033996470272541046,
156          "idea_oblique_abs_derivative": 0.007851922884583473,
157          "baseline_normal_abs_derivative": 0.060647912323474884,
158          "idea_normal_abs_derivative": 0.005143672227859497
159        }
160      ],
161      "confirmed": true
162    },
163    "custom_track": {
164      "name": "anisotropic_oblique_bvp",
165      "file": "pde_boundary_track.py",
166      "domain": "pde"
167    },
168    "idea_sweep": [
169      {
170        "cfg": {
171          "lr": 0.003,
172          "weight_decay": 0.0,
173          "bc_weight": 0.1
174        },
175        "mean": 0.00011699842434609309,
176        "std": 3.095430559427717e-05,
177        "per_seed": [
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179          0.0001437541941413656,
180          6.513581320177764e-05,
181          9.932620014296845e-05,
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183          0.0001362798793707043,
184          0.00012959061132278293,
185          8.550836355425417e-05
186        ]
187      },
188      {
189        "cfg": {
190          "lr": 0.003,
191          "weight_decay": 0.0,
192          "bc_weight": 1.0
193        },
194        "mean": 0.00016314282402163371,
195        "std": 5.0713334733415886e-05,
196        "per_seed": [
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198          0.0002775485045276582,
199          9.841256542131305e-05,
200          0.00013486476382240653,
201          0.00015113064728211612,
202          0.00019398487347643822,
203          0.00017369228589814156,
204          0.00013726879842579365
205        ]
206      },
207      {
208        "cfg": {
209          "lr": 0.003,
210          "weight_decay": 0.0,
211          "bc_weight": 5.0
212        },
213        "mean": 0.00022120710127637722,
214        "std": 5.5719673809869554e-05,
215        "per_seed": [
216          0.00020971496996935457,
217          0.0002884801651816815,
218          0.00013389925879891962,
219          0.0002538147964514792,
220          0.00018812052439898252,
221          0.00022245440050028265,
222          0.0003070295206271112,
223          0.00016614317428320646
224        ]
225      }
226    ]
227  },
228  "protocol_note": "Custom PDE track required: no built-in track contains boundary-value/PDE structure."
229}