1{
  2  "seed": 2891,
  3  "graph_nodes": 8,
  4  "module_dimension": 3,
  5  "lambda_min_Gamma": 0.9690295087725669,
  6  "degrees": [
  7    1.6199999999999999,
  8    0.98,
  9    1.55,
 10    1.98,
 11    0.6,
 12    0.98,
 13    1.67,
 14    1.08
 15  ],
 16  "predictions": {
 17    "decay_rate": "late log(V) slope = -2*c*lambda_min(L+P)*lambda_min(Gamma)",
 18    "pinning": "lambda_min and decay magnitude increase with p, with diminishing gains",
 19    "selection": "greedy marginal gap maximization beats random choices on this graph"
 20  },
 21  "greedy_pins": [
 22    3,
 23    6
 24  ],
 25  "greedy_marginal_gains": [
 26    0.08143654881021675,
 27    0.09544569911833947
 28  ],
 29  "scaling_sweep": [
 30    {
 31      "c": 0.25,
 32      "observed_slope": -0.08570218630880942,
 33      "predicted_slope": -0.0857020589103981,
 34      "ratio_abs_observed_to_predicted": 1.0319618520116174
 35    },
 36    {
 37      "c": 0.5,
 38      "observed_slope": -0.17140437261761884,
 39      "predicted_slope": -0.1714041178207962,
 40      "ratio_abs_observed_to_predicted": 1.0319618520116174
 41    },
 42    {
 43      "c": 1.0,
 44      "observed_slope": -0.3428087452352377,
 45      "predicted_slope": -0.3428082356415924,
 46      "ratio_abs_observed_to_predicted": 1.0319618520116174
 47    },
 48    {
 49      "c": 2.0,
 50      "observed_slope": -0.6856174904704754,
 51      "predicted_slope": -0.6856164712831848,
 52      "ratio_abs_observed_to_predicted": 1.0319618520116174
 53    }
 54  ],
 55  "pin_strength_sweep": [
 56    {
 57      "p": 0.05,
 58      "lambda_min": 0.012274561681676233,
 59      "observed_slope": -0.023788842772816114,
 60      "predicted_slope": -0.023788824953586585,
 61      "ratio": 1.000000749058836
 62    },
 63    {
 64      "p": 0.1,
 65      "lambda_min": 0.024107687807851906,
 66      "observed_slope": -0.04672215819424911,
 67      "predicted_slope": -0.04672212174817027,
 68      "ratio": 1.0000007800604398
 69    },
 70    {
 71      "p": 0.25,
 72      "lambda_min": 0.05709962496552992,
 73      "observed_slope": -0.11066254039589309,
 74      "predicted_slope": -0.11066244306289051,
 75      "ratio": 1.0000008795486515
 76    },
 77    {
 78      "p": 0.5,
 79      "lambda_min": 0.10455555469231693,
 80      "observed_slope": -0.20263505142140711,
 81      "predicted_slope": -0.20263483560587825,
 82      "ratio": 1.0000010650465316
 83    },
 84    {
 85      "p": 1.0,
 86      "lambda_min": 0.17688224792855622,
 87      "observed_slope": -0.3428087452352377,
 88      "predicted_slope": -0.34280823564159246,
 89      "ratio": 1.0000014865268458
 90    },
 91    {
 92      "p": 2.0,
 93      "lambda_min": 0.264036365197708,
 94      "observed_slope": -0.511719448148651,
 95      "predicted_slope": -0.5117180585312582,
 96      "ratio": 1.000002715591857
 97    },
 98    {
 99      "p": 4.0,
100      "lambda_min": 0.3397351317422959,
101      "observed_slope": -0.6585219726421622,
102      "predicted_slope": -0.6584267356500406,
103      "ratio": 1.0001446432639578
104    }
105  ],
106  "selection_comparison": {
107    "greedy": {
108      "pins": [
109        3,
110        6
111      ],
112      "gap": 0.17688224792855622,
113      "observed_slope": -0.3428087452352377,
114      "predicted_slope": -0.3428082356415924
115    },
116    "high_degree": {
117      "pins": [
118        3,
119        6
120      ],
121      "gap": 0.17688224792855622,
122      "observed_slope": -0.3428087452352377,
123      "predicted_slope": -0.3428082356415924
124    },
125    "random_sets": [
126      {
127        "pins": [
128          0,
129          1
130        ],
131        "gap": 0.1378763027946528
132      },
133      {
134        "pins": [
135          2,
136          7
137        ],
138        "gap": 0.14899242322323586
139      },
140      {
141        "pins": [
142          1,
143          6
144        ],
145        "gap": 0.14554145114847472
146      },
147      {
148        "pins": [
149          3,
150          5
151        ],
152        "gap": 0.1674522400235533
153      },
154      {
155        "pins": [
156          0,
157          4
158        ],
159        "gap": 0.13354348526672344
160      }
161    ],
162    "random_mean_gap": 0.14668118049132803,
163    "random_mean_observed_slope": -0.28427703144968575
164  },
165  "max_rate_prediction_ratio_error": 0.03196185201161739,
166  "all_rate_ratios_within_25pct": true,
167  "greedy_beats_random_mean_gap": true,
168  "greedy_beats_high_degree_gap": false
169}