1{
  2  "seed": 7,
  3  "ell": 2,
  4  "dimension": 2,
  5  "threshold_r": 0.7071067811865475,
  6  "contraction": {
  7    "observed_log_slope": -0.2231435513142087,
  8    "predicted_log_slope": -0.2231435513142097,
  9    "observed_ratio_n30": 0.0012379400392854149,
 10    "predicted_ratio_n30": 0.0012379400392853823
 11  },
 12  "sweep": [
 13    {
 14      "r": 0.55,
 15      "ell_det": 0.6050000000000001,
 16      "g": -0.5025268209512955,
 17      "predicted_dimension": 2.159425026694333,
 18      "box_dimension": 1.534505200322887,
 19      "correlation_dimension": 2.4340495485942877,
 20      "boxes": [
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 28      ]
 29    },
 30    {
 31      "r": 0.65,
 32      "ell_det": 0.8450000000000001,
 33      "g": -0.16841865162496317,
 34      "predicted_dimension": 2.6090405507426917,
 35      "box_dimension": 1.5432495866148117,
 36      "correlation_dimension": 2.4835570657562323,
 37      "boxes": [
 38        451,
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 40        3057,
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 44        26305
 45      ]
 46    },
 47    {
 48      "r": 0.7,
 49      "ell_det": 0.9799999999999999,
 50      "g": -0.020202707317519608,
 51      "predicted_dimension": 2.9433582098747317,
 52      "box_dimension": 1.562703735059463,
 53      "correlation_dimension": 2.5318648358582614,
 54      "boxes": [
 55        440,
 56        1349,
 57        2964,
 58        8034,
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 60        22285,
 61        26223
 62      ]
 63    },
 64    {
 65      "r": 0.7071067811865475,
 66      "ell_det": 0.9999999999999998,
 67      "g": -2.220446049250313e-16,
 68      "predicted_dimension": 2.999999999999999,
 69      "box_dimension": 1.567461156237267,
 70      "correlation_dimension": 2.5263220077054758,
 71      "boxes": [
 72        434,
 73        1343,
 74        2946,
 75        7933,
 76        13740,
 77        22207,
 78        26166
 79      ]
 80    },
 81    {
 82      "r": 0.75,
 83      "ell_det": 1.125,
 84      "g": 0.11778303565638348,
 85      "predicted_dimension": 3.0,
 86      "box_dimension": 1.5913098807768284,
 87      "correlation_dimension": 2.557771614084822,
 88      "boxes": [
 89        428,
 90        1308,
 91        2846,
 92        7706,
 93        13533,
 94        22022,
 95        26080
 96      ]
 97    },
 98    {
 99      "r": 0.85,
100      "ell_det": 1.4449999999999998,
101      "g": 0.3681093215643954,
102      "predicted_dimension": 3.0,
103      "box_dimension": 1.708556519589037,
104      "correlation_dimension": 2.529461527629673,
105      "boxes": [
106        388,
107        1134,
108        2347,
109        6222,
110        11181,
111        19983,
112        24907
113      ]
114    },
115    {
116      "r": 0.95,
117      "ell_det": 1.805,
118      "g": 0.5905605917848441,
119      "predicted_dimension": 3.0,
120      "box_dimension": 1.7745885108114106,
121      "correlation_dimension": 2.3684401231295875,
122      "boxes": [
123        366,
124        1033,
125        2083,
126        5354,
127        9829,
128        18541,
129        23918
130      ]
131    }
132  ],
133  "notes": "Volume exponent is exact for A=rI: log(ell)+log|det(A)|=log(ell*r^2)."
134}