1{
  2  "weak_coupling_prediction": [
  3    {
  4      "gap": 0.5,
  5      "eps": 5e-06,
  6      "observed_shift_over_eps2": 2.0000001654807416,
  7      "predicted_limit_1_over_gap": 2.0,
  8      "certificate_ratio": 1.000000082840371
  9    },
 10    {
 11      "gap": 1.0,
 12      "eps": 1e-05,
 13      "observed_shift_over_eps2": 1.0000000827403708,
 14      "predicted_limit_1_over_gap": 1.0,
 15      "certificate_ratio": 1.000000082840371
 16    },
 17    {
 18      "gap": 2.0,
 19      "eps": 2e-05,
 20      "observed_shift_over_eps2": 0.5000000413701854,
 21      "predicted_limit_1_over_gap": 0.5,
 22      "certificate_ratio": 1.000000082840371
 23    },
 24    {
 25      "gap": 4.0,
 26      "eps": 4e-05,
 27      "observed_shift_over_eps2": 0.2500000206850927,
 28      "predicted_limit_1_over_gap": 0.25,
 29      "certificate_ratio": 1.000000082840371
 30    }
 31  ],
 32  "strong_coupling_prediction": [
 33    {
 34      "eps": 1,
 35      "observed_shift_over_eps": 0.6180339887498949,
 36      "predicted_limit": 1.0,
 37      "certificate_ratio": 1.0000000000000002
 38    },
 39    {
 40      "eps": 3,
 41      "observed_shift_over_eps": 0.8471270883830367,
 42      "predicted_limit": 1.0,
 43      "certificate_ratio": 1.0
 44    },
 45    {
 46      "eps": 10,
 47      "observed_shift_over_eps": 0.9512492197250394,
 48      "predicted_limit": 1.0,
 49      "certificate_ratio": 1.0000000000000002
 50    },
 51    {
 52      "eps": 30,
 53      "observed_shift_over_eps": 0.9834722125784999,
 54      "predicted_limit": 1.0,
 55      "certificate_ratio": 1.0
 56    },
 57    {
 58      "eps": 100,
 59      "observed_shift_over_eps": 0.9950124999218759,
 60      "predicted_limit": 1.0,
 61      "certificate_ratio": 1.0
 62    }
 63  ],
 64  "zero_gap_prediction": [
 65    {
 66      "eps": 0.01,
 67      "observed_shift": 0.01,
 68      "predicted_eps": 0.01,
 69      "certificate_ratio": 1.0
 70    },
 71    {
 72      "eps": 0.1,
 73      "observed_shift": 0.1,
 74      "predicted_eps": 0.1,
 75      "certificate_ratio": 1.0
 76    },
 77    {
 78      "eps": 1.0,
 79      "observed_shift": 1.0,
 80      "predicted_eps": 1.0,
 81      "certificate_ratio": 1.0
 82    },
 83    {
 84      "eps": 10.0,
 85      "observed_shift": 10.0,
 86      "predicted_eps": 10.0,
 87      "certificate_ratio": 1.0
 88    }
 89  ],
 90  "rank_one_frobenius_check": {
 91    "trials": 100,
 92    "max_actual_over_bound": 0.7408804083528778,
 93    "violations": 0
 94  },
 95  "adaptive_merge_demo": {
 96    "gap": 1.0,
 97    "threshold": 0.08,
 98    "rows": [
 99      {
100        "eps": 0.01,
101        "certificate_fro": 0.00014140721692940602,
102        "decision": "retain separate blocks"
103      },
104      {
105        "eps": 0.03,
106        "certificate_fro": 0.0012716487504459695,
107        "decision": "retain separate blocks"
108      },
109      {
110        "eps": 0.1,
111        "certificate_fro": 0.014003473906250336,
112        "decision": "retain separate blocks"
113      },
114      {
115        "eps": 0.3,
116        "certificate_fro": 0.11751434393698458,
117        "decision": "merge blocks"
118      },
119      {
120        "eps": 1.0,
121        "certificate_fro": 0.8740320488976421,
122        "decision": "merge blocks"
123      }
124    ]
125  }
126}