files / problems / simon-ionization-excess / compute / record.json

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{
  "constants": {
    "b3": 1.1184337992027067,
    "b3_window": [
      1.1184,
      1.1185
    ],
    "half_sqrt2_plus_one": 1.2071067811865475,
    "s2_window": [
      1.2071,
      1.2072
    ]
  },
  "crossovers": {
    "Nam_beats_Lieb_first_integer_Z": 6,
    "HPS_s2_beats_Nam_first_integer_Z": 2,
    "HPS_s3_beats_HPS_s2_first_integer_Z": 36,
    "paper_Nam_beats_Lieb": 6,
    "paper_s3_beats_s2_remark": 35.8
  },
  "at_Z_118": {
    "Lieb": 237.0,
    "Nam": 158.67460439457204,
    "HPS_s3": 151.15590247641137,
    "HPS_coarse": 151.60247252609608
  },
  "sample_rows": [
    {
      "Z": 1,
      "Lieb": 3.0,
      "Nam": 4.22
    },
    {
      "Z": 5,
      "Lieb": 11.0,
      "Nam": 11.22992784003009,
      "HPS_s2": 11.09706270809576,
      "HPS_s3": 12.388782146529858,
      "HPS_coarse": 12.432403786706788
    },
    {
      "Z": 6,
      "Lieb": 13.0,
      "Nam": 12.77136177849642,
      "HPS_s2": 12.621317641902419,
      "HPS_s3": 13.91796813683094,
      "HPS_coarse": 13.979482371328558
    },
    {
      "Z": 36,
      "Lieb": 73.0,
      "Nam": 53.82578174668388,
      "HPS_s2": 53.2295487794438,
      "HPS_s3": 53.21205578944662,
      "HPS_coarse": 53.47370899557851
    },
    {
      "Z": 118,
      "Lieb": 237.0,
      "Nam": 158.67460439457204,
      "HPS_s2": 156.9570098493237,
      "HPS_s3": 151.15590247641137,
      "HPS_coarse": 151.60247252609608
    }
  ],
  "note": "These are already-published upper bounds on Nc(Z). Replaying the comparison is not a new bound."
}