files / problems / simon-ionization-excess / compute / q9 / certs / smallz.json

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{
  "status": "residue",
  "reason": "Lieb N_c<2Z+1 still excludes the most integers at Z=2..6. The q8 simplified envelope sits above 2Z+1 there. A leading coefficient >1 cannot bound N0(Z)-Z.",
  "rows": [
    {
      "Z": 2,
      "Lieb_2Z+1": 5,
      "Lieb_integer_Nc_le": 4,
      "q8_1.1020_3.937": 7.164309173436116,
      "Nam_1.22_3": 6.219763149684619,
      "q8_excludes_new_integer": false
    },
    {
      "Z": 3,
      "Lieb_2Z+1": 7,
      "Lieb_integer_Nc_le": 6,
      "q8_1.1020_3.937": 8.984136558300266,
      "Nam_1.22_3": 7.986748710922225,
      "q8_excludes_new_integer": false
    },
    {
      "Z": 4,
      "Lieb_2Z+1": 9,
      "Lieb_integer_Nc_le": 8,
      "q8_1.1020_3.937": 10.657597941598802,
      "Nam_1.22_3": 9.642203155904598,
      "q8_excludes_new_integer": false
    },
    {
      "Z": 5,
      "Lieb_2Z+1": 11,
      "Lieb_integer_Nc_le": 10,
      "q8_1.1020_3.937": 12.242175302066155,
      "Nam_1.22_3": 11.22992784003009,
      "q8_excludes_new_integer": false
    },
    {
      "Z": 6,
      "Lieb_2Z+1": 13,
      "Lieb_integer_Nc_le": 12,
      "q8_1.1020_3.937": 13.766003773980135,
      "Nam_1.22_3": 12.77136177849642,
      "q8_excludes_new_integer": false
    }
  ]
}