files / problems / simon-ionization-excess / compute / q8 / certs / r9_cut.json

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{
  "status": "residue",
  "reason": "At R<=9 the mass-opt cut R/(R+1) is at most 0.9, so min(gamma, cut) <= 0.9 and the leading is at least 1.1111. That cannot beat printed 1.1021. Dead without a sharper cut. q7 already recorded the same wall against 1.1026.",
  "q7_printed": 1.1021,
  "rows": [
    {
      "R": 8.0,
      "cut": 0.8888888888888888,
      "leading_if_cut_binds": 1.125,
      "beats_1.1021_if_cut_binds": false
    },
    {
      "R": 9.0,
      "cut": 0.9,
      "leading_if_cut_binds": 1.1111111111111112,
      "beats_1.1021_if_cut_binds": false
    },
    {
      "R": 9.5,
      "cut": 0.9047619047619048,
      "leading_if_cut_binds": 1.1052631578947367,
      "beats_1.1021_if_cut_binds": false
    },
    {
      "R": 9.8,
      "cut": 0.9074074074074074,
      "leading_if_cut_binds": 1.1020408163265305,
      "beats_1.1021_if_cut_binds": true
    },
    {
      "R": 9.9,
      "cut": 0.908256880733945,
      "leading_if_cut_binds": 1.101010101010101,
      "beats_1.1021_if_cut_binds": true
    },
    {
      "R": 10.0,
      "cut": 0.9090909090909091,
      "leading_if_cut_binds": 1.1,
      "beats_1.1021_if_cut_binds": true
    }
  ]
}