files / problems / simon-ionization-excess / compute / q3 / certs / aspect_identities.json

1.9 KB · on GitHub

{
  "status": "ok",
  "R_split": 12,
  "Q_cut": "12/13",
  "Q_cut_value": "0.9230769230769230769230769230769230769231",
  "Q_cut_inv": "1.083333333333333333333333333333333333333",
  "compact_gamma_R12": "0.8995260524666926617922278920310721986121",
  "compact_inv_R12": "1.111696539814256966877569616043574522930",
  "cut_exceeds_compact_gamma": true,
  "algebra": "Mass-stationarity at inf=1 and sup=R gives M_{-1}=Q+(Q-1)D>0 and M_3=(Q-1)R^3+Q D R>0, hence R<Q/(1-Q) and Q>R/(R+1).",
  "nonempty_D_interval_at_Q_0.93_R_12": true,
  "empty_D_interval_for_Q_le_12_13_at_R_12": true,
  "samples_Q_0.895_to_0.999": [
    {
      "Q": "0.895000000000",
      "D_lo_at_R12": "16.8938547486",
      "D_hi": "8.52380952381",
      "interval_empty": true,
      "R_star": "8.52380952381"
    },
    {
      "Q": "0.915000000000",
      "D_lo_at_R12": "13.3770491803",
      "D_hi": "10.7647058824",
      "interval_empty": true,
      "R_star": "10.7647058824"
    },
    {
      "Q": "0.935000000000",
      "D_lo_at_R12": "10.0106951872",
      "D_hi": "14.3846153846",
      "interval_empty": false,
      "R_star": "14.3846153846"
    },
    {
      "Q": "0.955000000000",
      "D_lo_at_R12": "6.78534031414",
      "D_hi": "21.2222222222",
      "interval_empty": false,
      "R_star": "21.2222222222"
    },
    {
      "Q": "0.975000000000",
      "D_lo_at_R12": "3.69230769231",
      "D_hi": "39.0000000000",
      "interval_empty": false,
      "R_star": "39.0000000000"
    },
    {
      "Q": "0.995000000000",
      "D_lo_at_R12": "0.723618090452",
      "D_hi": "199.000000000",
      "interval_empty": false,
      "R_star": "199.000000000"
    }
  ],
  "leading_from_compact_gamma": "1.111696539814256966877569616043574522930",
  "beats_1.1185_if_lifted": true,
  "faces_row": {
    "copositive": 1,
    "singular_or_illconditioned": 5,
    "min_mMm_safe": 0.004479592204425791,
    "certified_phi": 0.9055
  }
}