files / problems / caccetta-haggkvist-k3 / compute / certs / f4_certificate.json

3.4 KB · on GitHub

{
  "c": 0.34645,
  "published_hkn": 0.3465,
  "personal_communication_3388": 0.3388,
  "method": "F4 flag-algebra Farkas certificate: Q\u227d0 on the 8\u00d78 \u03b2-flag Cauchy\u2013Schwarz slices, plus out-regularity, order-3 induction, and the CSS-fork inequality. Matrices independently rebuilt in flags4.py / ind_fork.py and matched to Hladk\u00fd\u2013Kr\u00e1l'\u2013Norin Combinatorica 37 (2017) Tables 1\u20132 and (4.14)\u2013(4.15).",
  "worst_F": -0.12343037279396185,
  "worst_index": 0,
  "all_negative": true,
  "Q_min_eig": 9.527376867242648e-09,
  "b": [
    -29.20261165126803,
    -29.20261165132466,
    10674.203416874827,
    7653.907252139246,
    0.0,
    119790.20005946088,
    72019.12680466054,
    86737.38016512505,
    6283.218766808585,
    16305.068923820409,
    77024.15863663288,
    6852.666753480612,
    17217.32027522853,
    -39006.42197900125
  ],
  "cT": 124246.99291786623,
  "cV": 62229.36495656363,
  "d": 6540.547344785617,
  "Q": [
    [
      45233.50667740926,
      25549.733181374704,
      12006.31362635327,
      30360.373812565722,
      -5807.726487635728,
      -6260.432198292773,
      -14378.53984215022,
      -34004.1105581197
    ],
    [
      25549.733181374704,
      15206.46337380151,
      8192.32422402067,
      16638.946038381455,
      -3746.2577417111083,
      -2253.968000722963,
      -10176.776710784572,
      -18739.14085484782
    ],
    [
      12006.31362635327,
      8192.32422402067,
      16139.344763773877,
      2771.576529681114,
      -372.3301557335652,
      5112.804014749996,
      -12018.978034506632,
      -10229.827303795619
    ],
    [
      30360.373812565722,
      16638.946038381455,
      2771.576529681114,
      22651.654232294022,
      -4401.208512761961,
      -7006.980843381698,
      -6333.938929647709,
      -22306.118199442266
    ],
    [
      -5807.726487635728,
      -3746.2577417111083,
      -372.3301557335652,
      -4401.208512761961,
      1430.1671392745648,
      862.3651289929827,
      2246.3060358155003,
      3672.527892959783
    ],
    [
      -6260.432198292773,
      -2253.968000722963,
      5112.804014749996,
      -7006.980843381698,
      862.3651289929827,
      4974.101158778165,
      -3400.58091163687,
      4635.19119690688
    ],
    [
      -14378.53984215022,
      -10176.776710784572,
      -12018.978034506632,
      -6333.938929647709,
      2246.3060358155003,
      -3400.58091163687,
      12015.54680860411,
      10419.499187942765
    ],
    [
      -34004.1105581197,
      -18739.14085484782,
      -10229.827303795619,
      -22306.118199442266,
      3672.527892959783,
      4635.19119690688,
      10419.499187942765,
      26264.93690234405
    ]
  ],
  "F": [
    -0.12343037279396185,
    -1.5668351848219118,
    -13101.211507659333,
    -2.39142764934536,
    -3416.431742149649,
    -1825.807186627608,
    -2.2970276853959604,
    -3.5899386679047893,
    -12541.410479613263,
    -2.8883909518265227,
    -3.0102399969694034,
    -4157.891339288428,
    -8259.581043017006,
    -2.493810907035595,
    -45625.42630446108,
    -3.216020113861532,
    -3.0941710687186514,
    -35219.58820212426,
    -3.0941710687113755,
    -48733.522202652006,
    -4.019885082903784,
    -3.1611028226907365,
    -2.0278757757407675,
    -31117.97392980845,
    -108.16784624639718,
    -3.2914515266111266,
    -2.841973319718818,
    -2.97232202372129,
    -3.4218002305935897,
    -9462.991846591689,
    -3.311984777537873,
    -1.835842405802623
  ]
}