files / problems / kissing-5d / compute / q5 / dual_more.json

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{
  "delsarte_deg12": {
    "numerical": 46.336869215638316,
    "trials": [
      {
        "den": 100,
        "certified": false,
        "bound": "927/20",
        "float_bound": 46.35,
        "error": null
      },
      {
        "den": 1000,
        "certified": false,
        "bound": "46337/1000",
        "float_bound": 46.337,
        "error": null
      },
      {
        "den": 10000,
        "certified": false,
        "bound": "463369/10000",
        "float_bound": 46.3369,
        "error": null
      }
    ]
  },
  "delsarte_deg16": {
    "numerical": 46.336869215638316,
    "trials": [
      {
        "den": 1000,
        "certified": false,
        "bound": "46337/1000",
        "float_bound": 46.337,
        "error": null
      },
      {
        "den": 10000,
        "certified": false,
        "bound": "463369/10000",
        "float_bound": 46.3369,
        "error": null
      }
    ]
  },
  "ansatz_q34": [
    {
      "q": [
        "1/3",
        "7/4",
        "10/3",
        "7/4"
      ],
      "deg_q": 3,
      "c": [
        "1243/2520",
        "18475/8316",
        "14117/2970",
        "5374/819",
        "59567/9828",
        "1027/270",
        "1946/1287",
        "196/715"
      ],
      "c_k_nonneg": true,
      "unrestricted": true,
      "certified": true,
      "bound": "64715/1243",
      "float_bound": 52.06355591311343,
      "n_squarefree_roots": 0
    },
    {
      "q": [
        "1",
        "3",
        "3",
        "1"
      ],
      "deg_q": 3,
      "c": [
        "8/15",
        "104/33",
        "112/15",
        "1360/143",
        "280/39",
        "536/165",
        "32/39",
        "64/715"
      ],
      "c_k_nonneg": true,
      "unrestricted": true,
      "certified": true,
      "bound": "60",
      "float_bound": 60.0,
      "n_squarefree_roots": 0
    },
    {
      "q": [
        "1",
        "3",
        "4",
        "2"
      ],
      "deg_q": 3,
      "c": [
        "13/15",
        "1075/231",
        "1742/165",
        "13796/1001",
        "448/39",
        "1024/165",
        "896/429",
        "256/715"
      ],
      "c_k_nonneg": true,
      "unrestricted": true,
      "certified": true,
      "bound": "750/13",
      "float_bound": 57.69230769230769,
      "n_squarefree_roots": 0
    },
    {
      "q": [
        "1",
        "0",
        "0",
        "0",
        "1"
      ],
      "deg_q": 4,
      "c": [
        "-694/1155",
        "4748/3003",
        "-1424/2145",
        "1376/1001",
        "-160/273",
        "2368/2805",
        "-896/7293",
        "2304/13585",
        "-64/2431",
        "128/4199"
      ],
      "c_k_nonneg": false,
      "unrestricted": true,
      "certified": false,
      "bound": null,
      "float_bound": null
    },
    {
      "q": [
        "1",
        "2",
        "2",
        "2",
        "1"
      ],
      "deg_q": 4,
      "c": [
        "32/77",
        "8336/3003",
        "928/143",
        "8160/1001",
        "48/7",
        "2432/561",
        "384/187",
        "1920/2717",
        "448/2431",
        "128/4199"
      ],
      "c_k_nonneg": true,
      "unrestricted": true,
      "certified": true,
      "bound": "77",
      "float_bound": 77.0,
      "n_squarefree_roots": 0
    }
  ],
  "gapped_interpolation": {
    "name": "Q5_minus_antipode",
    "unrestricted": false,
    "label": "NOT unrestricted \u2014 f may be positive on the antipodal gap",
    "T_zero": [
      "-4/5",
      "-1/2",
      "-3/10",
      "0",
      "1/5",
      "1/2"
    ],
    "c": [
      "1",
      "459/113",
      "10948/1243",
      "71964/6215",
      "19216/1469",
      "10080/1243",
      "89600/16159"
    ],
    "c_k_nonneg": true,
    "f_le_0_on_T_zero": true,
    "f_at_minus_1": "2646/565",
    "f_at_minus_1_float": 4.6831858407079645,
    "f_on_T_zero": {
      "-4/5": "0",
      "-1/2": "0",
      "-3/10": "0",
      "0": "0",
      "1/5": "0",
      "1/2": "0"
    },
    "bound_on_T_zero": "29484/565",
    "float_bound_on_T_zero": 52.184070796460176,
    "certified_unrestricted": false,
    "comment": "Exact interpolation on the published Q5 angles except t=\u22121.  Positive at the antipode, so this is not an unrestricted dual and does not move \u03c45."
  },
  "comment": "1-point continuum Delsarte cannot go below Odlyzko\u2013Sloane ~46.34.  Degree-3/4 (t-1/2)q^2 duals that certify sit near 52 or higher.  The Q5-minus-antipode interpolant is NOT unrestricted.  No certified unrestricted dual below 44.",
  "best_certified": "64715/1243",
  "best_certified_float": 52.06355591311343,
  "best_certified_source": "ansatz_q34",
  "below_44": false
}