files / problems / affine-013 / compute / certs / half_bound.json

1.8 KB · on GitHub

{
  "bound": "T(S) <= ceil(n^2 / 2)",
  "implies": "gamma_{1,2,-3} <= 1/2",
  "beats": "Hardy-Littlewood / Aaronson 3/4",
  "ok": true,
  "identity_ok": true,
  "interval_ok": true,
  "exhaustive": [
    {
      "n": 3,
      "dmax": 12,
      "n_sets": 66,
      "T_max_observed": 4,
      "bound": 5,
      "T_interval": 3
    },
    {
      "n": 4,
      "dmax": 12,
      "n_sets": 220,
      "T_max_observed": 6,
      "bound": 8,
      "T_interval": 6
    },
    {
      "n": 5,
      "dmax": 12,
      "n_sets": 495,
      "T_max_observed": 9,
      "bound": 13,
      "T_interval": 9
    },
    {
      "n": 6,
      "dmax": 12,
      "n_sets": 792,
      "T_max_observed": 13,
      "bound": 18,
      "T_interval": 12
    },
    {
      "n": 7,
      "dmax": 14,
      "n_sets": 3003,
      "T_max_observed": 17,
      "bound": 25,
      "T_interval": 17
    }
  ],
  "n_random": 2360,
  "random_ok": true,
  "witnesses": [
    {
      "name": "interval_30",
      "n": 30,
      "T": 300,
      "bound": 450,
      "T_interval": 300,
      "fibre_ok": true,
      "bound_sum": 450
    },
    {
      "name": "n3_013",
      "n": 3,
      "T": 4,
      "bound": 5,
      "T_interval": 3,
      "fibre_ok": true,
      "bound_sum": 5
    },
    {
      "name": "n6_hole",
      "n": 6,
      "T": 13,
      "bound": 18,
      "T_interval": 12,
      "fibre_ok": true,
      "bound_sum": 18
    },
    {
      "name": "n7_sparse",
      "n": 7,
      "T": 18,
      "bound": 25,
      "T_interval": 17,
      "fibre_ok": true,
      "bound_sum": 25
    },
    {
      "name": "n9_hole",
      "n": 9,
      "T": 28,
      "bound": 41,
      "T_interval": 27,
      "fibre_ok": true,
      "bound_sum": 41
    },
    {
      "name": "plus1_n36",
      "n": 36,
      "T": 433,
      "bound": 648,
      "T_interval": 432,
      "fibre_ok": true,
      "bound_sum": 648
    }
  ]
}