files / problems / kissing-5d / compute / q5_extend.json

1.7 KB · on GitHub

{
  "A4_vs_D4": {
    "A4_histogram": {
      "-1": 10,
      "-1/2": 60,
      "0": 60,
      "1/2": 60
    },
    "n_antipodal_20_subsets_of_D4": 66,
    "n_matching_A4_histogram": 0,
    "A4_is_D4_minus_two_pairs": false
  },
  "Q5_equator": {
    "max_norm2_on_A4_polytope_sum0": "6/5",
    "target_norm2": "2",
    "max_norm2_lt_2": true,
    "equatorial_extension_impossible": true,
    "two_level_vertices": [
      {
        "k_high": 1,
        "a^2": "8/5",
        "(a-b)^2": "5/2",
        "A4_feasible": false
      },
      {
        "k_high": 2,
        "a^2": "3/5",
        "(a-b)^2": "5/3",
        "A4_feasible": false
      },
      {
        "k_high": 3,
        "a^2": "4/15",
        "(a-b)^2": "5/3",
        "A4_feasible": false
      },
      {
        "k_high": 4,
        "a^2": "1/10",
        "(a-b)^2": "5/2",
        "A4_feasible": false
      }
    ]
  },
  "numerical_41st_L5": {
    "method": "Powell-on-sphere",
    "n_starts": 91,
    "best_slack": -0.26491106406735176,
    "best_x": [
      1.2649110640673515,
      0.0,
      0.0,
      0.0,
      0.632455532033676
    ],
    "positive_slack": false
  },
  "numerical_41st_Q5": {
    "method": "Powell-on-sphere",
    "n_starts": 91,
    "best_slack": -0.264911064067352,
    "best_x": [
      0.632455532033676,
      0.632455532033676,
      0.632455532033676,
      0.632455532033676,
      0.632455532033676
    ],
    "positive_slack": false
  },
  "numerical_41st_R5": {
    "method": "Powell-on-sphere",
    "n_starts": 91,
    "best_slack": -0.264911064067352,
    "best_x": [
      0.632455532033676,
      0.632455532033676,
      0.632455532033676,
      0.632455532033676,
      0.632455532033676
    ],
    "positive_slack": false
  }
}