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

3.3 KB · on GitHub

{
  "n": 240,
  "n_seeds": 240,
  "n_four": 160,
  "n_six": 80,
  "edges": 27720,
  "min_deg": 231,
  "max_deg": 231,
  "mean_deg": 231.0,
  "regular": true,
  "seed_clique_20_exists": true,
  "seed_clique_20": [
    222,
    223,
    236,
    219,
    234,
    217,
    214,
    212,
    211,
    230,
    209,
    207,
    205,
    204,
    202,
    200,
    199,
    197,
    196,
    195
  ],
  "seed_clique_20_union": 29,
  "seed_clique_20_promising": false,
  "seed_clique_20_nodes": 20,
  "seed_clique_20_complete": true,
  "seed_clique_best": 80,
  "seed_clique_best_union": 40,
  "seed_clique_best_source": "all 80 six-seeds form a clique",
  "omega_ge": 80,
  "omega_81": {
    "best": 80,
    "nodes": 400001,
    "node_limit": 400000,
    "complete": false,
    "status": "residue"
  },
  "leftover_search": {
    "target": "|C|>=20 and |U|<=|C|-1",
    "prune": "|U_so_far| > |stack| + remaining - 1",
    "nodes": 33,
    "node_limit": 5000000,
    "best_seen": 33,
    "hit": {
      "seed_clique": [
        222,
        223,
        236,
        219,
        234,
        217,
        214,
        212,
        211,
        230,
        209,
        207,
        205,
        204,
        202,
        200,
        199,
        197,
        196,
        195,
        194,
        193,
        192,
        188,
        186,
        180,
        174,
        172,
        170,
        168,
        162,
        158,
        154
      ],
      "size": 33,
      "union": 32
    },
    "existence_complete": true,
    "census_complete": false,
    "status": "hit"
  },
  "triple_star_leftover": {
    "n_pools": 120,
    "pairs": [
      {
        "best": 22,
        "union": 21,
        "star_union": 21,
        "n_seeds_in_pool": 52,
        "complete": true,
        "n_pools": 80,
        "promising": true
      },
      {
        "best": 23,
        "union": 22,
        "star_union": 22,
        "n_seeds_in_pool": 48,
        "complete": true,
        "n_pools": 40,
        "promising": true
      }
    ],
    "witness": {
      "seed_clique": [
        163,
        160,
        138,
        137,
        135,
        132,
        130,
        129,
        82,
        81,
        59,
        56,
        54,
        53,
        51,
        48,
        15,
        12,
        10,
        9,
        6,
        5
      ],
      "size": 22,
      "union": 21,
      "star_union": 21,
      "n_seeds_in_pool": 52
    }
  },
  "promising": [
    {
      "size": 33,
      "union": 32,
      "source": "coloured B&B"
    },
    {
      "size": 80,
      "union": 40,
      "source": "all 80 six-seeds"
    },
    {
      "size": 22,
      "union": 21,
      "source": "3-star leftover",
      "n_pools": 80
    },
    {
      "size": 23,
      "union": 22,
      "source": "3-star leftover",
      "n_pools": 40
    }
  ],
  "found_41": false,
  "comment": "A seed-clique is a pool for extras SAT/B&B, not a 41-code. Compatibility only asks that some extras of the two seeds kiss.  The 80 six-seeds are a clique of union 40.  Three coordinate-stars give leftover-tight pools (22, 21) and (23, 22).  The coloured leftover search found a pair and stopped; that is existence, not a census.  No 81-clique inside the node limit (residue, not omega=80).  This file does not claim tau5=40 and does not write certs/code41.json."
}