files / problems / caccetta-haggkvist-k3 / compute / q3 / certs / keep / summary.json

5.7 KB · on GitHub

{
  "published_hkn": 0.3465,
  "repo_f4": 0.34645,
  "personal_communication_3388": 0.3388,
  "exact_orders": [
    38,
    39,
    41,
    42,
    44,
    45,
    47,
    48,
    50,
    51,
    52,
    53,
    54,
    55,
    56,
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    58,
    59,
    60,
    61,
    62,
    63,
    64,
    65,
    66,
    67,
    68,
    69,
    70,
    71,
    72
  ],
  "n_orders": 31,
  "n_cubes": 534,
  "failures": 0,
  "orders": [
    {
      "n": 38,
      "d": 13,
      "cubes": 11,
      "k_min": 13,
      "k_max": 23,
      "drat_bytes": 3926383,
      "all_verified": true
    },
    {
      "n": 39,
      "d": 13,
      "cubes": 12,
      "k_min": 13,
      "k_max": 24,
      "drat_bytes": 4590711,
      "all_verified": true
    },
    {
      "n": 41,
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      "k_min": 14,
      "k_max": 25,
      "drat_bytes": 5483804,
      "all_verified": true
    },
    {
      "n": 42,
      "d": 14,
      "cubes": 13,
      "k_min": 14,
      "k_max": 26,
      "drat_bytes": 6355700,
      "all_verified": true
    },
    {
      "n": 44,
      "d": 15,
      "cubes": 13,
      "k_min": 15,
      "k_max": 27,
      "drat_bytes": 7427300,
      "all_verified": true
    },
    {
      "n": 45,
      "d": 15,
      "cubes": 14,
      "k_min": 15,
      "k_max": 28,
      "drat_bytes": 8543755,
      "all_verified": true
    },
    {
      "n": 47,
      "d": 16,
      "cubes": 14,
      "k_min": 16,
      "k_max": 29,
      "drat_bytes": 9870092,
      "all_verified": true
    },
    {
      "n": 48,
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      "k_min": 16,
      "k_max": 30,
      "drat_bytes": 11216225,
      "all_verified": true
    },
    {
      "n": 50,
      "d": 17,
      "cubes": 15,
      "k_min": 17,
      "k_max": 31,
      "drat_bytes": 13046416,
      "all_verified": true
    },
    {
      "n": 51,
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      "cubes": 16,
      "k_min": 17,
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      "drat_bytes": 14569776,
      "all_verified": true
    },
    {
      "n": 52,
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      "all_verified": true
    },
    {
      "n": 53,
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      "drat_bytes": 16623123,
      "all_verified": true
    },
    {
      "n": 54,
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      "drat_bytes": 18590473,
      "all_verified": true
    },
    {
      "n": 55,
      "d": 19,
      "cubes": 16,
      "k_min": 19,
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      "drat_bytes": 18759950,
      "all_verified": true
    },
    {
      "n": 56,
      "d": 19,
      "cubes": 17,
      "k_min": 19,
      "k_max": 35,
      "drat_bytes": 21568043,
      "all_verified": true
    },
    {
      "n": 57,
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      "k_min": 19,
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      "drat_bytes": 23480432,
      "all_verified": true
    },
    {
      "n": 58,
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      "all_verified": true
    },
    {
      "n": 59,
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      "all_verified": true
    },
    {
      "n": 60,
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      "k_min": 20,
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      "drat_bytes": 29113772,
      "all_verified": true
    },
    {
      "n": 61,
      "d": 21,
      "cubes": 18,
      "k_min": 21,
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      "drat_bytes": 30311190,
      "all_verified": true
    },
    {
      "n": 62,
      "d": 21,
      "cubes": 19,
      "k_min": 21,
      "k_max": 39,
      "drat_bytes": 32933513,
      "all_verified": true
    },
    {
      "n": 63,
      "d": 21,
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      "k_min": 21,
      "k_max": 40,
      "drat_bytes": 36334158,
      "all_verified": true
    },
    {
      "n": 64,
      "d": 22,
      "cubes": 19,
      "k_min": 22,
      "k_max": 40,
      "drat_bytes": 35980866,
      "all_verified": true
    },
    {
      "n": 65,
      "d": 22,
      "cubes": 20,
      "k_min": 22,
      "k_max": 41,
      "drat_bytes": 40470466,
      "all_verified": true
    },
    {
      "n": 66,
      "d": 22,
      "cubes": 21,
      "k_min": 22,
      "k_max": 42,
      "drat_bytes": 45383370,
      "all_verified": true
    },
    {
      "n": 67,
      "d": 23,
      "cubes": 20,
      "k_min": 23,
      "k_max": 42,
      "drat_bytes": 44277073,
      "all_verified": true
    },
    {
      "n": 68,
      "d": 23,
      "cubes": 21,
      "k_min": 23,
      "k_max": 43,
      "drat_bytes": 48680730,
      "all_verified": true
    },
    {
      "n": 69,
      "d": 23,
      "cubes": 22,
      "k_min": 23,
      "k_max": 44,
      "drat_bytes": 54484084,
      "all_verified": true
    },
    {
      "n": 70,
      "d": 24,
      "cubes": 21,
      "k_min": 24,
      "k_max": 44,
      "drat_bytes": 52783393,
      "all_verified": true
    },
    {
      "n": 71,
      "d": 24,
      "cubes": 22,
      "k_min": 24,
      "k_max": 45,
      "drat_bytes": 58333816,
      "all_verified": true
    },
    {
      "n": 72,
      "d": 24,
      "cubes": 23,
      "k_min": 24,
      "k_max": 46,
      "drat_bytes": 63979405,
      "all_verified": true
    }
  ],
  "method": "Sinz sequential counters, N+(0)={1..d}, cubes on k=|N-(0)| with N-(0)={d+1..d+k}. Pigeonhole: n*d arcs so some in-degree is at least d. Each needed cube has a stored DRAT.",
  "soundness": "n=21 d=6 k=6 SAT with a checked C3-free model; n=38 d=12 circulant is C3-free and satisfies the cube arc clauses after placing neighbourhoods of 0.",
  "f4": "unchanged at 0.34645; extra non-edge SOS did not certify any c<0.34645",
  "next_hole": {
    "n": 73,
    "d": 25
  },
  "replay": "./run_all.sh from compute/q3 after ./build_solvers.sh"
}