files / problems / one-third-two-thirds / compute / q1 / ladder_census.json

7.8 KB · on GitHub

{
  "named": [
    {
      "n": 7,
      "broken": [
        1,
        2
      ],
      "delta": [
        9,
        25
      ],
      "e": 25,
      "pair": [
        0,
        1,
        16,
        9
      ],
      "width": 2,
      "n_summands": 1,
      "published_delta": [
        9,
        25
      ]
    },
    {
      "n": 8,
      "broken": [
        1,
        2,
        3
      ],
      "delta": [
        17,
        46
      ],
      "e": 46,
      "pair": [
        3,
        4,
        29,
        17
      ],
      "width": 2,
      "n_summands": 1,
      "published_delta": [
        17,
        46
      ]
    },
    {
      "n": 9,
      "broken": [
        1,
        2,
        3,
        4
      ],
      "delta": [
        6,
        17
      ],
      "e": 85,
      "pair": [
        0,
        1,
        55,
        30
      ],
      "width": 2,
      "n_summands": 1,
      "published_delta": [
        6,
        17
      ]
    },
    {
      "n": 10,
      "broken": [
        1,
        5
      ],
      "delta": [
        37,
        106
      ],
      "e": 106,
      "pair": [
        0,
        1,
        69,
        37
      ],
      "width": 2,
      "n_summands": 1,
      "published_delta": [
        37,
        106
      ]
    },
    {
      "n": 11,
      "broken": [
        1,
        6
      ],
      "delta": [
        20,
        57
      ],
      "e": 171,
      "pair": [
        0,
        1,
        111,
        60
      ],
      "width": 2,
      "n_summands": 1,
      "published_delta": [
        20,
        57
      ]
    },
    {
      "n": 12,
      "broken": [
        1,
        7
      ],
      "delta": [
        97,
        277
      ],
      "e": 277,
      "pair": [
        0,
        1,
        180,
        97
      ],
      "width": 2,
      "n_summands": 1,
      "published_delta": [
        97,
        277
      ]
    },
    {
      "n": 13,
      "broken": [
        1,
        8
      ],
      "delta": [
        157,
        448
      ],
      "e": 448,
      "pair": [
        0,
        1,
        291,
        157
      ],
      "width": 2,
      "n_summands": 1,
      "published_delta": [
        157,
        448
      ]
    },
    {
      "n": 14,
      "broken": [
        1,
        9
      ],
      "delta": [
        254,
        725
      ],
      "e": 725,
      "pair": [
        0,
        1,
        471,
        254
      ],
      "width": 2,
      "n_summands": 1,
      "published_delta": [
        254,
        725
      ]
    },
    {
      "n": 15,
      "broken": [
        1,
        5,
        6,
        10
      ],
      "delta": [
        166,
        475
      ],
      "e": 1425,
      "pair": [
        0,
        1,
        927,
        498
      ],
      "width": 2,
      "n_summands": 1,
      "published_delta": null
    },
    {
      "n": 17,
      "broken": [
        1,
        5,
        8,
        12
      ],
      "delta": [
        1304,
        3737
      ],
      "e": 3737,
      "pair": [
        0,
        1,
        2433,
        1304
      ],
      "width": null,
      "n_summands": 1,
      "published_delta": null
    }
  ],
  "census": [
    {
      "n": 7,
      "min_delta": [
        9,
        25
      ],
      "broken": [
        1,
        2
      ],
      "e": 25,
      "n_non_sum": 16,
      "n_skipped_sums": 0,
      "pair": [
        0,
        1,
        16,
        9
      ]
    },
    {
      "n": 8,
      "min_delta": [
        17,
        46
      ],
      "broken": [
        1,
        2,
        3
      ],
      "e": 46,
      "n_non_sum": 32,
      "n_skipped_sums": 0,
      "pair": [
        3,
        4,
        29,
        17
      ]
    },
    {
      "n": 9,
      "min_delta": [
        6,
        17
      ],
      "broken": [
        1,
        2,
        3,
        4
      ],
      "e": 85,
      "n_non_sum": 64,
      "n_skipped_sums": 0,
      "pair": [
        0,
        1,
        55,
        30
      ]
    },
    {
      "n": 10,
      "min_delta": [
        37,
        106
      ],
      "broken": [
        1,
        5
      ],
      "e": 106,
      "n_non_sum": 128,
      "n_skipped_sums": 0,
      "pair": [
        0,
        1,
        69,
        37
      ]
    },
    {
      "n": 11,
      "min_delta": [
        20,
        57
      ],
      "broken": [
        1,
        6
      ],
      "e": 171,
      "n_non_sum": 256,
      "n_skipped_sums": 0,
      "pair": [
        0,
        1,
        111,
        60
      ]
    },
    {
      "n": 12,
      "min_delta": [
        97,
        277
      ],
      "broken": [
        1,
        7
      ],
      "e": 277,
      "n_non_sum": 512,
      "n_skipped_sums": 0,
      "pair": [
        0,
        1,
        180,
        97
      ]
    },
    {
      "n": 13,
      "min_delta": [
        157,
        448
      ],
      "broken": [
        1,
        8
      ],
      "e": 448,
      "n_non_sum": 1024,
      "n_skipped_sums": 0,
      "pair": [
        0,
        1,
        291,
        157
      ]
    },
    {
      "n": 14,
      "min_delta": [
        254,
        725
      ],
      "broken": [
        1,
        9
      ],
      "e": 725,
      "n_non_sum": 2048,
      "n_skipped_sums": 0,
      "pair": [
        0,
        1,
        471,
        254
      ]
    },
    {
      "n": 15,
      "min_delta": [
        166,
        475
      ],
      "broken": [
        1,
        5,
        6,
        10
      ],
      "e": 1425,
      "n_non_sum": 4096,
      "n_skipped_sums": 0,
      "c_replay": true,
      "pair": [
        0,
        1,
        927,
        498
      ]
    },
    {
      "n": 16,
      "min_delta": [
        665,
        1898
      ],
      "broken": [
        1,
        11
      ],
      "e": 1898,
      "n_non_sum": 8192,
      "n_skipped_sums": 0,
      "c_replay": true,
      "pair": [
        0,
        1,
        1233,
        665
      ]
    },
    {
      "n": 17,
      "min_delta": [
        1304,
        3737
      ],
      "broken": [
        1,
        5,
        8,
        12
      ],
      "e": 3737,
      "n_non_sum": 16384,
      "n_skipped_sums": 0,
      "c_replay": true,
      "pair": [
        0,
        1,
        2433,
        1304
      ]
    },
    {
      "n": 18,
      "min_delta": [
        387,
        1108
      ],
      "broken": [
        1,
        5,
        6,
        9,
        13
      ],
      "e": 6648,
      "n_non_sum": 32768,
      "n_skipped_sums": 0,
      "c_replay": true,
      "pair": [
        0,
        1,
        4326,
        2322
      ]
    },
    {
      "n": 19,
      "min_delta": [
        458,
        1311
      ],
      "broken": [
        1,
        5,
        6,
        9,
        10,
        14
      ],
      "e": 11799,
      "source": "C exhaustive; Python replay of the witness",
      "pair": [
        0,
        1,
        7677,
        4122
      ]
    },
    {
      "n": 20,
      "min_delta": [
        6059,
        17366
      ],
      "broken": [
        1,
        5,
        8,
        11,
        15
      ],
      "e": 17366,
      "source": "C exhaustive; Python replay of the witness",
      "pair": [
        0,
        1,
        11307,
        6059
      ]
    },
    {
      "n": 21,
      "min_delta": [
        5402,
        15485
      ],
      "broken": [
        1,
        5,
        8,
        9,
        12,
        16
      ],
      "e": 30970,
      "source": "C exhaustive; Python replay of the witness",
      "pair": [
        0,
        1,
        20166,
        10804
      ]
    }
  ],
  "note": "Non-sum broken-rung ladder minima. n=7..18: Python combinations over every rung subset, independently matching Gupta Table 1 through 14 and Peczarski's named broken sets at 15 and 17. n=15..18 also from the C enumerator (same mins). n=19..21: C enumerator over every 2^{n-3} subset; the winning ladder is replayed by ladders.named. n=22 was left running and is not a row. Fractions reduced."
}