files / problems / ramsey-r55 / compute / q7 / certs / cases.json

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{
  "degree_window": [
    18,
    24
  ],
  "n": 43,
  "note": "Representatives for leftover order-2/3/5 automorphisms on 43 vertices after q3. q4 closed 5^6 1^13 (k=2,3) and 5^7 1^8 (k=3). q5 closed 5^4 1^23 at k=4 (covers k=0). q6 closed 5^5 1^18 at k=2 (covers k=3). leftover_q7 skips those five. This list is not a bound on R(5,5).",
  "primes": [
    2,
    3,
    5
  ],
  "q4_closed": [
    "p5_c6_k2",
    "p5_c6_k3",
    "p5_c7_k3"
  ],
  "q5_closed": [
    "p5_c4_k4"
  ],
  "q6_closed": [
    "p5_c5_k2"
  ],
  "q7_names": [
    "p2_c1_k1",
    "p2_c2_k1",
    "p2_c2_k2",
    "p2_c3_k1",
    "p2_c3_k3",
    "p2_c4_k1",
    "p2_c4_k2",
    "p2_c4_k4",
    "p2_c5_k1",
    "p2_c5_k2",
    "p2_c5_k5",
    "p2_c6_k1",
    "p2_c6_k2",
    "p2_c6_k3",
    "p2_c6_k6",
    "p2_c7_k1",
    "p2_c7_k2",
    "p2_c7_k3",
    "p2_c7_k7",
    "p2_c8_k1",
    "p2_c8_k2",
    "p2_c8_k3",
    "p2_c8_k4",
    "p2_c8_k8",
    "p2_c9_k1",
    "p2_c9_k2",
    "p2_c9_k3",
    "p2_c9_k4",
    "p2_c9_k9",
    "p2_c10_k1",
    "p2_c10_k2",
    "p2_c10_k3",
    "p2_c10_k4",
    "p2_c10_k5",
    "p2_c10_k10",
    "p2_c11_k1",
    "p2_c11_k2",
    "p2_c11_k3",
    "p2_c11_k4",
    "p2_c11_k5",
    "p2_c11_k11",
    "p2_c12_k1",
    "p2_c12_k2",
    "p2_c12_k3",
    "p2_c12_k4",
    "p2_c12_k5",
    "p2_c12_k6",
    "p2_c12_k12",
    "p2_c13_k1",
    "p2_c13_k2",
    "p2_c13_k3",
    "p2_c13_k4",
    "p2_c13_k5",
    "p2_c13_k6",
    "p2_c14_k2",
    "p2_c14_k3",
    "p2_c14_k4",
    "p2_c14_k5",
    "p2_c14_k6",
    "p2_c14_k7",
    "p2_c15_k3",
    "p2_c15_k4",
    "p2_c15_k5",
    "p2_c15_k6",
    "p2_c15_k7",
    "p2_c16_k4",
    "p2_c16_k5",
    "p2_c16_k6",
    "p2_c16_k7",
    "p2_c16_k8",
    "p2_c17_k5",
    "p2_c17_k6",
    "p2_c17_k7",
    "p2_c17_k8",
    "p2_c18_k6",
    "p2_c18_k7",
    "p2_c18_k8",
    "p2_c18_k9",
    "p2_c19_k7",
    "p2_c19_k8",
    "p2_c19_k9",
    "p2_c20_k8",
    "p2_c20_k9",
    "p2_c20_k10",
    "p2_c21_k9",
    "p2_c21_k10",
    "p3_c1_k1",
    "p3_c2_k1",
    "p3_c2_k2",
    "p3_c3_k1",
    "p3_c3_k3",
    "p3_c4_k1",
    "p3_c4_k2",
    "p3_c4_k4",
    "p3_c5_k1",
    "p3_c5_k2",
    "p3_c5_k5",
    "p3_c6_k1",
    "p3_c6_k2",
    "p3_c6_k3",
    "p3_c6_k6",
    "p3_c7_k1",
    "p3_c7_k2",
    "p3_c7_k3",
    "p3_c7_k7",
    "p3_c8_k1",
    "p3_c8_k2",
    "p3_c8_k3",
    "p3_c8_k4",
    "p3_c8_k8",
    "p3_c9_k1",
    "p3_c9_k2",
    "p3_c9_k3",
    "p3_c9_k4",
    "p3_c10_k2",
    "p3_c10_k3",
    "p3_c10_k4",
    "p3_c10_k5",
    "p3_c11_k3",
    "p3_c11_k4",
    "p3_c11_k5",
    "p3_c12_k4",
    "p3_c12_k5",
    "p3_c12_k6",
    "p3_c13_k5",
    "p3_c13_k6",
    "p3_c14_k6",
    "p3_c14_k7",
    "p5_c1_k1",
    "p5_c2_k1",
    "p5_c2_k2",
    "p5_c3_k1",
    "p5_c3_k3",
    "p5_c4_k1",
    "p5_c4_k2",
    "p5_c5_k1",
    "p5_c8_k4"
  ],
  "q7_total": 137,
  "representatives": [
    {
      "anchor_symbreak": true,
      "covers_k": [
        0,
        1
      ],
      "cycle_type": "2^1 1^41",
      "cycles": 1,
      "expected_cnf_sha256": null,
      "fixed": 41,
      "fixed_cycle_count": 1,
      "maximum_cycle": false,
      "name": "p2_c1_k1",
      "p": 2,
      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
      "covers_k": [
        1
      ],
      "cycle_type": "2^2 1^39",
      "cycles": 2,
      "expected_cnf_sha256": null,
      "fixed": 39,
      "fixed_cycle_count": 1,
      "maximum_cycle": false,
      "name": "p2_c2_k1",
      "p": 2,
      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
      "covers_k": [
        0,
        2
      ],
      "cycle_type": "2^2 1^39",
      "cycles": 2,
      "expected_cnf_sha256": null,
      "fixed": 39,
      "fixed_cycle_count": 2,
      "maximum_cycle": false,
      "name": "p2_c2_k2",
      "p": 2,
      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
      "covers_k": [
        1,
        2
      ],
      "cycle_type": "2^3 1^37",
      "cycles": 3,
      "expected_cnf_sha256": null,
      "fixed": 37,
      "fixed_cycle_count": 1,
      "maximum_cycle": false,
      "name": "p2_c3_k1",
      "p": 2,
      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
      "covers_k": [
        0,
        3
      ],
      "cycle_type": "2^3 1^37",
      "cycles": 3,
      "expected_cnf_sha256": null,
      "fixed": 37,
      "fixed_cycle_count": 3,
      "maximum_cycle": false,
      "name": "p2_c3_k3",
      "p": 2,
      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
      "covers_k": [
        1,
        3
      ],
      "cycle_type": "2^4 1^35",
      "cycles": 4,
      "expected_cnf_sha256": null,
      "fixed": 35,
      "fixed_cycle_count": 1,
      "maximum_cycle": false,
      "name": "p2_c4_k1",
      "p": 2,
      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
      "covers_k": [
        2
      ],
      "cycle_type": "2^4 1^35",
      "cycles": 4,
      "expected_cnf_sha256": null,
      "fixed": 35,
      "fixed_cycle_count": 2,
      "maximum_cycle": false,
      "name": "p2_c4_k2",
      "p": 2,
      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
      "covers_k": [
        0,
        4
      ],
      "cycle_type": "2^4 1^35",
      "cycles": 4,
      "expected_cnf_sha256": null,
      "fixed": 35,
      "fixed_cycle_count": 4,
      "maximum_cycle": false,
      "name": "p2_c4_k4",
      "p": 2,
      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
      "covers_k": [
        1,
        4
      ],
      "cycle_type": "2^5 1^33",
      "cycles": 5,
      "expected_cnf_sha256": null,
      "fixed": 33,
      "fixed_cycle_count": 1,
      "maximum_cycle": false,
      "name": "p2_c5_k1",
      "p": 2,
      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
      "covers_k": [
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        3
      ],
      "cycle_type": "2^5 1^33",
      "cycles": 5,
      "expected_cnf_sha256": null,
      "fixed": 33,
      "fixed_cycle_count": 2,
      "maximum_cycle": false,
      "name": "p2_c5_k2",
      "p": 2,
      "p5_symbreak": false
    },
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      "anchor_symbreak": true,
      "covers_k": [
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        5
      ],
      "cycle_type": "2^5 1^33",
      "cycles": 5,
      "expected_cnf_sha256": null,
      "fixed": 33,
      "fixed_cycle_count": 5,
      "maximum_cycle": false,
      "name": "p2_c5_k5",
      "p": 2,
      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
      "covers_k": [
        1,
        5
      ],
      "cycle_type": "2^6 1^31",
      "cycles": 6,
      "expected_cnf_sha256": null,
      "fixed": 31,
      "fixed_cycle_count": 1,
      "maximum_cycle": false,
      "name": "p2_c6_k1",
      "p": 2,
      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
      "covers_k": [
        2,
        4
      ],
      "cycle_type": "2^6 1^31",
      "cycles": 6,
      "expected_cnf_sha256": null,
      "fixed": 31,
      "fixed_cycle_count": 2,
      "maximum_cycle": false,
      "name": "p2_c6_k2",
      "p": 2,
      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
      "covers_k": [
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      ],
      "cycle_type": "2^6 1^31",
      "cycles": 6,
      "expected_cnf_sha256": null,
      "fixed": 31,
      "fixed_cycle_count": 3,
      "maximum_cycle": false,
      "name": "p2_c6_k3",
      "p": 2,
      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
      "covers_k": [
        0,
        6
      ],
      "cycle_type": "2^6 1^31",
      "cycles": 6,
      "expected_cnf_sha256": null,
      "fixed": 31,
      "fixed_cycle_count": 6,
      "maximum_cycle": false,
      "name": "p2_c6_k6",
      "p": 2,
      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
      "covers_k": [
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        6
      ],
      "cycle_type": "2^7 1^29",
      "cycles": 7,
      "expected_cnf_sha256": null,
      "fixed": 29,
      "fixed_cycle_count": 1,
      "maximum_cycle": false,
      "name": "p2_c7_k1",
      "p": 2,
      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
      "covers_k": [
        2,
        5
      ],
      "cycle_type": "2^7 1^29",
      "cycles": 7,
      "expected_cnf_sha256": null,
      "fixed": 29,
      "fixed_cycle_count": 2,
      "maximum_cycle": false,
      "name": "p2_c7_k2",
      "p": 2,
      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
      "covers_k": [
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        4
      ],
      "cycle_type": "2^7 1^29",
      "cycles": 7,
      "expected_cnf_sha256": null,
      "fixed": 29,
      "fixed_cycle_count": 3,
      "maximum_cycle": false,
      "name": "p2_c7_k3",
      "p": 2,
      "p5_symbreak": false
    },
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      "anchor_symbreak": true,
      "covers_k": [
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        7
      ],
      "cycle_type": "2^7 1^29",
      "cycles": 7,
      "expected_cnf_sha256": null,
      "fixed": 29,
      "fixed_cycle_count": 7,
      "maximum_cycle": false,
      "name": "p2_c7_k7",
      "p": 2,
      "p5_symbreak": false
    },
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      "anchor_symbreak": true,
      "covers_k": [
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        7
      ],
      "cycle_type": "2^8 1^27",
      "cycles": 8,
      "expected_cnf_sha256": null,
      "fixed": 27,
      "fixed_cycle_count": 1,
      "maximum_cycle": false,
      "name": "p2_c8_k1",
      "p": 2,
      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
      "covers_k": [
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        6
      ],
      "cycle_type": "2^8 1^27",
      "cycles": 8,
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      "maximum_cycle": false,
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      "p": 2,
      "p5_symbreak": false
    },
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      "anchor_symbreak": true,
      "covers_k": [
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        5
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      "cycles": 8,
      "expected_cnf_sha256": null,
      "fixed": 27,
      "fixed_cycle_count": 3,
      "maximum_cycle": false,
      "name": "p2_c8_k3",
      "p": 2,
      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
      "covers_k": [
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      ],
      "cycle_type": "2^8 1^27",
      "cycles": 8,
      "expected_cnf_sha256": null,
      "fixed": 27,
      "fixed_cycle_count": 4,
      "maximum_cycle": false,
      "name": "p2_c8_k4",
      "p": 2,
      "p5_symbreak": false
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      "anchor_symbreak": true,
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        8
      ],
      "cycle_type": "2^8 1^27",
      "cycles": 8,
      "expected_cnf_sha256": null,
      "fixed": 27,
      "fixed_cycle_count": 8,
      "maximum_cycle": false,
      "name": "p2_c8_k8",
      "p": 2,
      "p5_symbreak": false
    },
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      "anchor_symbreak": true,
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        8
      ],
      "cycle_type": "2^9 1^25",
      "cycles": 9,
      "expected_cnf_sha256": null,
      "fixed": 25,
      "fixed_cycle_count": 1,
      "maximum_cycle": false,
      "name": "p2_c9_k1",
      "p": 2,
      "p5_symbreak": false
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      "anchor_symbreak": true,
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        7
      ],
      "cycle_type": "2^9 1^25",
      "cycles": 9,
      "expected_cnf_sha256": null,
      "fixed": 25,
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      "maximum_cycle": false,
      "name": "p2_c9_k2",
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      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
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        6
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      "cycle_type": "2^9 1^25",
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      "name": "p2_c9_k3",
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      "p5_symbreak": false
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    {
      "anchor_symbreak": true,
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        5
      ],
      "cycle_type": "2^9 1^25",
      "cycles": 9,
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      "fixed": 25,
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      "maximum_cycle": false,
      "name": "p2_c9_k4",
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      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
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        9
      ],
      "cycle_type": "2^9 1^25",
      "cycles": 9,
      "expected_cnf_sha256": null,
      "fixed": 25,
      "fixed_cycle_count": 9,
      "maximum_cycle": false,
      "name": "p2_c9_k9",
      "p": 2,
      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
      "covers_k": [
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        9
      ],
      "cycle_type": "2^10 1^23",
      "cycles": 10,
      "expected_cnf_sha256": null,
      "fixed": 23,
      "fixed_cycle_count": 1,
      "maximum_cycle": false,
      "name": "p2_c10_k1",
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      "p5_symbreak": false
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    {
      "anchor_symbreak": true,
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        8
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      "cycles": 10,
      "expected_cnf_sha256": null,
      "fixed": 23,
      "fixed_cycle_count": 2,
      "maximum_cycle": false,
      "name": "p2_c10_k2",
      "p": 2,
      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
      "covers_k": [
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        7
      ],
      "cycle_type": "2^10 1^23",
      "cycles": 10,
      "expected_cnf_sha256": null,
      "fixed": 23,
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      "maximum_cycle": false,
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      "p5_symbreak": false
    },
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      "anchor_symbreak": true,
      "covers_k": [
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        6
      ],
      "cycle_type": "2^10 1^23",
      "cycles": 10,
      "expected_cnf_sha256": null,
      "fixed": 23,
      "fixed_cycle_count": 4,
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      "p5_symbreak": false
    },
    {
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      "covers_k": [
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      "cycle_type": "2^10 1^23",
      "cycles": 10,
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      "fixed": 23,
      "fixed_cycle_count": 5,
      "maximum_cycle": false,
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    {
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        10
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      "cycle_type": "2^10 1^23",
      "cycles": 10,
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      "fixed": 23,
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      "maximum_cycle": false,
      "name": "p2_c10_k10",
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        10
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        9
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      "fixed": 21,
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      "anchor_symbreak": true,
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        8
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      "cycles": 11,
      "expected_cnf_sha256": null,
      "fixed": 21,
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      "maximum_cycle": false,
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      "p": 2,
      "p5_symbreak": false
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    {
      "anchor_symbreak": true,
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        7
      ],
      "cycle_type": "2^11 1^21",
      "cycles": 11,
      "expected_cnf_sha256": null,
      "fixed": 21,
      "fixed_cycle_count": 4,
      "maximum_cycle": false,
      "name": "p2_c11_k4",
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      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
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        6
      ],
      "cycle_type": "2^11 1^21",
      "cycles": 11,
      "expected_cnf_sha256": null,
      "fixed": 21,
      "fixed_cycle_count": 5,
      "maximum_cycle": false,
      "name": "p2_c11_k5",
      "p": 2,
      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
      "covers_k": [
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        11
      ],
      "cycle_type": "2^11 1^21",
      "cycles": 11,
      "expected_cnf_sha256": null,
      "fixed": 21,
      "fixed_cycle_count": 11,
      "maximum_cycle": false,
      "name": "p2_c11_k11",
      "p": 2,
      "p5_symbreak": false
    },
    {
      "anchor_symbreak": true,
      "covers_k": [
        1,
        11
      ],
      "cycle_type": "2^12 1^19",
      "cycles": 12,
      "expected_cnf_sha256": null,
      "fixed": 19,
      "fixed_cycle_count": 1,
      "maximum_cycle": false,
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      "name": "p5_c6_k3",
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      "cycle_type": "5^7 1^8",
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      "fixed": 8,
      "fixed_cycle_count": 3,
      "maximum_cycle": false,
      "name": "p5_c7_k3",
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    {
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      "cycle_type": "5^8 1^3",
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      "expected_cnf_sha256": "de64155ef134bc37a27659db67cbba31ee6d998e52dedd8ce9f4c80cabda627d",
      "fixed": 3,
      "fixed_cycle_count": 4,
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  ],
  "total": 142,
  "totals_by_prime": {
    "2": 86,
    "3": 42,
    "5": 14
  }
}