{
  "status": "PASS",
  "version": "0.1",
  "reading_edition": "0.10",
  "physical_promotion": 0,
  "constructor_team_AI": true,
  "independent_human_review": "PENDING",
  "scope": "Exact finite algebra and family-specific full-generator exclusion; no endpoint-error lower bound or source-selected metric.",
  "gram_cases": [
    {
      "q": "1/4",
      "rule": "A",
      "p": 1,
      "squared_frequencies": [
        "32/5",
        "26/5",
        "5",
        "13/2",
        "8"
      ],
      "signed_multiplicities": [
        1,
        2,
        1,
        2,
        1
      ],
      "distinct_positive_bands": 5,
      "characteristic_coefficients": [
        "1",
        "0",
        "214/5",
        "0",
        "15633/20",
        "0",
        "3948453/500",
        "0",
        "5958732/125",
        "0",
        "4298853/25",
        "0",
        "42903016/125",
        "0",
        "7311616/25",
        "0"
      ]
    },
    {
      "q": "1/4",
      "rule": "B",
      "p": 2,
      "squared_frequencies": [
        "256/25",
        "178/25",
        "25/4",
        "89/8",
        "16"
      ],
      "signed_multiplicities": [
        1,
        2,
        1,
        2,
        1
      ],
      "distinct_positive_bands": 5,
      "characteristic_coefficients": [
        "1",
        "0",
        "3449/50",
        "0",
        "16037601/8000",
        "0",
        "127358369249/4000000",
        "0",
        "298615999817/1000000",
        "0",
        "330904123629/200000",
        "0",
        "313542717409/62500",
        "0",
        "4015503424/625",
        "0"
      ]
    },
    {
      "q": "1",
      "rule": "A",
      "p": 1,
      "squared_frequencies": [
        "4",
        "4",
        "4",
        "4",
        "4"
      ],
      "signed_multiplicities": [
        1,
        2,
        1,
        2,
        1
      ],
      "distinct_positive_bands": 1,
      "characteristic_coefficients": [
        "1",
        "0",
        "28",
        "0",
        "336",
        "0",
        "2240",
        "0",
        "8960",
        "0",
        "21504",
        "0",
        "28672",
        "0",
        "16384",
        "0"
      ]
    },
    {
      "q": "1",
      "rule": "B",
      "p": 2,
      "squared_frequencies": [
        "4",
        "4",
        "4",
        "4",
        "4"
      ],
      "signed_multiplicities": [
        1,
        2,
        1,
        2,
        1
      ],
      "distinct_positive_bands": 1,
      "characteristic_coefficients": [
        "1",
        "0",
        "28",
        "0",
        "336",
        "0",
        "2240",
        "0",
        "8960",
        "0",
        "21504",
        "0",
        "28672",
        "0",
        "16384",
        "0"
      ]
    },
    {
      "q": "4",
      "rule": "A",
      "p": 1,
      "squared_frequencies": [
        "8/5",
        "14/5",
        "10/3",
        "7/3",
        "3"
      ],
      "signed_multiplicities": [
        1,
        2,
        1,
        2,
        1
      ],
      "distinct_positive_bands": 5,
      "characteristic_coefficients": [
        "1",
        "0",
        "91/5",
        "0",
        "141",
        "0",
        "2033411/3375",
        "0",
        "1724282/1125",
        "0",
        "521948/225",
        "0",
        "6522488/3375",
        "0",
        "153664/225",
        "0"
      ]
    },
    {
      "q": "4",
      "rule": "B",
      "p": 2,
      "squared_frequencies": [
        "16/25",
        "58/25",
        "25/9",
        "29/18",
        "9/4"
      ],
      "signed_multiplicities": [
        1,
        2,
        1,
        2,
        1
      ],
      "distinct_positive_bands": 5,
      "characteristic_coefficients": [
        "1",
        "0",
        "1353/100",
        "0",
        "1038937/13500",
        "0",
        "43335872761/182250000",
        "0",
        "26065922999/60750000",
        "0",
        "227373601/506250",
        "0",
        "11382565801/45562500",
        "0",
        "2829124/50625",
        "0"
      ]
    },
    {
      "q": "9",
      "rule": "A",
      "p": 1,
      "squared_frequencies": [
        "4/5",
        "12/5",
        "60/19",
        "36/19",
        "76/27"
      ],
      "signed_multiplicities": [
        1,
        2,
        1,
        2,
        1
      ],
      "distinct_positive_bands": 5,
      "characteristic_coefficients": [
        "1",
        "0",
        "39404/2565",
        "0",
        "4843312/48735",
        "0",
        "900450752/2572125",
        "0",
        "619609344/857375",
        "0",
        "149134336/171475",
        "0",
        "480448512/857375",
        "0",
        "1327104/9025",
        "0"
      ]
    },
    {
      "q": "9",
      "rule": "B",
      "p": 2,
      "squared_frequencies": [
        "4/25",
        "52/25",
        "900/361",
        "468/361",
        "1444/729"
      ],
      "signed_multiplicities": [
        1,
        2,
        1,
        2,
        1
      ],
      "distinct_positive_bands": 5,
      "characteristic_coefficients": [
        "1",
        "0",
        "74915452/6579225",
        "0",
        "7878701456/146611125",
        "0",
        "24114160363569728/178627329421875",
        "0",
        "102854206185073408/535881988265625",
        "0",
        "595096954596352/3969496209375",
        "0",
        "40796990500864/735091890625",
        "0",
        "467943424/81450625",
        "0"
      ]
    }
  ],
  "degree_cases": [
    {
      "g": [
        "1",
        "1",
        "1",
        "1"
      ],
      "squared_frequencies": [
        "4",
        "4",
        "4"
      ]
    },
    {
      "g": [
        "2",
        "3",
        "5",
        "7"
      ],
      "squared_frequencies": [
        "8/3",
        "12/5",
        "20/7"
      ]
    }
  ],
  "gram_target_assignments": [
    {
      "U": 1,
      "V": 4,
      "X": 9,
      "Y": 16,
      "signed_relation_gap": "-19/16"
    },
    {
      "U": 1,
      "V": 4,
      "X": 9,
      "Y": 25,
      "signed_relation_gap": "-139/100"
    },
    {
      "U": 1,
      "V": 4,
      "X": 16,
      "Y": 9,
      "signed_relation_gap": "1/36"
    },
    {
      "U": 1,
      "V": 4,
      "X": 16,
      "Y": 25,
      "signed_relation_gap": "-111/100"
    },
    {
      "U": 1,
      "V": 4,
      "X": 25,
      "Y": 9,
      "signed_relation_gap": "37/36"
    },
    {
      "U": 1,
      "V": 4,
      "X": 25,
      "Y": 16,
      "signed_relation_gap": "-3/16"
    },
    {
      "U": 1,
      "V": 9,
      "X": 4,
      "Y": 16,
      "signed_relation_gap": "-59/36"
    },
    {
      "U": 1,
      "V": 9,
      "X": 4,
      "Y": 25,
      "signed_relation_gap": "-389/225"
    },
    {
      "U": 1,
      "V": 9,
      "X": 16,
      "Y": 4,
      "signed_relation_gap": "19/9"
    },
    {
      "U": 1,
      "V": 9,
      "X": 16,
      "Y": 25,
      "signed_relation_gap": "-281/225"
    },
    {
      "U": 1,
      "V": 9,
      "X": 25,
      "Y": 4,
      "signed_relation_gap": "157/36"
    },
    {
      "U": 1,
      "V": 9,
      "X": 25,
      "Y": 16,
      "signed_relation_gap": "-47/144"
    },
    {
      "U": 1,
      "V": 16,
      "X": 4,
      "Y": 9,
      "signed_relation_gap": "-215/144"
    },
    {
      "U": 1,
      "V": 16,
      "X": 4,
      "Y": 25,
      "signed_relation_gap": "-711/400"
    },
    {
      "U": 1,
      "V": 16,
      "X": 9,
      "Y": 4,
      "signed_relation_gap": "5/16"
    },
    {
      "U": 1,
      "V": 16,
      "X": 9,
      "Y": 25,
      "signed_relation_gap": "-631/400"
    },
    {
      "U": 1,
      "V": 16,
      "X": 25,
      "Y": 4,
      "signed_relation_gap": "69/16"
    },
    {
      "U": 1,
      "V": 16,
      "X": 25,
      "Y": 9,
      "signed_relation_gap": "121/144"
    },
    {
      "U": 1,
      "V": 25,
      "X": 4,
      "Y": 9,
      "signed_relation_gap": "-341/225"
    },
    {
      "U": 1,
      "V": 25,
      "X": 4,
      "Y": 16,
      "signed_relation_gap": "-171/100"
    },
    {
      "U": 1,
      "V": 25,
      "X": 9,
      "Y": 4,
      "signed_relation_gap": "29/100"
    },
    {
      "U": 1,
      "V": 25,
      "X": 9,
      "Y": 16,
      "signed_relation_gap": "-559/400"
    },
    {
      "U": 1,
      "V": 25,
      "X": 16,
      "Y": 4,
      "signed_relation_gap": "51/25"
    },
    {
      "U": 1,
      "V": 25,
      "X": 16,
      "Y": 9,
      "signed_relation_gap": "-41/225"
    },
    {
      "U": 4,
      "V": 1,
      "X": 9,
      "Y": 16,
      "signed_relation_gap": "41/16"
    },
    {
      "U": 4,
      "V": 1,
      "X": 9,
      "Y": 25,
      "signed_relation_gap": "59/25"
    },
    {
      "U": 4,
      "V": 1,
      "X": 16,
      "Y": 9,
      "signed_relation_gap": "34/9"
    },
    {
      "U": 4,
      "V": 1,
      "X": 16,
      "Y": 25,
      "signed_relation_gap": "66/25"
    },
    {
      "U": 4,
      "V": 1,
      "X": 25,
      "Y": 9,
      "signed_relation_gap": "43/9"
    },
    {
      "U": 4,
      "V": 1,
      "X": 25,
      "Y": 16,
      "signed_relation_gap": "57/16"
    },
    {
      "U": 4,
      "V": 9,
      "X": 1,
      "Y": 16,
      "signed_relation_gap": "-215/144"
    },
    {
      "U": 4,
      "V": 9,
      "X": 1,
      "Y": 25,
      "signed_relation_gap": "-341/225"
    },
    {
      "U": 4,
      "V": 9,
      "X": 16,
      "Y": 1,
      "signed_relation_gap": "130/9"
    },
    {
      "U": 4,
      "V": 9,
      "X": 16,
      "Y": 25,
      "signed_relation_gap": "-206/225"
    },
    {
      "U": 4,
      "V": 9,
      "X": 25,
      "Y": 1,
      "signed_relation_gap": "211/9"
    },
    {
      "U": 4,
      "V": 9,
      "X": 25,
      "Y": 16,
      "signed_relation_gap": "1/144"
    },
    {
      "U": 4,
      "V": 16,
      "X": 1,
      "Y": 9,
      "signed_relation_gap": "-59/36"
    },
    {
      "U": 4,
      "V": 16,
      "X": 1,
      "Y": 25,
      "signed_relation_gap": "-171/100"
    },
    {
      "U": 4,
      "V": 16,
      "X": 9,
      "Y": 1,
      "signed_relation_gap": "29/4"
    },
    {
      "U": 4,
      "V": 16,
      "X": 9,
      "Y": 25,
      "signed_relation_gap": "-139/100"
    },
    {
      "U": 4,
      "V": 16,
      "X": 25,
      "Y": 1,
      "signed_relation_gap": "93/4"
    },
    {
      "U": 4,
      "V": 16,
      "X": 25,
      "Y": 9,
      "signed_relation_gap": "37/36"
    },
    {
      "U": 4,
      "V": 25,
      "X": 1,
      "Y": 9,
      "signed_relation_gap": "-389/225"
    },
    {
      "U": 4,
      "V": 25,
      "X": 1,
      "Y": 16,
      "signed_relation_gap": "-711/400"
    },
    {
      "U": 4,
      "V": 25,
      "X": 9,
      "Y": 1,
      "signed_relation_gap": "179/25"
    },
    {
      "U": 4,
      "V": 25,
      "X": 9,
      "Y": 16,
      "signed_relation_gap": "-511/400"
    },
    {
      "U": 4,
      "V": 25,
      "X": 16,
      "Y": 1,
      "signed_relation_gap": "354/25"
    },
    {
      "U": 4,
      "V": 25,
      "X": 16,
      "Y": 9,
      "signed_relation_gap": "-14/225"
    },
    {
      "U": 9,
      "V": 1,
      "X": 4,
      "Y": 16,
      "signed_relation_gap": "29/4"
    },
    {
      "U": 9,
      "V": 1,
      "X": 4,
      "Y": 25,
      "signed_relation_gap": "179/25"
    },
    {
      "U": 9,
      "V": 1,
      "X": 16,
      "Y": 4,
      "signed_relation_gap": "11"
    },
    {
      "U": 9,
      "V": 1,
      "X": 16,
      "Y": 25,
      "signed_relation_gap": "191/25"
    },
    {
      "U": 9,
      "V": 1,
      "X": 25,
      "Y": 4,
      "signed_relation_gap": "53/4"
    },
    {
      "U": 9,
      "V": 1,
      "X": 25,
      "Y": 16,
      "signed_relation_gap": "137/16"
    },
    {
      "U": 9,
      "V": 4,
      "X": 1,
      "Y": 16,
      "signed_relation_gap": "5/16"
    },
    {
      "U": 9,
      "V": 4,
      "X": 1,
      "Y": 25,
      "signed_relation_gap": "29/100"
    },
    {
      "U": 9,
      "V": 4,
      "X": 16,
      "Y": 1,
      "signed_relation_gap": "65/4"
    },
    {
      "U": 9,
      "V": 4,
      "X": 16,
      "Y": 25,
      "signed_relation_gap": "89/100"
    },
    {
      "U": 9,
      "V": 4,
      "X": 25,
      "Y": 1,
      "signed_relation_gap": "101/4"
    },
    {
      "U": 9,
      "V": 4,
      "X": 25,
      "Y": 16,
      "signed_relation_gap": "29/16"
    },
    {
      "U": 9,
      "V": 16,
      "X": 1,
      "Y": 4,
      "signed_relation_gap": "-19/16"
    },
    {
      "U": 9,
      "V": 16,
      "X": 1,
      "Y": 25,
      "signed_relation_gap": "-559/400"
    },
    {
      "U": 9,
      "V": 16,
      "X": 4,
      "Y": 1,
      "signed_relation_gap": "41/16"
    },
    {
      "U": 9,
      "V": 16,
      "X": 4,
      "Y": 25,
      "signed_relation_gap": "-511/400"
    },
    {
      "U": 9,
      "V": 16,
      "X": 25,
      "Y": 1,
      "signed_relation_gap": "377/16"
    },
    {
      "U": 9,
      "V": 16,
      "X": 25,
      "Y": 4,
      "signed_relation_gap": "77/16"
    },
    {
      "U": 9,
      "V": 25,
      "X": 1,
      "Y": 4,
      "signed_relation_gap": "-139/100"
    },
    {
      "U": 9,
      "V": 25,
      "X": 1,
      "Y": 16,
      "signed_relation_gap": "-631/400"
    },
    {
      "U": 9,
      "V": 25,
      "X": 4,
      "Y": 1,
      "signed_relation_gap": "59/25"
    },
    {
      "U": 9,
      "V": 25,
      "X": 4,
      "Y": 16,
      "signed_relation_gap": "-139/100"
    },
    {
      "U": 9,
      "V": 25,
      "X": 16,
      "Y": 1,
      "signed_relation_gap": "359/25"
    },
    {
      "U": 9,
      "V": 25,
      "X": 16,
      "Y": 4,
      "signed_relation_gap": "59/25"
    },
    {
      "U": 16,
      "V": 1,
      "X": 4,
      "Y": 9,
      "signed_relation_gap": "130/9"
    },
    {
      "U": 16,
      "V": 1,
      "X": 4,
      "Y": 25,
      "signed_relation_gap": "354/25"
    },
    {
      "U": 16,
      "V": 1,
      "X": 9,
      "Y": 4,
      "signed_relation_gap": "65/4"
    },
    {
      "U": 16,
      "V": 1,
      "X": 9,
      "Y": 25,
      "signed_relation_gap": "359/25"
    },
    {
      "U": 16,
      "V": 1,
      "X": 25,
      "Y": 4,
      "signed_relation_gap": "81/4"
    },
    {
      "U": 16,
      "V": 1,
      "X": 25,
      "Y": 9,
      "signed_relation_gap": "151/9"
    },
    {
      "U": 16,
      "V": 4,
      "X": 1,
      "Y": 9,
      "signed_relation_gap": "19/9"
    },
    {
      "U": 16,
      "V": 4,
      "X": 1,
      "Y": 25,
      "signed_relation_gap": "51/25"
    },
    {
      "U": 16,
      "V": 4,
      "X": 9,
      "Y": 1,
      "signed_relation_gap": "11"
    },
    {
      "U": 16,
      "V": 4,
      "X": 9,
      "Y": 25,
      "signed_relation_gap": "59/25"
    },
    {
      "U": 16,
      "V": 4,
      "X": 25,
      "Y": 1,
      "signed_relation_gap": "27"
    },
    {
      "U": 16,
      "V": 4,
      "X": 25,
      "Y": 9,
      "signed_relation_gap": "43/9"
    },
    {
      "U": 16,
      "V": 9,
      "X": 1,
      "Y": 4,
      "signed_relation_gap": "1/36"
    },
    {
      "U": 16,
      "V": 9,
      "X": 1,
      "Y": 25,
      "signed_relation_gap": "-41/225"
    },
    {
      "U": 16,
      "V": 9,
      "X": 4,
      "Y": 1,
      "signed_relation_gap": "34/9"
    },
    {
      "U": 16,
      "V": 9,
      "X": 4,
      "Y": 25,
      "signed_relation_gap": "-14/225"
    },
    {
      "U": 16,
      "V": 9,
      "X": 25,
      "Y": 1,
      "signed_relation_gap": "223/9"
    },
    {
      "U": 16,
      "V": 9,
      "X": 25,
      "Y": 4,
      "signed_relation_gap": "217/36"
    },
    {
      "U": 16,
      "V": 25,
      "X": 1,
      "Y": 4,
      "signed_relation_gap": "-111/100"
    },
    {
      "U": 16,
      "V": 25,
      "X": 1,
      "Y": 9,
      "signed_relation_gap": "-281/225"
    },
    {
      "U": 16,
      "V": 25,
      "X": 4,
      "Y": 1,
      "signed_relation_gap": "66/25"
    },
    {
      "U": 16,
      "V": 25,
      "X": 4,
      "Y": 9,
      "signed_relation_gap": "-206/225"
    },
    {
      "U": 16,
      "V": 25,
      "X": 9,
      "Y": 1,
      "signed_relation_gap": "191/25"
    },
    {
      "U": 16,
      "V": 25,
      "X": 9,
      "Y": 4,
      "signed_relation_gap": "89/100"
    },
    {
      "U": 25,
      "V": 1,
      "X": 4,
      "Y": 9,
      "signed_relation_gap": "211/9"
    },
    {
      "U": 25,
      "V": 1,
      "X": 4,
      "Y": 16,
      "signed_relation_gap": "93/4"
    },
    {
      "U": 25,
      "V": 1,
      "X": 9,
      "Y": 4,
      "signed_relation_gap": "101/4"
    },
    {
      "U": 25,
      "V": 1,
      "X": 9,
      "Y": 16,
      "signed_relation_gap": "377/16"
    },
    {
      "U": 25,
      "V": 1,
      "X": 16,
      "Y": 4,
      "signed_relation_gap": "27"
    },
    {
      "U": 25,
      "V": 1,
      "X": 16,
      "Y": 9,
      "signed_relation_gap": "223/9"
    },
    {
      "U": 25,
      "V": 4,
      "X": 1,
      "Y": 9,
      "signed_relation_gap": "157/36"
    },
    {
      "U": 25,
      "V": 4,
      "X": 1,
      "Y": 16,
      "signed_relation_gap": "69/16"
    },
    {
      "U": 25,
      "V": 4,
      "X": 9,
      "Y": 1,
      "signed_relation_gap": "53/4"
    },
    {
      "U": 25,
      "V": 4,
      "X": 9,
      "Y": 16,
      "signed_relation_gap": "77/16"
    },
    {
      "U": 25,
      "V": 4,
      "X": 16,
      "Y": 1,
      "signed_relation_gap": "81/4"
    },
    {
      "U": 25,
      "V": 4,
      "X": 16,
      "Y": 9,
      "signed_relation_gap": "217/36"
    },
    {
      "U": 25,
      "V": 9,
      "X": 1,
      "Y": 4,
      "signed_relation_gap": "37/36"
    },
    {
      "U": 25,
      "V": 9,
      "X": 1,
      "Y": 16,
      "signed_relation_gap": "121/144"
    },
    {
      "U": 25,
      "V": 9,
      "X": 4,
      "Y": 1,
      "signed_relation_gap": "43/9"
    },
    {
      "U": 25,
      "V": 9,
      "X": 4,
      "Y": 16,
      "signed_relation_gap": "37/36"
    },
    {
      "U": 25,
      "V": 9,
      "X": 16,
      "Y": 1,
      "signed_relation_gap": "151/9"
    },
    {
      "U": 25,
      "V": 9,
      "X": 16,
      "Y": 4,
      "signed_relation_gap": "43/9"
    },
    {
      "U": 25,
      "V": 16,
      "X": 1,
      "Y": 4,
      "signed_relation_gap": "-3/16"
    },
    {
      "U": 25,
      "V": 16,
      "X": 1,
      "Y": 9,
      "signed_relation_gap": "-47/144"
    },
    {
      "U": 25,
      "V": 16,
      "X": 4,
      "Y": 1,
      "signed_relation_gap": "57/16"
    },
    {
      "U": 25,
      "V": 16,
      "X": 4,
      "Y": 9,
      "signed_relation_gap": "1/144"
    },
    {
      "U": 25,
      "V": 16,
      "X": 9,
      "Y": 1,
      "signed_relation_gap": "137/16"
    },
    {
      "U": 25,
      "V": 16,
      "X": 9,
      "Y": 4,
      "signed_relation_gap": "29/16"
    }
  ],
  "gram_target_assignment_count": 120,
  "gram_target_hits": 0,
  "minimum_relation_gap": "1/144",
  "relation_gap_is_operator_bound": false,
  "three_center_default": {
    "radius": 1,
    "centers": [
      3,
      7,
      10
    ],
    "distances": [
      1,
      1,
      1,
      1,
      0
    ]
  },
  "three_center_radius_M1_to64": [
    0,
    0,
    0,
    1,
    1,
    1,
    2,
    2,
    2,
    2,
    3,
    3,
    3,
    4,
    4,
    4,
    4,
    5,
    5,
    5,
    6,
    6,
    6,
    6,
    7,
    7,
    7,
    8,
    8,
    8,
    8,
    9,
    9,
    9,
    10,
    10,
    10,
    10,
    11,
    11,
    11,
    12,
    12,
    12,
    12,
    13,
    13,
    13,
    14,
    14,
    14,
    14,
    15,
    15,
    15,
    16,
    16,
    16,
    16,
    17,
    17,
    17,
    18,
    18
  ],
  "source_selected_parameters": "OPEN",
  "glued_integer_grid_matches_max": 3,
  "checker_sha256": "96f13a7ca0a9c059cbb0feacf8f276b006b7d28ce41ba69ccd850ef04123897a"
}