Resolved inputs: {"model": {"food": ["f"], "reactions": [{"id": 0, "reactants": ["f"], "products": ["x1"], "catalysts": ["z2"]}, {"id": 1, "reactants": ["f"], "products": ["x1"], "catalysts": ["z2"]}, {"id": 2, "reactants": ["f"], "products": ["x2"], "catalysts": ["z2"]}, {"id": 3, "reactants": ["f"], "products": ["x2"], "catalysts": ["z2"]}, {"id": 4, "reactants": ["x1"], "products": ["z1"], "catalysts": ["z2"]}, {"id": 5, "reactants": ["x2", "z1"], "products": ["z2"], "catalysts": ["z2"]}]}, "resolution_budget": 4096, "availability": "1/2", "deletion_costs": {"0": 2, "1": 3, "2": 4, "3": 1, "4": 7, "5": 6}, "required": [0], "forbidden": [2], "deleted": [0], "scaling_sizes": [1, 2, 3, 4, 5, 6], "large_modules": 64, "chain_length": 64}
{
  "inputs": {
    "model": {
      "food": [
        "f"
      ],
      "reactions": [
        {
          "id": 0,
          "reactants": [
            "f"
          ],
          "products": [
            "x1"
          ],
          "catalysts": [
            "z2"
          ]
        },
        {
          "id": 1,
          "reactants": [
            "f"
          ],
          "products": [
            "x1"
          ],
          "catalysts": [
            "z2"
          ]
        },
        {
          "id": 2,
          "reactants": [
            "f"
          ],
          "products": [
            "x2"
          ],
          "catalysts": [
            "z2"
          ]
        },
        {
          "id": 3,
          "reactants": [
            "f"
          ],
          "products": [
            "x2"
          ],
          "catalysts": [
            "z2"
          ]
        },
        {
          "id": 4,
          "reactants": [
            "x1"
          ],
          "products": [
            "z1"
          ],
          "catalysts": [
            "z2"
          ]
        },
        {
          "id": 5,
          "reactants": [
            "x2",
            "z1"
          ],
          "products": [
            "z2"
          ],
          "catalysts": [
            "z2"
          ]
        }
      ]
    },
    "resolution_budget": 4096,
    "availability": "1/2",
    "deletion_costs": {
      "0": 2,
      "1": 3,
      "2": 4,
      "3": 1,
      "4": 7,
      "5": 6
    },
    "required": [
      0
    ],
    "forbidden": [
      2
    ],
    "deleted": [
      0
    ],
    "scaling_sizes": [
      1,
      2,
      3,
      4,
      5,
      6
    ],
    "large_modules": 64,
    "chain_length": 64
  },
  "catalogue": {
    "members": [
      [
        0,
        2,
        4,
        5
      ],
      [
        0,
        3,
        4,
        5
      ],
      [
        1,
        2,
        4,
        5
      ],
      [
        1,
        3,
        4,
        5
      ]
    ],
    "beta": 2,
    "global_resolution_count": 4,
    "resolutions_inspected": 4,
    "candidates": 4,
    "rejected": 0,
    "validation_calls": 16,
    "component_count": 1,
    "largest_local_beta": 2,
    "frequencies": {
      "0": 2,
      "1": 2,
      "2": 2,
      "3": 2,
      "4": 4,
      "5": 4
    },
    "total_memberships": 16
  },
  "worked_queries": {
    "required": [
      0
    ],
    "forbidden": [
      2
    ],
    "matching": [
      [
        0,
        3,
        4,
        5
      ]
    ],
    "after_deletion": [
      [
        1,
        2,
        4,
        5
      ],
      [
        1,
        3,
        4,
        5
      ]
    ],
    "minimal_cuts": [
      [
        4
      ],
      [
        5
      ],
      [
        0,
        1
      ],
      [
        2,
        3
      ]
    ],
    "minimum_cut_cost": 5,
    "greedy_cut": [
      3,
      0,
      1
    ],
    "greedy_cost": "6",
    "availability_probability": "9/64"
  },
  "necessary_validation": {
    "members": [
      [
        0
      ]
    ],
    "beta": 1,
    "global_resolution_count": 2,
    "resolutions_inspected": 2,
    "candidates": 2,
    "rejected": 1,
    "validation_calls": 3,
    "component_count": 1,
    "largest_local_beta": 1,
    "frequencies": {
      "0": 1
    },
    "total_memberships": 1
  },
  "large_independent": {
    "members": [
      [
        0,
        2
      ],
      [
        1,
        2
      ],
      [
        3,
        5
      ],
      [
        4,
        5
      ],
      [
        6,
        8
      ],
      [
        7,
        8
      ],
      [
        9,
        11
      ],
      [
        10,
        11
      ],
      [
        12,
        14
      ],
      [
        13,
        14
      ],
      [
        15,
        17
      ],
      [
        16,
        17
      ],
      [
        18,
        20
      ],
      [
        19,
        20
      ],
      [
        21,
        23
      ],
      [
        22,
        23
      ],
      [
        24,
        26
      ],
      [
        25,
        26
      ],
      [
        27,
        29
      ],
      [
        28,
        29
      ],
      [
        30,
        32
      ],
      [
        31,
        32
      ],
      [
        33,
        35
      ],
      [
        34,
        35
      ],
      [
        36,
        38
      ],
      [
        37,
        38
      ],
      [
        39,
        41
      ],
      [
        40,
        41
      ],
      [
        42,
        44
      ],
      [
        43,
        44
      ],
      [
        45,
        47
      ],
      [
        46,
        47
      ],
      [
        48,
        50
      ],
      [
        49,
        50
      ],
      [
        51,
        53
      ],
      [
        52,
        53
      ],
      [
        54,
        56
      ],
      [
        55,
        56
      ],
      [
        57,
        59
      ],
      [
        58,
        59
      ],
      [
        60,
        62
      ],
      [
        61,
        62
      ],
      [
        63,
        65
      ],
      [
        64,
        65
      ],
      [
        66,
        68
      ],
      [
        67,
        68
      ],
      [
        69,
        71
      ],
      [
        70,
        71
      ],
      [
        72,
        74
      ],
      [
        73,
        74
      ],
      [
        75,
        77
      ],
      [
        76,
        77
      ],
      [
        78,
        80
      ],
      [
        79,
        80
      ],
      [
        81,
        83
      ],
      [
        82,
        83
      ],
      [
        84,
        86
      ],
      [
        85,
        86
      ],
      [
        87,
        89
      ],
      [
        88,
        89
      ],
      [
        90,
        92
      ],
      [
        91,
        92
      ],
      [
        93,
        95
      ],
      [
        94,
        95
      ],
      [
        96,
        98
      ],
      [
        97,
        98
      ],
      [
        99,
        101
      ],
      [
        100,
        101
      ],
      [
        102,
        104
      ],
      [
        103,
        104
      ],
      [
        105,
        107
      ],
      [
        106,
        107
      ],
      [
        108,
        110
      ],
      [
        109,
        110
      ],
      [
        111,
        113
      ],
      [
        112,
        113
      ],
      [
        114,
        116
      ],
      [
        115,
        116
      ],
      [
        117,
        119
      ],
      [
        118,
        119
      ],
      [
        120,
        122
      ],
      [
        121,
        122
      ],
      [
        123,
        125
      ],
      [
        124,
        125
      ],
      [
        126,
        128
      ],
      [
        127,
        128
      ],
      [
        129,
        131
      ],
      [
        130,
        131
      ],
      [
        132,
        134
      ],
      [
        133,
        134
      ],
      [
        135,
        137
      ],
      [
        136,
        137
      ],
      [
        138,
        140
      ],
      [
        139,
        140
      ],
      [
        141,
        143
      ],
      [
        142,
        143
      ],
      [
        144,
        146
      ],
      [
        145,
        146
      ],
      [
        147,
        149
      ],
      [
        148,
        149
      ],
      [
        150,
        152
      ],
      [
        151,
        152
      ],
      [
        153,
        155
      ],
      [
        154,
        155
      ],
      [
        156,
        158
      ],
      [
        157,
        158
      ],
      [
        159,
        161
      ],
      [
        160,
        161
      ],
      [
        162,
        164
      ],
      [
        163,
        164
      ],
      [
        165,
        167
      ],
      [
        166,
        167
      ],
      [
        168,
        170
      ],
      [
        169,
        170
      ],
      [
        171,
        173
      ],
      [
        172,
        173
      ],
      [
        174,
        176
      ],
      [
        175,
        176
      ],
      [
        177,
        179
      ],
      [
        178,
        179
      ],
      [
        180,
        182
      ],
      [
        181,
        182
      ],
      [
        183,
        185
      ],
      [
        184,
        185
      ],
      [
        186,
        188
      ],
      [
        187,
        188
      ],
      [
        189,
        191
      ],
      [
        190,
        191
      ]
    ],
    "beta": 64,
    "global_resolution_count": 18446744073709551616,
    "resolutions_inspected": 128,
    "candidates": 128,
    "rejected": 0,
    "validation_calls": 256,
    "component_count": 64,
    "largest_local_beta": 1,
    "frequencies": {
      "0": 1,
      "1": 1,
      "2": 2,
      "3": 1,
      "4": 1,
      "5": 2,
      "6": 1,
      "7": 1,
      "8": 2,
      "9": 1,
      "10": 1,
      "11": 2,
      "12": 1,
      "13": 1,
      "14": 2,
      "15": 1,
      "16": 1,
      "17": 2,
      "18": 1,
      "19": 1,
      "20": 2,
      "21": 1,
      "22": 1,
      "23": 2,
      "24": 1,
      "25": 1,
      "26": 2,
      "27": 1,
      "28": 1,
      "29": 2,
      "30": 1,
      "31": 1,
      "32": 2,
      "33": 1,
      "34": 1,
      "35": 2,
      "36": 1,
      "37": 1,
      "38": 2,
      "39": 1,
      "40": 1,
      "41": 2,
      "42": 1,
      "43": 1,
      "44": 2,
      "45": 1,
      "46": 1,
      "47": 2,
      "48": 1,
      "49": 1,
      "50": 2,
      "51": 1,
      "52": 1,
      "53": 2,
      "54": 1,
      "55": 1,
      "56": 2,
      "57": 1,
      "58": 1,
      "59": 2,
      "60": 1,
      "61": 1,
      "62": 2,
      "63": 1,
      "64": 1,
      "65": 2,
      "66": 1,
      "67": 1,
      "68": 2,
      "69": 1,
      "70": 1,
      "71": 2,
      "72": 1,
      "73": 1,
      "74": 2,
      "75": 1,
      "76": 1,
      "77": 2,
      "78": 1,
      "79": 1,
      "80": 2,
      "81": 1,
      "82": 1,
      "83": 2,
      "84": 1,
      "85": 1,
      "86": 2,
      "87": 1,
      "88": 1,
      "89": 2,
      "90": 1,
      "91": 1,
      "92": 2,
      "93": 1,
      "94": 1,
      "95": 2,
      "96": 1,
      "97": 1,
      "98": 2,
      "99": 1,
      "100": 1,
      "101": 2,
      "102": 1,
      "103": 1,
      "104": 2,
      "105": 1,
      "106": 1,
      "107": 2,
      "108": 1,
      "109": 1,
      "110": 2,
      "111": 1,
      "112": 1,
      "113": 2,
      "114": 1,
      "115": 1,
      "116": 2,
      "117": 1,
      "118": 1,
      "119": 2,
      "120": 1,
      "121": 1,
      "122": 2,
      "123": 1,
      "124": 1,
      "125": 2,
      "126": 1,
      "127": 1,
      "128": 2,
      "129": 1,
      "130": 1,
      "131": 2,
      "132": 1,
      "133": 1,
      "134": 2,
      "135": 1,
      "136": 1,
      "137": 2,
      "138": 1,
      "139": 1,
      "140": 2,
      "141": 1,
      "142": 1,
      "143": 2,
      "144": 1,
      "145": 1,
      "146": 2,
      "147": 1,
      "148": 1,
      "149": 2,
      "150": 1,
      "151": 1,
      "152": 2,
      "153": 1,
      "154": 1,
      "155": 2,
      "156": 1,
      "157": 1,
      "158": 2,
      "159": 1,
      "160": 1,
      "161": 2,
      "162": 1,
      "163": 1,
      "164": 2,
      "165": 1,
      "166": 1,
      "167": 2,
      "168": 1,
      "169": 1,
      "170": 2,
      "171": 1,
      "172": 1,
      "173": 2,
      "174": 1,
      "175": 1,
      "176": 2,
      "177": 1,
      "178": 1,
      "179": 2,
      "180": 1,
      "181": 1,
      "182": 2,
      "183": 1,
      "184": 1,
      "185": 2,
      "186": 1,
      "187": 1,
      "188": 2,
      "189": 1,
      "190": 1,
      "191": 2
    },
    "total_memberships": 256
  },
  "deterministic_chain": {
    "members": [
      [
        0,
        1,
        2,
        3,
        4,
        5,
        6,
        7,
        8,
        9,
        10,
        11,
        12,
        13,
        14,
        15,
        16,
        17,
        18,
        19,
        20,
        21,
        22,
        23,
        24,
        25,
        26,
        27,
        28,
        29,
        30,
        31,
        32,
        33,
        34,
        35,
        36,
        37,
        38,
        39,
        40,
        41,
        42,
        43,
        44,
        45,
        46,
        47,
        48,
        49,
        50,
        51,
        52,
        53,
        54,
        55,
        56,
        57,
        58,
        59,
        60,
        61,
        62,
        63
      ]
    ],
    "beta": 0,
    "global_resolution_count": 1,
    "resolutions_inspected": 1,
    "candidates": 1,
    "rejected": 0,
    "validation_calls": 64,
    "component_count": 1,
    "largest_local_beta": 0,
    "frequencies": {
      "0": 1,
      "1": 1,
      "2": 1,
      "3": 1,
      "4": 1,
      "5": 1,
      "6": 1,
      "7": 1,
      "8": 1,
      "9": 1,
      "10": 1,
      "11": 1,
      "12": 1,
      "13": 1,
      "14": 1,
      "15": 1,
      "16": 1,
      "17": 1,
      "18": 1,
      "19": 1,
      "20": 1,
      "21": 1,
      "22": 1,
      "23": 1,
      "24": 1,
      "25": 1,
      "26": 1,
      "27": 1,
      "28": 1,
      "29": 1,
      "30": 1,
      "31": 1,
      "32": 1,
      "33": 1,
      "34": 1,
      "35": 1,
      "36": 1,
      "37": 1,
      "38": 1,
      "39": 1,
      "40": 1,
      "41": 1,
      "42": 1,
      "43": 1,
      "44": 1,
      "45": 1,
      "46": 1,
      "47": 1,
      "48": 1,
      "49": 1,
      "50": 1,
      "51": 1,
      "52": 1,
      "53": 1,
      "54": 1,
      "55": 1,
      "56": 1,
      "57": 1,
      "58": 1,
      "59": 1,
      "60": 1,
      "61": 1,
      "62": 1,
      "63": 1
    },
    "total_memberships": 64,
    "closure_depth": 64
  },
  "zero_excess_availability": "175/256",
  "evidence": "Exact finite set computations and rational availability probabilities. Bounded independent tests, not Lean extraction or compilation. Structural RAF membership does not assert kinetic function."
}