{
  "chain_length": 3,
  "M_including_empty": 11,
  "counts": {
    "a1": 7,
    "a2": 7,
    "a3": 7,
    "b1": 6,
    "b2": 5,
    "b3": 4,
    "c1": 7,
    "c2": 7,
    "c3": 7,
    "gA": 7,
    "gB": 7,
    "gC": 7
  },
  "certificates": {
    "A": {
      "core": [
        "a1",
        "a2",
        "a3",
        "gA"
      ],
      "rank": {
        "a2": 0,
        "a3": 0,
        "a1": 0,
        "gA": 1
      },
      "supplier": {
        "a1": "gA",
        "a2": "a1",
        "a3": "a2",
        "gA": "a3"
      }
    },
    "B": {
      "core": [
        "b1",
        "b2",
        "b3",
        "gB"
      ],
      "rank": {
        "b1": 0,
        "b3": 0,
        "b2": 0,
        "gB": 1
      },
      "supplier": {
        "b1": "gB",
        "b2": "b1",
        "b3": "b2",
        "gB": "b3"
      }
    },
    "C": {
      "core": [
        "c1",
        "c2",
        "c3",
        "gC"
      ],
      "rank": {
        "gC": 1,
        "c1": 0,
        "c2": 0,
        "c3": 0
      },
      "supplier": {
        "c1": "gC",
        "c2": "c1",
        "c3": "c2",
        "gC": "c3"
      }
    }
  },
  "uniform": {
    "partition": "11",
    "kappa": "1",
    "expected_core_size": "2",
    "normalized_core_occupancy": "1/2",
    "guaranteed_frequency": "1/2",
    "frequencies": {
      "b1": "6/11",
      "b2": "5/11",
      "b3": "4/11",
      "gB": "7/11"
    },
    "witnesses": [
      "b1",
      "gB"
    ]
  },
  "exterior_weighted": {
    "partition": "1346",
    "kappa": "1",
    "expected_core_size": "2",
    "normalized_core_occupancy": "1/2",
    "guaranteed_frequency": "1/2",
    "frequencies": {
      "b1": "801/1346",
      "b2": "545/1346",
      "b3": "289/1346",
      "gB": "1057/1346"
    },
    "witnesses": [
      "b1",
      "gB"
    ]
  },
  "distorted": {
    "partition": "2436",
    "kappa": "3",
    "expected_core_size": "267/203",
    "normalized_core_occupancy": "267/812",
    "guaranteed_frequency": "1/4",
    "frequencies": {
      "b1": "267/812",
      "b2": "545/2436",
      "b3": "289/2436",
      "gB": "523/812"
    },
    "witnesses": [
      "b1",
      "gB"
    ]
  },
  "sharp_two_member": {
    "partition": "4",
    "kappa": "3",
    "expected_core_size": "1/2",
    "normalized_core_occupancy": "1/4",
    "guaranteed_frequency": "1/4",
    "frequencies": {
      "a": "1/4",
      "b": "1/4"
    },
    "witnesses": [
      "a",
      "b"
    ]
  },
  "deletion": {
    "nonempty_before": 10,
    "remaining": {
      "b1": 4,
      "b2": 5,
      "b3": 6,
      "gB": 3
    },
    "uniform_core_expected_remaining": "9/2",
    "theorem_expected_upper": "9/2",
    "theorem_some_deletion_upper": 4
  },
  "structure": {
    "irreducible": [
      [
        "a1",
        "a2",
        "a3",
        "gA"
      ],
      [
        "b1",
        "b2",
        "b3",
        "gB"
      ],
      [
        "c1",
        "c2",
        "c3",
        "gC"
      ]
    ],
    "members_missing_from_irreducible_unions": [
      [
        "a1",
        "a2",
        "a3",
        "c1",
        "c2",
        "c3",
        "gA",
        "gB",
        "gC"
      ],
      [
        "a1",
        "a2",
        "a3",
        "b1",
        "c1",
        "c2",
        "c3",
        "gA",
        "gB",
        "gC"
      ],
      [
        "a1",
        "a2",
        "a3",
        "b1",
        "b2",
        "c1",
        "c2",
        "c3",
        "gA",
        "gB",
        "gC"
      ]
    ],
    "elementary_rafs": [],
    "minimum_raf_size": 4,
    "gates_hit_every_nonempty": true,
    "digraph_support_obstruction": {
      "A_member": true,
      "C_member": true,
      "A_plus_gB_member": false,
      "C_plus_gB_member": false,
      "AC_plus_gB_member": true
    }
  },
  "lift": {
    "balanced": true,
    "family_unchanged": true,
    "mass_units": {
      "yA1": 1,
      "f": 2,
      "zA": 1,
      "w": 1,
      "yA2": 1,
      "u": 1,
      "xA": 1,
      "yB1": 1,
      "zB": 2,
      "yB2": 1,
      "v": 1,
      "yC1": 1,
      "zC": 1,
      "yC2": 1,
      "xC": 1
    }
  },
  "strict_extension": {
    "family": [
      [],
      [
        "a",
        "b"
      ],
      [
        "a",
        "b",
        "e"
      ]
    ],
    "local_certificate": {
      "core": [
        "a",
        "b"
      ],
      "rank": {
        "a": 0,
        "b": 1
      },
      "supplier": {
        "a": "b",
        "b": "a"
      }
    },
    "global_candidate": {
      "status": "FAILED_CANDIDATE",
      "reason": "internal substrate cycle",
      "unprocessed": [
        "b",
        "e"
      ]
    },
    "exterior_alone_is_raf": false
  },
  "scope": "Exact finite set-family computations; large-chain sweep uses the paper family formula. Structural abundance is not kinetic persistence or flux. Lean not rerun."
}