{
  "checks": [
    {
      "case": "four_vertex_graph_0",
      "passed": true,
      "optimum": 0
    },
    {
      "case": "four_vertex_graph_1",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_2",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_3",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_4",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_5",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_6",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_7",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_8",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_9",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_10",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_11",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_12",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_13",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_14",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_15",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_16",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_17",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_18",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_19",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_20",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_21",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_22",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_23",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_24",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_25",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_26",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_27",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_28",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_29",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_30",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_31",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_32",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_33",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_34",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_35",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_36",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_37",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_38",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_39",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_40",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_41",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_42",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_43",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_44",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_45",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_46",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_47",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_48",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_49",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_50",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_51",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_52",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_53",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_54",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_55",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_56",
      "passed": true,
      "optimum": 1
    },
    {
      "case": "four_vertex_graph_57",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_58",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_59",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_60",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_61",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_62",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "four_vertex_graph_63",
      "passed": true,
      "optimum": 2
    },
    {
      "case": "limited_subset_proposal_returns_unknown",
      "passed": true
    },
    {
      "case": "weighted_input_rejected",
      "passed": true
    },
    {
      "case": "vertex_cap_rejected",
      "passed": true
    },
    {
      "case": "boolean_call_cap_rejected",
      "passed": true
    },
    {
      "case": "duplicate_edge_rejected",
      "passed": true
    },
    {
      "case": "public_karate_club_attaining_integer_bound",
      "passed": true
    },
    {
      "case": "generated_star_41_attaining_integer_bound",
      "passed": true
    },
    {
      "case": "generated_regular_80_attaining_integer_bound",
      "passed": true
    }
  ],
  "passed": 72,
  "total": 72,
  "independent_brute_force_graphs": 64,
  "formal_program_verification": "not_run",
  "interpretation": "Small adapter integration checks; solver proposals are accepted only when a separate feasible-matching/attaining-bound audit verifies them."
}