{
  "input_record_sha256": "0d391fd604453b1a24412d819c11d8efc1bd814232dcc4abd207a302d4ef6776",
  "vertices": 6,
  "edges": 7,
  "objective": "number_of_labeled_unweighted_perfect_matchings",
  "method": "conventional_exact_subset_dynamic_program",
  "source_connection": {
    "family": "113",
    "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
    "source_fpras_implemented": false,
    "source_proof_verification": "not_run"
  },
  "formal_program_verification": "not_run",
  "limits": {
    "vertices": 24,
    "memo_states": 200000,
    "count_work_units": 1000000,
    "requested_ranks": 100,
    "wall_time_deadline": "none"
  },
  "work_unit_definition": "New subset evaluations plus partner-branch visits; not bit operations or measured time.",
  "status": "complete",
  "exact_count": 1,
  "feasible": true,
  "memo_states": 16,
  "work_units": 28,
  "edge_sensitivity": [
    {
      "edge": [
        0,
        1
      ],
      "containing_matchings": 1,
      "surviving_matchings_if_edge_removed": 0,
      "uniform_edge_marginal": "1",
      "uniform_survival_fraction": "0",
      "forced_when_feasible": true,
      "belongs_to_any_perfect_matching": true
    },
    {
      "edge": [
        0,
        2
      ],
      "containing_matchings": 0,
      "surviving_matchings_if_edge_removed": 1,
      "uniform_edge_marginal": "0",
      "uniform_survival_fraction": "1",
      "forced_when_feasible": false,
      "belongs_to_any_perfect_matching": false
    },
    {
      "edge": [
        1,
        2
      ],
      "containing_matchings": 0,
      "surviving_matchings_if_edge_removed": 1,
      "uniform_edge_marginal": "0",
      "uniform_survival_fraction": "1",
      "forced_when_feasible": false,
      "belongs_to_any_perfect_matching": false
    },
    {
      "edge": [
        2,
        3
      ],
      "containing_matchings": 1,
      "surviving_matchings_if_edge_removed": 0,
      "uniform_edge_marginal": "1",
      "uniform_survival_fraction": "0",
      "forced_when_feasible": true,
      "belongs_to_any_perfect_matching": true
    },
    {
      "edge": [
        3,
        4
      ],
      "containing_matchings": 0,
      "surviving_matchings_if_edge_removed": 1,
      "uniform_edge_marginal": "0",
      "uniform_survival_fraction": "1",
      "forced_when_feasible": false,
      "belongs_to_any_perfect_matching": false
    },
    {
      "edge": [
        3,
        5
      ],
      "containing_matchings": 0,
      "surviving_matchings_if_edge_removed": 1,
      "uniform_edge_marginal": "0",
      "uniform_survival_fraction": "1",
      "forced_when_feasible": false,
      "belongs_to_any_perfect_matching": false
    },
    {
      "edge": [
        4,
        5
      ],
      "containing_matchings": 1,
      "surviving_matchings_if_edge_removed": 0,
      "uniform_edge_marginal": "1",
      "uniform_survival_fraction": "0",
      "forced_when_feasible": true,
      "belongs_to_any_perfect_matching": true
    }
  ],
  "ranked_matchings": [
    {
      "rank": 0,
      "matching": [
        [
          0,
          1
        ],
        [
          2,
          3
        ],
        [
          4,
          5
        ]
      ]
    }
  ],
  "interpretation": "Exact for this bounded graph. Edge-failure counts measure surviving unweighted perfect pairings, not weighted plan quality, fairness or resilience to arbitrary failures. Uniform rank would induce a uniform matching law; this utility does not draw random ranks."
}