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      "result": {
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              0,
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              40
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              74
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              14
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              26
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              12,
              42
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              13,
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              32
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              56
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              51
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              40
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              35
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              68
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              20,
              47
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              49
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              23,
              31
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              55
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              24,
              75
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              24,
              79
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              25,
              32
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              25,
              37
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              26,
              53
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              26,
              64
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              31
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              27,
              45
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              28,
              29
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              71
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              41
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              61
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              50
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              36,
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              37,
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              75
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              44
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              38,
              70
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              39,
              51
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              39,
              65
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              40,
              58
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            [
              41,
              60
            ],
            [
              42,
              50
            ],
            [
              43,
              50
            ],
            [
              43,
              56
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            [
              43,
              62
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            [
              46,
              69
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            [
              46,
              77
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            [
              47,
              73
            ],
            [
              48,
              52
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            [
              48,
              64
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            [
              49,
              70
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            [
              49,
              77
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            [
              51,
              75
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            [
              52,
              79
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            [
              53,
              54
            ],
            [
              53,
              57
            ],
            [
              54,
              62
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            [
              54,
              64
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            [
              56,
              63
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              57,
              65
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              59,
              60
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            [
              59,
              78
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            [
              60,
              65
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              67,
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              67,
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          ],
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              2,
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              15
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              4,
              69
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            [
              5,
              55
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              6,
              72
            ],
            [
              7,
              47
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            [
              8,
              63
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            [
              9,
              58
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            [
              10,
              62
            ],
            [
              11,
              34
            ],
            [
              12,
              42
            ],
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              13,
              74
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            [
              14,
              56
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              16,
              68
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              17,
              40
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              18,
              48
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              19,
              35
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              20,
              49
            ],
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              21,
              70
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            [
              22,
              52
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            [
              23,
              31
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              24,
              79
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            [
              25,
              32
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              26,
              64
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            [
              28,
              29
            ],
            [
              30,
              66
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            [
              33,
              61
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            [
              36,
              73
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              37,
              75
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            [
              38,
              44
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            [
              39,
              51
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              41,
              60
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            [
              43,
              50
            ],
            [
              46,
              77
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            [
              53,
              54
            ],
            [
              57,
              65
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            [
              59,
              78
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            [
              67,
              76
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          ],
          "barrier": []
        },
        "audit": {
          "vertices": 80,
          "edges": 120,
          "input_record_sha256": "501bc6b2ba31ac26d7376c12275df5074c0c560d0d33c7740b59e21a9c4dfd60",
          "matching_feasible": true,
          "matching_size": 40,
          "candidate_issues": [],
          "barrier": [],
          "component_sizes": [
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          ],
          "odd_components": 0,
          "cardinality_upper_bound": 40,
          "maximum_cardinality_certificate_verified": true,
          "optimality_status": "certified_by_matching_and_upper_bound",
          "upper_bound_gap": 0,
          "objective": "unweighted_maximum_cardinality",
          "arithmetic": "exact_integer_graph_operations",
          "limits": {
            "vertices": 100000,
            "edges": 500000
          },
          "source_connection": {
            "family": "120",
            "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
            "new_source_matching_algorithm_implemented": false,
            "source_proof_verification": "not_run"
          },
          "formal_program_verification": "not_run",
          "interpretation": "A feasible matching attaining the checked odd-component or vertex bound is maximum cardinality. A nonzero gap is inconclusive. Weight, fairness, multiway assignment and source algorithm correctness are outside this audit."
        },
        "proposal": {
          "solver": "NetworkX max_weight_matching",
          "networkx_version": "3.4.2",
          "objective": "unweighted_maximum_cardinality",
          "integer_edge_weight": 1,
          "solver_calls": 1,
          "max_solver_calls": 257,
          "vertex_deletion_attempted": false,
          "vertex_deletion_complete": false,
          "deletion_selected_vertices": [],
          "subset_method": "empty subset",
          "constructor_guarantee": "Only the final attaining-bound audit grants a certificate; incomplete deletion or a loose bound can return unknown."
        },
        "timings_seconds": {
          "graph_validation_and_mapping": 0.0001355829881504178,
          "primary_solver": 0.0009950420062523335,
          "initial_audit": 0.0001188750029541552,
          "subset_proposal": 2.500019036233425e-07,
          "final_audit": 0.0001154169876826927,
          "measured_total": 0.0013651669869432226,
          "excludes": "Module imports, input file read, JSON serialization and output file write"
        },
        "environment": {
          "python": "3.10.19",
          "platform": "macOS-27.2-arm64-arm-64bit"
        },
        "limits": {
          "vertices": 256,
          "solver_calls": 257,
          "wall_time_deadline": "none; call cap is not a runtime guarantee"
        },
        "source_backend_implemented": false,
        "interpretation": "Finite existing-solver integration. Certificate scope is this supplied simple unweighted graph. No source-algorithm speed advantage, buyer workload, fairness, weighted-optimality or formal program verification is established."
      }
    }
  ],
  "public_fixture_source": "https://networkx.org/documentation/stable/reference/generated/networkx.generators.social.karate_club_graph.html",
  "conversion": "NetworkX public graph converted to node indices 0..33 and unweighted edges; club labels and interaction-context weights discarded explicitly.",
  "limitations": "Three technical fixtures, one run each. Timings exclude imports and I/O; no statistical performance claim, realistic allocation customer workload, source-backend comparison or buyer-value validation.",
  "scipy_runtime_check": {
    "status": "unavailable",
    "reason": "Local SciPy 3.10 extension failed to load: __DATA/__thread_bss zero-fill offset error. No global environment repair attempted. Exact table-law fractions were derived separately."
  }
}