{
  "path": {
    "vertices": 4,
    "support_pairs": 6,
    "original_edge_copies": 6,
    "spanning_tree_valid": true,
    "candidate_issues": [],
    "target_alpha": "1/3",
    "source_connection": {
      "family": "174",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "source_polynomial_constructor_implemented": false,
      "source_proof_verification": "not_run"
    },
    "arithmetic": "exact integers and fractions",
    "formal_program_verification": "not_run",
    "limits": {
      "vertices": 16,
      "multiplicity_bits": 256,
      "cut_edge_examinations": 5000000
    },
    "work_unit_definition": "Each original pair or tree edge examined at one cut; validation and fundamental-cut setup are additional bounded work.",
    "status": "complete",
    "cuts_completed": 7,
    "work_units": 63,
    "exact_thinness": "3/4",
    "worst_cut": {
      "vertices": [
        0,
        2
      ],
      "tree_edges": 3,
      "graph_edge_copies": 4
    },
    "exact_edge_connectivity": 3,
    "mincut_vertices": [
      0
    ],
    "achieved_C_for_k": "9/4",
    "fundamental_tree_cut_max_ratio": "1/3",
    "target_all_cut_bound_verified": false,
    "interpretation": "All cuts are exhausted for this bounded graph/tree. Binary multiplicities count distinct copies, not arbitrary real traffic capacities. Fundamental tree cuts alone can understate thinness. No polynomial source constructor, routing throughput, latency or failure-tolerant backbone is established."
  },
  "parallel_example": {
    "vertices": 2,
    "support_pairs": 1,
    "original_edge_copies": 1267650600228229401496703205376,
    "spanning_tree_valid": true,
    "candidate_issues": [],
    "target_alpha": "1/1267650600228229401496703205376",
    "source_connection": {
      "family": "174",
      "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
      "source_polynomial_constructor_implemented": false,
      "source_proof_verification": "not_run"
    },
    "arithmetic": "exact integers and fractions",
    "formal_program_verification": "not_run",
    "limits": {
      "vertices": 16,
      "multiplicity_bits": 256,
      "cut_edge_examinations": 5000000
    },
    "work_unit_definition": "Each original pair or tree edge examined at one cut; validation and fundamental-cut setup are additional bounded work.",
    "status": "complete",
    "cuts_completed": 1,
    "work_units": 2,
    "exact_thinness": "1/1267650600228229401496703205376",
    "worst_cut": {
      "vertices": [
        0
      ],
      "tree_edges": 1,
      "graph_edge_copies": 1267650600228229401496703205376
    },
    "exact_edge_connectivity": 1267650600228229401496703205376,
    "mincut_vertices": [
      0
    ],
    "achieved_C_for_k": "1",
    "fundamental_tree_cut_max_ratio": "1/1267650600228229401496703205376",
    "target_all_cut_bound_verified": true,
    "interpretation": "All cuts are exhausted for this bounded graph/tree. Binary multiplicities count distinct copies, not arbitrary real traffic capacities. Fundamental tree cuts alone can understate thinness. No polynomial source constructor, routing throughput, latency or failure-tolerant backbone is established."
  },
  "declared_parameters": {
    "signing_Cs": 1048576,
    "declared_cut_upper_factor": "1/2 + 3*Cs*r^(-1/8)",
    "r_must_exceed_for_declared_upper_factor_less_than_one": "2454761534087181835861600303987592420342418794103177216",
    "decimal_digits": 55,
    "interpretation": "Algebraic condition for this stated conservative factor to certify strict cut contraction. Not an input lower bound, measured runtime, published final C, or impossibility for a different constructor. The absolute iteration cutoff R0 and final C remain unspecified."
  },
  "source_proof_verification": "not_run"
}