{
  "status": "PASS",
  "arithmetic": "Exact fractions.Fraction; no floating point in feasibility or energy checks.",
  "scope": "Finite reproducibility checks of an analytic universal packing theorem; not a numerical global-optimization claim.",
  "normalization": "Each cap has mass 1; pair capacity is 1-max(b_ij,b_ji).",
  "target_squared_flow": "5/9",
  "owner_tournaments": 64,
  "rational_profiles_per_tournament": 5,
  "structured_arrays": 320,
  "random_rational_arrays": 500,
  "random_seed": 20261029,
  "sharp_star_arrays": 1,
  "total_arrays": 821,
  "edge_capacity_checks": 9852,
  "node_capacity_checks": 3284,
  "weighted_Hall_subset_checks": 22988,
  "construction_cases": {
    "balanced_pair_and_third": 146,
    "complementary_outlier": 350,
    "source": 325
  },
  "minimum_squared_flow_observed": "5/9",
  "sharp_star": {
    "construction": {
      "flows": {
        "0-1": "2/3",
        "0-2": "1/3",
        "0-3": "0",
        "1-2": "0",
        "1-3": "0",
        "2-3": "0"
      },
      "owners": {
        "0-1": 0,
        "0-2": 0,
        "0-3": 0,
        "1-2": 1,
        "1-3": 3,
        "2-3": 2
      },
      "case": "source"
    },
    "squared_flow": "5/9",
    "feasible_star_polytope_vertices": 10,
    "exact_maximum_over_star_vertices": "5/9",
    "upper_bound_reason": "A convex squared norm attains its maximum over this bounded polytope at a vertex; all vertices were enumerated exactly."
  },
  "errors": [],
  "seconds": 0.159325,
  "sha256": {
    "cap_packing.py": "363f9b2c2382774b1173f3dcf0fa5e1fea278d9ca7b7b7b244136b2f8af629dc",
    "verify_cap_packing.py": "c610a3a31598a08d2393da1dd235323f8ede0847891b316497f7f810e1eccc2a"
  }
}