{
  "status": "passed",
  "scope": "Exact diagnostics of the local volume recurrence and elementary identities only; not a verification of all adversary trajectories or the asymptotic theorem.",
  "arithmetic": "Python integers and fractions.Fraction; no floating-point comparisons",
  "seed": 817,
  "random_case_total": 630,
  "random_case_design": "Random acyclic orientations of a random vertex ordering, edge probability 0.3; integer, common-dyadic, and mixed-dyadic intervals, including infeasible systems.",
  "random_cases_by_size": [
    {
      "vertices": 1,
      "cases": 90,
      "positive_volume": 90,
      "zero_volume": 0,
      "all_exactly_equal": true
    },
    {
      "vertices": 2,
      "cases": 90,
      "positive_volume": 83,
      "zero_volume": 7,
      "all_exactly_equal": true
    },
    {
      "vertices": 3,
      "cases": 90,
      "positive_volume": 73,
      "zero_volume": 17,
      "all_exactly_equal": true
    },
    {
      "vertices": 4,
      "cases": 90,
      "positive_volume": 66,
      "zero_volume": 24,
      "all_exactly_equal": true
    },
    {
      "vertices": 5,
      "cases": 90,
      "positive_volume": 46,
      "zero_volume": 44,
      "all_exactly_equal": true
    },
    {
      "vertices": 6,
      "cases": 90,
      "positive_volume": 41,
      "zero_volume": 49,
      "all_exactly_equal": true
    },
    {
      "vertices": 7,
      "cases": 90,
      "positive_volume": 27,
      "zero_volume": 63,
      "all_exactly_equal": true
    }
  ],
  "analytic_case_total": 27,
  "analytic_cases": [
    {
      "case": "independent_1_coordinates_in_0_3",
      "actual": "3",
      "expected": "3",
      "passed": true
    },
    {
      "case": "chain_1_coordinates_in_0_3",
      "actual": "3",
      "expected": "3",
      "passed": true
    },
    {
      "case": "independent_2_coordinates_in_0_3",
      "actual": "9",
      "expected": "9",
      "passed": true
    },
    {
      "case": "chain_2_coordinates_in_0_3",
      "actual": "9/2",
      "expected": "9/2",
      "passed": true
    },
    {
      "case": "independent_3_coordinates_in_0_3",
      "actual": "27",
      "expected": "27",
      "passed": true
    },
    {
      "case": "chain_3_coordinates_in_0_3",
      "actual": "9/2",
      "expected": "9/2",
      "passed": true
    },
    {
      "case": "independent_4_coordinates_in_0_3",
      "actual": "81",
      "expected": "81",
      "passed": true
    },
    {
      "case": "chain_4_coordinates_in_0_3",
      "actual": "27/8",
      "expected": "27/8",
      "passed": true
    },
    {
      "case": "independent_5_coordinates_in_0_3",
      "actual": "243",
      "expected": "243",
      "passed": true
    },
    {
      "case": "chain_5_coordinates_in_0_3",
      "actual": "81/40",
      "expected": "81/40",
      "passed": true
    },
    {
      "case": "independent_6_coordinates_in_0_3",
      "actual": "729",
      "expected": "729",
      "passed": true
    },
    {
      "case": "chain_6_coordinates_in_0_3",
      "actual": "81/80",
      "expected": "81/80",
      "passed": true
    },
    {
      "case": "independent_7_coordinates_in_0_3",
      "actual": "2187",
      "expected": "2187",
      "passed": true
    },
    {
      "case": "chain_7_coordinates_in_0_3",
      "actual": "243/560",
      "expected": "243/560",
      "passed": true
    },
    {
      "case": "empty_coordinate_set",
      "actual": "1",
      "expected": "1",
      "passed": true
    },
    {
      "case": "directed_cycle",
      "actual": "0",
      "expected": "0",
      "passed": true
    },
    {
      "case": "infeasible_intervals",
      "actual": "0",
      "expected": "0",
      "passed": true
    },
    {
      "case": "unequal_independent_box",
      "actual": "6",
      "expected": "6",
      "passed": true
    },
    {
      "case": "triangle_area",
      "actual": "2",
      "expected": "2",
      "passed": true
    },
    {
      "case": "Pr_A_less_B_uniform_0_1_and_0_2",
      "actual": "3/4",
      "expected": "3/4",
      "passed": true
    },
    {
      "case": "third_child_admission_gain",
      "actual": "3",
      "expected": "3",
      "passed": true
    },
    {
      "case": "triangle_density_at_1/2",
      "actual": "3/4",
      "expected": "3/4",
      "passed": true
    },
    {
      "case": "promotion_ratio_at_1/2",
      "actual": "9/4",
      "expected": "9/4",
      "passed": true
    },
    {
      "case": "triangle_density_at_1",
      "actual": "1/2",
      "expected": "1/2",
      "passed": true
    },
    {
      "case": "promotion_ratio_at_1",
      "actual": "3/2",
      "expected": "3/2",
      "passed": true
    },
    {
      "case": "triangle_density_at_3/2",
      "actual": "1/4",
      "expected": "1/4",
      "passed": true
    },
    {
      "case": "promotion_ratio_at_3/2",
      "actual": "3/4",
      "expected": "3/4",
      "passed": true
    }
  ]
}