{
  "P_support": [
    0,
    2
  ],
  "P_weights": [
    "1/2",
    "1/2"
  ],
  "Q_support": [
    1,
    3
  ],
  "Q_weights": [
    "3/4",
    "1/4"
  ],
  "CDF_interval_areas": [
    {
      "left": "0",
      "right": "1",
      "CDF_P": "1/2",
      "CDF_Q": "0",
      "absolute_gap": "1/2",
      "area": "1/2"
    },
    {
      "left": "1",
      "right": "2",
      "CDF_P": "1/2",
      "CDF_Q": "3/4",
      "absolute_gap": "1/4",
      "area": "1/4"
    },
    {
      "left": "2",
      "right": "3",
      "CDF_P": "1",
      "CDF_Q": "3/4",
      "absolute_gap": "1/4",
      "area": "1/4"
    }
  ],
  "W1": "1",
  "normalization": {
    "input_P_weight_total": "1",
    "input_Q_weight_total": "1",
    "positive_totals_normalized": true
  },
  "independent_all_feasible_quarter_mass_flows": [
    {
      "quarter_unit_flow_matrix": [
        [
          1,
          1
        ],
        [
          2,
          0
        ]
      ],
      "cost": "3/2"
    },
    {
      "quarter_unit_flow_matrix": [
        [
          2,
          0
        ],
        [
          1,
          1
        ]
      ],
      "cost": "1"
    }
  ],
  "translation_positive_scale_checks": [
    {
      "shift": "0",
      "positive_scale": "1",
      "distance": "1"
    },
    {
      "shift": "3",
      "positive_scale": "1",
      "distance": "1"
    },
    {
      "shift": "0",
      "positive_scale": "2",
      "distance": "2"
    },
    {
      "shift": "-2",
      "positive_scale": "1/2",
      "distance": "1/2"
    }
  ],
  "support_permutations_checked": 3,
  "identical_distribution_distance": "0",
  "duplicate_locations_aggregated_normalized": "1",
  "invalid_cases_rejected": [
    "negative_weight",
    "zero_total",
    "mismatch",
    "nonfinite_support",
    "nonfinite_weight",
    "over_budget"
  ],
  "scope": "own exact 1D discrete law, mass splitting allowed, distance in support-axis units; no multivariate optimization/SciPy run/population test/drift threshold/auto-retrain or one-to-one assignment"
}