{
  "weights": [
    1,
    2,
    3
  ],
  "probabilities": [
    "1/6",
    "1/3",
    "1/2"
  ],
  "scaled_threshold_q": [
    "1/2",
    "1",
    "1"
  ],
  "alias_indices": [
    2,
    1,
    2
  ],
  "construction": [
    {
      "under": 0,
      "over": 2,
      "q_under": "1/2",
      "over_before": "3/2",
      "over_after": "1"
    }
  ],
  "all_twelve_equal_probability_worlds": [
    {
      "uniform_bin": 0,
      "uniform_midpoint_coin": "1/8",
      "outcome": 0
    },
    {
      "uniform_bin": 0,
      "uniform_midpoint_coin": "3/8",
      "outcome": 0
    },
    {
      "uniform_bin": 0,
      "uniform_midpoint_coin": "5/8",
      "outcome": 2
    },
    {
      "uniform_bin": 0,
      "uniform_midpoint_coin": "7/8",
      "outcome": 2
    },
    {
      "uniform_bin": 1,
      "uniform_midpoint_coin": "1/8",
      "outcome": 1
    },
    {
      "uniform_bin": 1,
      "uniform_midpoint_coin": "3/8",
      "outcome": 1
    },
    {
      "uniform_bin": 1,
      "uniform_midpoint_coin": "5/8",
      "outcome": 1
    },
    {
      "uniform_bin": 1,
      "uniform_midpoint_coin": "7/8",
      "outcome": 1
    },
    {
      "uniform_bin": 2,
      "uniform_midpoint_coin": "1/8",
      "outcome": 2
    },
    {
      "uniform_bin": 2,
      "uniform_midpoint_coin": "3/8",
      "outcome": 2
    },
    {
      "uniform_bin": 2,
      "uniform_midpoint_coin": "5/8",
      "outcome": 2
    },
    {
      "uniform_bin": 2,
      "uniform_midpoint_coin": "7/8",
      "outcome": 2
    }
  ],
  "world_counts": {
    "0": 2,
    "1": 4,
    "2": 6
  },
  "independent_CDF_six_ticket_outcomes": [
    0,
    1,
    1,
    2,
    2,
    2
  ],
  "threshold_equal_uses_alias": {
    "q0": "1/2",
    "below": 0,
    "equal": 2
  },
  "coin_zero_accepted": true,
  "coin_one_rejected": true,
  "changed_weights_require_rebuild": {
    "new_weights": [
      3,
      2,
      1
    ],
    "new_probabilities": [
      "1/2",
      "1/3",
      "1/6"
    ],
    "old_table_still_represents_old_probabilities": [
      "1/6",
      "1/3",
      "1/2"
    ]
  },
  "additional_exact_tables": [
    {
      "weights": [
        0,
        1,
        0
      ],
      "probabilities": [
        "0",
        "1",
        "0"
      ],
      "q": [
        "0",
        "1",
        "0"
      ],
      "alias": [
        1,
        1,
        1
      ],
      "analytic_mass_equal": true
    },
    {
      "weights": [
        1
      ],
      "probabilities": [
        "1"
      ],
      "q": [
        "1"
      ],
      "alias": [
        0
      ],
      "analytic_mass_equal": true
    },
    {
      "weights": [
        1,
        1,
        1
      ],
      "probabilities": [
        "1/3",
        "1/3",
        "1/3"
      ],
      "q": [
        "1",
        "1",
        "1"
      ],
      "alias": [
        0,
        1,
        2
      ],
      "analytic_mass_equal": true
    },
    {
      "weights": [
        2,
        0,
        3,
        1
      ],
      "probabilities": [
        "1/3",
        "0",
        "1/2",
        "1/6"
      ],
      "q": [
        "1",
        "0",
        "2/3",
        "2/3"
      ],
      "alias": [
        0,
        2,
        0,
        2
      ],
      "analytic_mass_equal": true
    }
  ],
  "invalid_weights_rejected": [
    "[]",
    "[0, 0]",
    "[-1, 2]",
    "[True, 1]",
    "[nan, 1]",
    "[1, 1, 1, 1, 1, 1, 1, 1, 1]"
  ],
  "scope": "precomputed fixed weights with replacement; table rebuild for changed weights; no reservoir, MCMC, PRNG/security or product throughput claim"
}