{
  "sorted_data": [
    -2,
    0,
    0,
    0,
    3,
    7
  ],
  "query_zero": {
    "lower_bound": 1,
    "upper_bound": 4,
    "equal_halfopen_range": [
      1,
      4
    ],
    "count": 3
  },
  "lower_trace": [
    {
      "before_halfopen": [
        0,
        6
      ],
      "mid": 3,
      "value": 0,
      "after_halfopen": [
        0,
        3
      ]
    },
    {
      "before_halfopen": [
        0,
        3
      ],
      "mid": 1,
      "value": 0,
      "after_halfopen": [
        0,
        1
      ]
    },
    {
      "before_halfopen": [
        0,
        1
      ],
      "mid": 0,
      "value": -2,
      "after_halfopen": [
        1,
        1
      ]
    }
  ],
  "upper_trace": [
    {
      "before_halfopen": [
        0,
        6
      ],
      "mid": 3,
      "value": 0,
      "after_halfopen": [
        4,
        6
      ]
    },
    {
      "before_halfopen": [
        4,
        6
      ],
      "mid": 5,
      "value": 7,
      "after_halfopen": [
        4,
        5
      ]
    },
    {
      "before_halfopen": [
        4,
        5
      ],
      "mid": 4,
      "value": 3,
      "after_halfopen": [
        4,
        4
      ]
    }
  ],
  "edge_queries": [
    {
      "x": -3,
      "left": 0,
      "right": 0,
      "count_equal": 0,
      "membership": false
    },
    {
      "x": 0,
      "left": 1,
      "right": 4,
      "count_equal": 3,
      "membership": true
    },
    {
      "x": 1,
      "left": 4,
      "right": 4,
      "count_equal": 0,
      "membership": false
    },
    {
      "x": 8,
      "left": 6,
      "right": 6,
      "count_equal": 0,
      "membership": false
    }
  ],
  "sorted_array_query_checks": 420,
  "inclusive_value_range_count_checks": 1260,
  "rejected": [
    [
      "[2, 1]",
      "1"
    ],
    [
      "[0, 1]",
      "True"
    ],
    [
      "[0, False]",
      "0"
    ]
  ],
  "complexity_scope": "binary loop logarithmic; validation and executable invariant assertions scan data and are teaching overhead; no benchmark",
  "index_contract": "positions in already-sorted input, insertion position is not membership; no mutation or hidden sorting"
}