{
  "authored_values": [
    5,
    1,
    9,
    2,
    2,
    8
  ],
  "all_prefix_heap_states": [
    {
      "prefix_length": 1,
      "inserted_value": 5,
      "inserted_into": "lower_max_heap_stored_negated",
      "rebalance_moves": [],
      "lower_values_sorted": [
        5
      ],
      "upper_values_sorted": [],
      "lower_size": 1,
      "upper_size": 0,
      "median": "5"
    },
    {
      "prefix_length": 2,
      "inserted_value": 1,
      "inserted_into": "lower_max_heap_stored_negated",
      "rebalance_moves": [
        {
          "value": 5,
          "from": "lower",
          "to": "upper"
        }
      ],
      "lower_values_sorted": [
        1
      ],
      "upper_values_sorted": [
        5
      ],
      "lower_size": 1,
      "upper_size": 1,
      "median": "3"
    },
    {
      "prefix_length": 3,
      "inserted_value": 9,
      "inserted_into": "upper_min_heap",
      "rebalance_moves": [
        {
          "value": 5,
          "from": "upper",
          "to": "lower"
        }
      ],
      "lower_values_sorted": [
        1,
        5
      ],
      "upper_values_sorted": [
        9
      ],
      "lower_size": 2,
      "upper_size": 1,
      "median": "5"
    },
    {
      "prefix_length": 4,
      "inserted_value": 2,
      "inserted_into": "lower_max_heap_stored_negated",
      "rebalance_moves": [
        {
          "value": 5,
          "from": "lower",
          "to": "upper"
        }
      ],
      "lower_values_sorted": [
        1,
        2
      ],
      "upper_values_sorted": [
        5,
        9
      ],
      "lower_size": 2,
      "upper_size": 2,
      "median": "7/2"
    },
    {
      "prefix_length": 5,
      "inserted_value": 2,
      "inserted_into": "lower_max_heap_stored_negated",
      "rebalance_moves": [],
      "lower_values_sorted": [
        1,
        2,
        2
      ],
      "upper_values_sorted": [
        5,
        9
      ],
      "lower_size": 3,
      "upper_size": 2,
      "median": "2"
    },
    {
      "prefix_length": 6,
      "inserted_value": 8,
      "inserted_into": "upper_min_heap",
      "rebalance_moves": [],
      "lower_values_sorted": [
        1,
        2,
        2
      ],
      "upper_values_sorted": [
        5,
        8,
        9
      ],
      "lower_size": 3,
      "upper_size": 3,
      "median": "7/2"
    }
  ],
  "all1093_ternary_sequences_oracle_checks": {
    "sequences": 1093,
    "prefixes": 6015
  },
  "wrong_old_median_average": {
    "prefix": [
      5,
      1,
      9
    ],
    "previous_median": "3",
    "new_value": 9,
    "wrong_average": "6",
    "correct_median": "5"
  },
  "empty_median": null,
  "retained_heap_values": 6,
  "invalid_inputs_rejected": [
    "[True]",
    "[1.5]",
    "[nan]",
    "[inf]",
    "[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]"
  ],
  "scope": "exact append-only prefix median, two heaps retain allnvalues O(n) memory, no fixed-memory sketch/sliding deletion/realcallstats/benchmark; full teaching traces and oracle also have separate storage cost"
}