{
  "kind": "Synthetic exact-arithmetic counterexample; no empirical observations",
  "matrix": [
    [
      "39/50",
      "1/5",
      "1/100",
      "1/100"
    ],
    [
      "1/5",
      "39/50",
      "1/100",
      "1/100"
    ],
    [
      "1/100",
      "1/100",
      "39/50",
      "1/5"
    ],
    [
      "1/100",
      "1/100",
      "1/5",
      "39/50"
    ]
  ],
  "threshold": 7.0,
  "question": "At the stated observation step, is any value at least 7?",
  "within_room_difference_factor": "29/50",
  "between_room_mean_difference_factor": "24/25",
  "grid_states_checked": 6561,
  "mean_closure": "Exact in this symmetric construction",
  "same_summary_class": {
    "restriction": "Integer initial values 0 through 8, both room means 4",
    "states": 81,
    "immediate_flag_required": 56,
    "immediate_no_flag_required": 25,
    "flag_required_after_one_step": 0,
    "maximum_after_one_step": 6.32,
    "note": "The exhaustive count is for this chosen finite class, not a probability estimate."
  },
  "A": [
    {
      "step": 0,
      "values": [
        8.0,
        0.0,
        4.0,
        4.0
      ],
      "room_means": [
        4.0,
        4.0
      ],
      "flag_required": true
    },
    {
      "step": 1,
      "values": [
        6.32,
        1.68,
        4.0,
        4.0
      ],
      "room_means": [
        4.0,
        4.0
      ],
      "flag_required": false
    },
    {
      "step": 2,
      "values": [
        5.3456,
        2.6544,
        4.0,
        4.0
      ],
      "room_means": [
        4.0,
        4.0
      ],
      "flag_required": false
    },
    {
      "step": 3,
      "values": [
        4.780448,
        3.219552,
        4.0,
        4.0
      ],
      "room_means": [
        4.0,
        4.0
      ],
      "flag_required": false
    },
    {
      "step": 4,
      "values": [
        4.45265984,
        3.54734016,
        4.0,
        4.0
      ],
      "room_means": [
        4.0,
        4.0
      ],
      "flag_required": false
    },
    {
      "step": 5,
      "values": [
        4.2625427072,
        3.7374572928,
        4.0,
        4.0
      ],
      "room_means": [
        4.0,
        4.0
      ],
      "flag_required": false
    }
  ],
  "B": [
    {
      "step": 0,
      "values": [
        4.0,
        4.0,
        4.0,
        4.0
      ],
      "room_means": [
        4.0,
        4.0
      ],
      "flag_required": false
    },
    {
      "step": 1,
      "values": [
        4.0,
        4.0,
        4.0,
        4.0
      ],
      "room_means": [
        4.0,
        4.0
      ],
      "flag_required": false
    },
    {
      "step": 2,
      "values": [
        4.0,
        4.0,
        4.0,
        4.0
      ],
      "room_means": [
        4.0,
        4.0
      ],
      "flag_required": false
    },
    {
      "step": 3,
      "values": [
        4.0,
        4.0,
        4.0,
        4.0
      ],
      "room_means": [
        4.0,
        4.0
      ],
      "flag_required": false
    },
    {
      "step": 4,
      "values": [
        4.0,
        4.0,
        4.0,
        4.0
      ],
      "room_means": [
        4.0,
        4.0
      ],
      "flag_required": false
    },
    {
      "step": 5,
      "values": [
        4.0,
        4.0,
        4.0,
        4.0
      ],
      "room_means": [
        4.0,
        4.0
      ],
      "flag_required": false
    }
  ],
  "post_equilibrium_disturbance": {
    "A": [
      8,
      4,
      4,
      4
    ],
    "B": [
      6,
      6,
      4,
      4
    ],
    "room_means": [
      6,
      4
    ],
    "A_requires_flag": true,
    "B_requires_flag": false,
    "note": "Equal heat added locally or evenly; the new disturbance invalidates an old mixing bound."
  }
}