{
  "format": "inward-discovery-scan-v1",
  "scope": "Exact rational arithmetic over this finite grid only; unrefuted is not proved.",
  "sourceSha256": "5aa654b506dcb020201540a9716ed08e5f1f778edc3e1420531096db1dba107e",
  "domain": {
    "readingValues": [
      "0",
      "25",
      "50",
      "75",
      "100"
    ],
    "targetValues": [
      "0",
      "25",
      "50",
      "75",
      "100"
    ],
    "readingMultisets": 126
  },
  "candidates": [
    {
      "id": "median-never-worse",
      "claim": "Median is at least as close as mean for every chosen target.",
      "status": "counterexample-found",
      "casesChecked": 7,
      "counterexample": {
        "readings": [
          "0",
          "0",
          "0",
          "0",
          "25"
        ],
        "target": "25",
        "mean": "5",
        "median": "0",
        "actualWinner": "mean"
      }
    },
    {
      "id": "mean-never-worse",
      "claim": "Mean is at least as close as median for every chosen target.",
      "status": "counterexample-found",
      "casesChecked": 6,
      "counterexample": {
        "readings": [
          "0",
          "0",
          "0",
          "0",
          "25"
        ],
        "target": "0",
        "mean": "5",
        "median": "0",
        "actualWinner": "median"
      }
    },
    {
      "id": "target-independent",
      "claim": "Changing the target cannot reverse a strict winner for fixed readings.",
      "status": "counterexample-found",
      "casesChecked": 2,
      "counterexample": {
        "readings": [
          "0",
          "0",
          "0",
          "0",
          "25"
        ],
        "first": {
          "readings": [
            "0",
            "0",
            "0",
            "0",
            "25"
          ],
          "target": "0",
          "mean": "5",
          "median": "0",
          "actualWinner": "median"
        },
        "second": {
          "readings": [
            "0",
            "0",
            "0",
            "0",
            "25"
          ],
          "target": "25",
          "mean": "5",
          "median": "0",
          "actualWinner": "mean"
        }
      }
    },
    {
      "id": "midpoint-tie",
      "claim": "For distinct estimates, their exact midpoint is an equal-error target.",
      "status": "unrefuted-on-finite-grid",
      "casesChecked": 108,
      "counterexample": null
    },
    {
      "id": "permutation-invariant",
      "claim": "Permuting the five readings cannot change the winner at a fixed target.",
      "status": "unrefuted-on-finite-grid",
      "casesChecked": 15625,
      "counterexample": null
    }
  ]
}