{
  "format": "inward-estimator-identities-v1",
  "model": "Five real readings, their mean and median, and any real target",
  "factorization": {
    "statement": "(a-t)^2-(b-t)^2=(a-b)(a+b-2t)",
    "expandedTerms": {
      "a^2": "1",
      "b^2": "-1",
      "a*t": "-2",
      "b*t": "2"
    }
  },
  "midpoint": {
    "statement": "At t=(a+b)/2, the two absolute errors are equal",
    "firstResidual": {"a": "1/2", "b": "-1/2"},
    "secondResidual": {"a": "-1/2", "b": "1/2"}
  },
  "permutation": {
    "statement": "Reordering five readings preserves mean, median, and both absolute errors at every target",
    "readingCount": 5,
    "permutationsChecked": 120,
    "meanCoefficients": ["1/5", "1/5", "1/5", "1/5", "1/5"],
    "medianRank": 3
  }
}