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      "kernel_and_reflection": "(-1,1)",
      "exact_fold_coordinate_identity": true,
      "full_map_preserved_by_actual_involution": true,
      "passed": true
    },
    {
      "name": "square-descent jets including odd division",
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          "odd_boundary_derivative": "1/60"
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          "odd_boundary_derivative": "-1/840"
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        {
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          "even_boundary_derivative": "(z + 1)/1680",
          "odd_boundary_derivative": "1/15120"
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      ],
      "passed": true
    },
    {
      "name": "Lagrange extension coefficients and finite all-jet identities",
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          "absolute_weighted_sum": 5792055.782241191
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      ],
      "scope": "Finite high-precision comparisons; analytic infinite-product and domination proof is in the lesson.",
      "passed": true
    },
    {
      "name": "ordinary frequency estimates through the square boundary",
      "external_order": 0.75,
      "models": [
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      "kind": "Independent central differences versus exact gradient on a normalized cone.",
      "passed": true
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    {
      "name": "critical coefficient order shifts and odd sign",
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      "correct_odd_product": "(-i)*i=1",
      "opposite_sign_gives": "F0-s F1",
      "full_Airy_integral_identity_checked": false,
      "passed": true
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  ],
  "scope": "Six bounded exact fold/jet/interpolation/order models and independent high-precision/numerical comparisons. They test coordinates, signs, coefficient moments and selected frequency estimates; they do not certify the general smooth extension, simultaneous fold geometry or Airy continuity.",
  "independent_mathematical_review": false
}