{
  "schema": "positive-ideal-finite-author-controls/v1",
  "passed": true,
  "lesson": "positive-lagrangian-ideals-and-distributions.md",
  "lesson_sha256": "5477f8105fa2a8d3ce17b928ac5555e86b4a7283d73a8a5ed794f59784766af8",
  "script_sha256": "db6b6163940019418866f7061c5187ba587618a8b07a178a2edf81ffa26a23a8",
  "checks": [
    {
      "name": "Eight retained source-preparation model families",
      "passed": true,
      "scope": "Exact graph degrees, full normal phase, crossing/rank change, cubic sign obstruction, twelve actual Gaussian integrations, complete orders/constants, six flat derivatives and actual Mellin partitions.",
      "script_sha256": "914915fd257395cff05f302054dd42a89a0aeac328ea7ae950bee909afbfceae"
    },
    {
      "name": "Three retained uniform-division controls",
      "passed": true,
      "scope": "Whole bivariate polynomial identity, twelve genuinely nonholomorphic path integrals with wrong-sign negative control, and thirteen diagonal cutoff levels.",
      "report_sha256": "e2af4f50287ce9fa6235b8b9202d5cdab15091f07a36ad91e3fc311f6c7a7ac1"
    },
    {
      "name": "Full critical-value matrix with a null imaginary direction",
      "passed": true,
      "scope": "Actual invertible symmetric matrix with singular nonnegative imaginary part; complete quadratic identity and positive lower bound 7/16."
    },
    {
      "name": "Actual complex evaluation by real polynomial interpolation",
      "passed": true,
      "scope": "Four real nodes reproduce evaluation at i for all cubic polynomials, and annihilate the three positive powers of s-i used in flat-residue necessity."
    },
    {
      "name": "Actual failure of damping for nonuniform smooth-ideal coefficients",
      "passed": true,
      "scope": "Degree-one flat-imaginary H and exact nonzero transverse derivative, with four increasing frequencies verifying e^-1 r^-1/2 on the moving angular support. Written derivative estimates establish S^0; this finite sampling does not prove the general symbol assertion.",
      "samples": [
        {
          "log_radius": 12.0,
          "imaginary_damping": 1.0000000000000036,
          "normalized_damped_value": 0.367879441171441
        },
        {
          "log_radius": 24.0,
          "imaginary_damping": 1.000000000000007,
          "normalized_damped_value": 0.3678794411714397
        },
        {
          "log_radius": 48.0,
          "imaginary_damping": 1.0000000000000142,
          "normalized_damped_value": 0.3678794411714371
        },
        {
          "log_radius": 72.0,
          "imaginary_damping": 1.0000000000000142,
          "normalized_damped_value": 0.36787944117143717
        }
      ]
    },
    {
      "name": "Absolute error cannot be divided by exponential damping",
      "passed": true,
      "scope": "Four explicit positive frequencies for E=e^-sqrt(t) illustrate the written rapid-error counterexample."
    },
    {
      "name": "Authored lesson and explicit hypothesis boundaries",
      "passed": true,
      "scope": "Seventeen paired original solutions and explicit source degree, bounded-ideal, Gaussian branch, absolute-error and two-way representation contracts. This is a content guard, not proof verification."
    }
  ],
  "independent_review": false,
  "full_source_parent_closed": false,
  "limitations": "Finite models and explicit hypothesis controls support the original written proofs. The complete written analytic proofs are checked separately; finite controls do not certify general theorems or whole-course completion."
}