{
  "schema": "author-quadratic-form-computational-check/v1",
  "passed": true,
  "lesson": "quadratic-hamilton-maps-and-positive-complex-planes.md",
  "lesson_sha256": "11bee27367f59f85f306f7eb7c02e056edb0cbed4ae024f768f30c34139c7db1",
  "script_sha256": "3e4e537bb528733d58bbfd6cd76581fa203668dae7f982be2f09cee680bed19f",
  "checks": [
    {
      "name": "Retained eight preparation model families",
      "passed": true,
      "preparation_script_sha256": "af2b27dcb15fff31d8f5aafcb4679accf5776d86c78600ed9d0a2ae0cde3c466",
      "scope": "All eight finite matrix, spectral, graph and hypothesis model families run without state writes or book inputs."
    },
    {
      "name": "Exact critical-point factor and complete oscillator coordinate change",
      "passed": true,
      "scope": "Full Hamilton derivative, entire canonical matrix, normalized quadratic form and one-form coefficient difference."
    },
    {
      "name": "Full nilpotent exponential and all graded real block invariants",
      "passed": true,
      "scope": "Whole polynomial flow and conserved matrices, same-inertia inequivalence by spectra, and exact mixed 8-dimensional ranks and characteristic polynomial."
    },
    {
      "name": "Actual sectorial Jordan homotopy, exact generalized projection and flow",
      "passed": true,
      "parameter_scope": "Exact polynomial identities for every real u; sector/positivity samples u=0,1/3,2/3,1",
      "scope": "Full 4-by-4 Hamilton matrix, nonsemisimple spectrum, changing geometric multiplicity, fixed positive generalized plane, Hermite projector and entire restricted exponential."
    },
    {
      "name": "Independent oriented resolvent integration through the Jordan degeneracy",
      "passed": true,
      "parameter_samples": 4,
      "angular_samples_each": 1024,
      "maximum_projection_residual": 1.4588859517969432e-15,
      "scope": "Actual numerical resolvent quadrature compared with the independently derived exact Hermite projection; wrong-sign control fails. Not a general spectral-continuity proof."
    },
    {
      "name": "Exact full graph normalization, Hermitian factor and compatible metric",
      "passed": true,
      "scope": "Closed radical square root, whole real canonical matrix, positive complex graph, full structure identities and every leading metric minor."
    },
    {
      "name": "Complex scalar numerical range, sector failures including C=0 and non-strict planes",
      "passed": true,
      "scope": "Exact scalar value, genuine kernel failures, indefinite real form under the vacuous zero-sector inequality, all weak-plane pairings and full Fourier rotation; does not establish the arbitrary quotient proof."
    }
  ],
  "exercise_solution_count": 14,
  "general_mathematical_certification": false,
  "limitations": "The unrestricted signature exhaustion, generalized spectral pairing, common-contour continuation, compatible-structure uniqueness and positive quotient arguments are written proofs; finite models do not certify them. Independent review remains open."
}