{
  "title": "Homogeneous phase equivalence and stabilization — restored proof edition",
  "original_source_sha256": "d2c2eceab1911c0a12892d93953412c9c7b593bafb17966e0dd7b45d6d6b2442",
  "restored_source_sha256": "d62be990dcf5e284b3942ed539653ed8631901281069715abfc80bec64b38ee2",
  "original_authorship": "AN-04 course-writing task, 1 October 2026",
  "restoration_review": "GPT-6 Astra (OpenAI), Ultra, 5 October 2026",
  "source_policy": "Independent exposition with complete programme proofs and exact scholarly references.",
  "source_references": [
    {
      "edition_id": "ISBN-978-3-540-49938-1-pdf",
      "pdf_pages_read": [
        307,
        308,
        309
      ]
    },
    {
      "edition_id": "ISBN-978-3-642-61497-2-pdf",
      "pdf_pages_read": [
        237,
        238
      ]
    }
  ],
  "historical_source_inspection_preserved": true,
  "historical_copy_admission_inferred": false,
  "book_files_redistributed": false,
  "original_lesson_and_figure_licence": "CC0-1.0",
  "font_notices": [
    "figures/notices/LICENSE_DEJAVU.txt",
    "figures/notices/LICENSE_STIX.txt"
  ],
  "linked_programme_component_rights_retained": "The separate AN03 flow extract remains GFDL-1.2-only with full notices.",
  "figure_bytes_unchanged": "4234d17ca94254036dafb3f2d92cb712b64b019260cbb4393bfdcb0a8d2b4200",
  "figure_caption_corrected": "Left/right changed to top/bottom to match the actual stacked panels.",
  "all_original_displayed_equations_and_twelve_solutions_unchanged": true,
  "computational_evidence": "checks/bounded-checks.json",
  "proof_review": [
    "Checked vertical critical tangents, congruence, positive/negative inertia and the radial Hessian kernel.",
    "Checked the complete parameter Taylor matrix, smooth signed LDL pivots and the nonlinear coordinate inverse, including empty blocks.",
    "Checked projective homogeneous coordinates, quadratic rank splitting and preservation of the critical map.",
    "Checked the minimal-phase graph and second-order difference, the full fixed-base coefficient derivative in C_t, inverse-transpose cancellation and time-one flow on the augmented base/fiber state.",
    "Checked homogeneous extension from a transverse ray section, common-radius direction, equal signatures and exact original-coordinate stable block maps.",
    "Checked mixed symbol orders, absolute Jacobian, x-dependent pulled cutoffs, transpose order reduction, integrable tail and Fourier half-density normalization.",
    "Checked the earlier explicit stabilized amplitude and its full parameter-smooth remainder; the base-dependent radius is handled by the proved homogeneous change.",
    "Checked both nonlinear examples, all twelve solutions and six current bounded calculation checks. All original display equations and exercise/solution blocks are unchanged.",
    "Read the admitted HIII generating-function pages and HI stationary-phase pages. They supply the stated contexts; the lesson writes its own full equivalence argument and teaching examples, and does not claim that the cited pages state that full theorem."
  ],
  "changes": [
    "Exact current geometry, oscillatory, finite-calculus and flow proof links.",
    "Explicit augmented-state flow justification.",
    "Approved-edition bibliography and truthful source comparison.",
    "Top/bottom figure-caption correction; figure data preserved.",
    "Retained reproducible figure, calculation checks and both font notices."
  ],
  "all_alternative_proofs_preserved": true,
  "bounded_lesson_P514_closed": true,
  "human_review_claimed": false,
  "full_course_complete": false,
  "public_release_authorized": false
}