{
  "title": "Phase space and generating families — restored proof edition",
  "original_source_sha256": "47acfadde1cba993e12014d5be4865ffabba5120b51f27ea375d4d884bbd9a2e",
  "restored_source_sha256": "4b6afe62e844cefee7f5ae064de4d06d798cecb5968a5bc028d250fc406bdfe2",
  "original_authorship": "GPT-6.1 Sol (OpenAI), Ultra; September 2026",
  "restoration_and_form_companion": "GPT-6 Astra (OpenAI), Ultra; 5 October 2026",
  "source_policy": "Independent exposition with complete programme proofs and exact scholarly references.",
  "free_sources": [
    "Guillemin–Sternberg, Semi-classical Analysis, author draft of 13 January 2010",
    "Hörmander, Fourier integral operators I, 1971, exact verified Project Euclid edition, Section 3.1"
  ],
  "programme_flow_provider": {
    "lesson": "AN03-U012: Detecting regularity without choosing coordinates",
    "source_sha256": "062b34207ea15696d61f1d6df881d91cef51f28bb87988f6100189cd3275f014",
    "sections": "17.1–17.7, NF1–NF21",
    "section_start_line": 1462,
    "section_end_line": 1774,
    "retained_body_sha256": "93460356660af719128b49d3606829ba1bbd2a749d057ba03399c7e60d171aed",
    "body_unchanged": true,
    "licence": "GFDL-1.2-only",
    "source": "finite-coordinate-flows.md",
    "title_page": "notices/TITLE_PAGE.md",
    "history": "notices/HISTORY.md",
    "rights": "notices/RIGHTS.md",
    "licence_text": "notices/COPYING"
  },
  "component_licences": {
    "phase-space-and-generating-families.md": "CC0",
    "differential-forms-and-flow-pullbacks.md": "CC0",
    "finite-coordinate-flows.md": "GFDL-1.2-only"
  },
  "book_files_or_source_figures_redistributed": false,
  "all_alternative_proofs_preserved": true,
  "checks": [
    "Checked Hamiltonian sign and commutator/Jacobi expansion with coordinate proofs of every form identity.",
    "Checked symplectic basis extension signs, nonzero determinant polynomial and quotient-rank formula.",
    "Checked radial homotopy through t=0, quadratic primitive, invertible deformation and common time-one neighborhood.",
    "Checked free dilation gives nonzero radial field and a local transverse slice; contact wedge calculation and conic vanishing.",
    "Checked clean tangent hypothesis, Hessian-transpose rank, local image, homogeneous branch, minimal variables and base-induced frequency chart.",
    "Checked middle-diagonal reduction, clean tangent matching, input sign, all-variable homogeneity and local/global scope.",
    "Checked both explicit models and all five original exercise solutions.",
    "Read the full retained NF1–NF21 flow argument; bound its finite norm, calculus, inverse, integral and interval inputs to exact current programme proofs.",
    "Compared the preserved geometry exposition with the admitted HIII pages actually recorded. The Moser proof and lesson organization differ from the book commutation-coordinate proof. Standard short identities are credited; no source PDF, book exercise collection or source figures are distributed."
  ],
  "changes": [
    "Replaced broad prerequisite assumptions by exact programme links and full proof graph.",
    "Reused AN03 flow body without changing it; retained GFDL licence, title and history, with exact input bindings.",
    "Added independent coordinate proofs of differential-form identities and time-one flow domain.",
    "Made local conic branch and transverse-slice reasoning explicit.",
    "Retained all original geometric theorems, both models, all five solutions, and all existing alternative lessons."
  ],
  "bounded_lesson_P514_closed": true,
  "human_review_claimed": false,
  "full_course_complete": false,
  "public_release_authorized": false
}