{
  "title": "Hamilton fields and subprincipal transport — restored proof edition",
  "original_source_sha256": "5a6c19c639d003d80b05ce7193f6ea2eb3f9784cef40cbecc918e58801c037d2",
  "restored_source_sha256": "6f4dbdc2071db89841b652484b0c1055839e04e5f16fe95b4a005242a831786d",
  "original_authorship": "GPT-6.1 Sol (OpenAI), Ultra, September 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-978-3-642-00136-9-pdf",
      "pdf_pages_read": [
        33,
        34,
        35
      ],
      "relevant_printed_pages": [
        22,
        23,
        24
      ]
    }
  ],
  "original_lesson_preserved": true,
  "book_files_redistributed": false,
  "original_lesson_licence": "CC0-1.0",
  "subprincipal_companion": {
    "source": "subprincipal-coordinate-invariance.md",
    "sha256": "a3ee16450fcce62e330243c3663724e4c7c48845e39049c1a323fc9f7830a54a",
    "licence": "GFDL-1.2-only",
    "source_lesson": "AN03-U012",
    "source_sha256": "062b34207ea15696d61f1d6df881d91cef51f28bb87988f6100189cd3275f014",
    "original_selection_sha256": "1ef5fce3321231c5e3e331c88e6e0ba918020d8c5fc0c69487ac6e0982ca5b0b",
    "adapted_selection_sha256": "00e97507eec0444c2abeef0f72b3a435c0123916ee591c89758f095d448d42d5",
    "mathematical_equations_and_index_calculation_unchanged": true,
    "notices": [
      "notices/COPYING",
      "notices/TITLE_PAGE.md",
      "notices/HISTORY.md",
      "notices/RIGHTS.md"
    ]
  },
  "linked_component_rights": "All earlier proof components retain their individual notices and licences.",
  "all_original_displayed_equations_and_six_exercise_solutions_unchanged": true,
  "proof_review": [
    "Read the complete retained scalar transport lesson and all six solutions; every original display and the full exercise section remain unchanged.",
    "Read AN03-U012 Sections 2-3 and the current T1-T2 and O1-O6 coordinate and amplitude proofs. Retained G11-G14 and the full scalar index calculation, with exact replacement prerequisites.",
    "Checked the two Jacobians in the coordinate amplitude, the half-Hessian derivative of its segment matrix, the determinant logarithmic derivative and cancellation of all first-frequency-derivative terms.",
    "Checked the exact first coordinate correction, including every differentiated S^(m-2) remainder for nonhomogeneous ordinary symbols, and the two leading homogeneous terms for classical symbols.",
    "Checked G11-G14: every mixed-index chain rule, function-symbol Jacobian correction, complex density cocycle, multiplication conjugation, half-density cancellation and global two-term scalar class.",
    "Bound the real smooth flow theorem to the full current NF1-NF21 proof. Checked arbitrary complex density weights, the determinant derivative, complex vector-field extension and locally constant Maslov transitions.",
    "Checked the skew half-density pairing with finite chart partitions and explicit cancellation of all derivatives of the partition.",
    "Checked Hamilton tangency for real and complex symbols using the exact symplectic sign and the input reflection.",
    "Checked the diagonal-complement induction, reduced symplectic quotient, nonzero determinant polynomial, finite-root proof and Fubini null-slice argument.",
    "Checked the separate quadratic base jets, both nonzero covectors, conic frequency projection, homogeneous generating function and nondegenerate phase.",
    "Checked the full frequency-only normal form and exact normalization, the base-removal integration by parts, supported asymptotic sum and smooth remainder.",
    "Checked actual PA even when A is not proper: proper intermediate localization, identity-graph composition, compact localized kernels and smooth errors from the adjoint mapping result.",
    "Checked Taylor division along the critical graph, frequency comparability, ordinary derivative budgets, cutoff limits and the exact one-order gain.",
    "Checked the total-versus-fixed-base derivative calculation and every sign in the half-divergence correction. Checked intrinsic patching, actual density degree, all differentiated symbol bounds and principal quotient independence.",
    "Checked the compact-circle lift, exact delta factor, operator order, full local integrating-factor solution and all six solutions, including the periodic monodromy obstruction.",
    "Read the admitted H IV. The retained lesson has independent explanations and six original solutions. No book text, figures or exercises are distributed. The adapted AN03 component retains GFDL 1.2 and complete notices."
  ],
  "changes": [
    "Exact current programme links, complete smooth-flow proof and approved-edition citation.",
    "Retained the AN03 scalar subprincipal calculation with its GFDL notices and current prerequisite links.",
    "Proved its precise first coordinate correction, both Jacobians, derivative cancellation and all second-order remainder estimates.",
    "Supplied the finite-root step and partition cancellation used in the retained proofs.",
    "Made proper intermediate localization explicit even for nonproper A and bound all final symbol derivatives and quotient remainders.",
    "Preserved every original display and all six solved exercises, plus all earlier alternatives."
  ],
  "all_alternative_proofs_preserved": true,
  "bounded_lesson_P514_closed": true,
  "human_review_claimed": false,
  "full_course_complete": false,
  "public_release_authorized": false
}