{
  "title": "Folded forms and symplectic target coordinates — restored proof edition",
  "original_source_sha256": "783d50f870c41091e5145140deae3517ed3f68f758ec275b93f3033c527f7fb1",
  "restored_source_sha256": "f516adc6b91dae6f87f35cfec39d71653b4da33c38571abcd1fe5e9ca4a3d2b8",
  "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-978-3-540-49938-1-pdf",
      "pdf_pages_read": [
        289,
        290,
        291,
        292,
        297,
        320,
        321,
        322,
        330
      ],
      "relevant_printed_pages": [
        274,
        275,
        276,
        277,
        282,
        305,
        306,
        307,
        315
      ]
    }
  ],
  "original_lesson_preserved": true,
  "book_files_redistributed": false,
  "original_lesson_licence": "CC0-1.0",
  "reproducible_model_checks": {
    "script": "check_models.py",
    "script_sha256": "089ca1bf75a0f0481854450d808e8af32dc87049d60193056804ba527420b7e7",
    "results": "model-check.json",
    "original_script_sha256": "2a81a4f2cb5c2aa52dc604bf7a77496f42829a22333bd9bdab4d19819c10de9b",
    "finite_checks": 6,
    "passed": true,
    "mathematical_checks_unchanged": true,
    "historical_archive_checks_removed": true,
    "removed_historical_check_flags": [
      "frozen_edition_11_lesson_hashes_unchanged",
      "all_prior_archive_hashes_unchanged"
    ],
    "scope": "Finite models support the written proof; they do not establish the general theorem."
  },
  "figure": {
    "path": "figures/folded-form-and-square-quotient.svg",
    "sha256": "ffdc33b9cab8f34cec96614a8f665bed14f4e9d96b1b91a07eca2123c2df9be2",
    "original_bytes_unchanged": true,
    "reproducible_source": "figures/draw_folded_form.py",
    "original_script_sha256": "33e89fc1cff139f49c9044d5c88ce0f287c5658d794da1b776f4723fc0959bc2",
    "portable_script_sha256": "37eb049d7d01cb88d877dcbfc916a08192a61a4eff7f0e4ee5fea6695adfeef9",
    "license": "CC0-1.0",
    "coordinates": "Exact square quotient r=s^2/2; x in [0,1/2], source s in [1/2,1] and [-1,-1/2], target r in [1/8,1/2]; integrals +3/16 and -3/16 with the displayed orientations",
    "font_outline_notices": [
      "figures/notices/LICENSE_DEJAVU.txt"
    ]
  },
  "linked_component_rights": "All earlier proof components retain their individual notices and licences.",
  "all_original_displayed_equations_and_ten_exercise_solutions_unchanged": true,
  "proof_review": [
    "Read the full preserved U016 lesson, its ten complete solutions, exact signed-patch figure and all six mathematical model checks. Every original displayed equation, exercise and SVG byte is retained.",
    "Checked both distinct rank hypotheses. Supplied the alternating-plane splitting proof relating rank and exterior powers, and exact smooth kernel-bundle and transverse-flow providers.",
    "Checked the characteristic coordinate and spectator Darboux section, the transverse ambient-kernel collar, and the antisymmetric field average for a single involution.",
    "Checked the first normal jet, nonzero top-wedge coefficient, mixed spectator changes, positive square-root normalization and the divisibility of the full form remainder.",
    "Checked the relative primitive on both signs of the normal variable. Made the inverse matrix factorization and smooth cancellation of its apparent singularity explicit, including every derivative of the resulting Moser field.",
    "Checked the full time interval using the equilibrium and open smooth solution domain, the variational first-jet equation, pullback differentiation and reflection equivariance. The primitive homotopy integrand extends smoothly at its zero endpoint.",
    "Checked the independent radial hypothesis, degree-zero characteristic field, homogeneous symplectic section, half-degree normal collar, exact pushforward weight, homogeneous first-jet corrections and degree-zero Moser field. Positive saturation of a normalized slice gives the actual time-one construction along the full ray.",
    "Checked the ordinary canonical pair retaining a prescribed defining function, its exact flow signs and pulled-back form, and the tangential-plus-transverse differential proof of forward fold coordinates.",
    "Checked smooth invariant descent in the target converse, nondegeneracy of the full boundary coordinate differential and the Hamiltonian collar. Proved equality of all first derivatives at the boundary before propagating every canonical bracket to the unattained side.",
    "Checked the homogeneous slice restriction retains the fold kernel, cokernel and quadratic Hessian. Supplied the positive homogeneous radius, exact normalized-map identity, unique homogeneous sheet exchange and full negative-side scaling of the Hamiltonian collar.",
    "Checked all hypotheses of the earlier zero-valued homogeneous canonical-pair theorem in the homogeneous forward construction, retaining the nonzero residual radial field and the odd half-degree square root.",
    "Checked parity descent of two-form coefficients, closedness and nondegeneracy on the attained quotient. Justified the radial homotopy on a closed half-neighborhood before extending its primitive. Checked the homogeneous primitive, absence of its radial component, and full closed nondegenerate extension.",
    "Checked all ten solutions, including the closed restricted-rank counterexample, actual implicit Moser flow, reflection-preserving normalization, failed arbitrary negative target and form extensions, exact homogeneous pullback, excluded radial example and both signed integrals of magnitude 3/16.",
    "Read the approved H III treatment at printed 274–277, 282, 305–307 and 315, PDF 289–292, 297, 320–322 and 330. Historical alternative pagination remains private evidence.",
    "Compared the source with this independently written relative-Moser lesson. Its explicit parameter and boundary arguments, examples, ten solutions and original signed-patch figure supply the course exposition. No book text, figure, exercise collection or book file is redistributed.",
    "Retained all six mathematical checks unchanged. Removed only obsolete edition/archive assertions from the portable verifier and recorded the exact removed preamble and flags. Preserved the original evidence, exact SVG, portable drawing source and embedded-font notice. Finite models support the proof without certifying its general statements."
  ],
  "changes": [
    "Restored all original displays, ten complete solutions and exact signed-patch figure with current prerequisite bindings.",
    "Supplied the alternating-form wedge/rank argument and explicit smooth kernel/collar providers.",
    "Made the inverse matrix factorization, full smooth Moser-field cancellation, compact-time flow and first-jet equation explicit.",
    "Checked homogeneous field weights and the full conic extension, using the precise earlier cone-chart construction.",
    "Proved matching of all boundary first derivatives before propagating target canonical brackets; supplied homogeneous descent and involution-equivariance details.",
    "Justified the half-neighborhood primitive before closed ordinary/homogeneous quotient extensions.",
    "Retained all six mathematical model calculations; removed unrelated historical edition/archive assertions from the portable verifier without altering preserved evidence. Retained the exact SVG, portable drawing source and embedded-font notice."
  ],
  "all_alternative_proofs_preserved": true,
  "bounded_lesson_P514_closed": true,
  "human_review_claimed": false,
  "full_course_complete": false,
  "public_release_authorized": false
}