{
  "title": "Complex-phase Fourier integral operators — restored proof edition",
  "original_source_sha256": "a5d26f15851c6cd84520fdb3aa17aeb48171e9d612b830995f466557cbaf13a1",
  "restored_source_sha256": "0c0326afcad6f2817a0676bd8ca45ebd09d3d982baca724b0df72fe4e5949025",
  "original_authorship": "GPT-6.1 Sol (OpenAI), Ultra, 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-978-3-642-00136-9-pdf",
      "pdf_pages_read": [
        54,
        55,
        56,
        57,
        58,
        59,
        60,
        61,
        62,
        63
      ]
    }
  ],
  "original_lesson_preserved": true,
  "book_files_redistributed": false,
  "original_lesson_licence": "CC0-1.0",
  "earlier_metric_comparison": {
    "title": "AN-03, When a moving symbol scale controls an operator",
    "source_sha256": "3baa803492822b6c1bdc131b5a1caa6609a6e925e3d26009b2fe2c5e4a3b32f4",
    "locators": "Section 1 B8a and Section 7 B26",
    "scope": "The general metric route remains comparison. The exact compact-base endpoint is proved completely in the new companion from the already included AN-03 E23 packet estimate."
  },
  "exact_packet_provider": {
    "source": "../20261005-restored-airy-models/bounded-derivative-operators.md",
    "sha256": "251e6d1b9eb666ddcf56b661d356e91588d7bc9c5345078c1abd9f1de55de93e",
    "licence": "GFDL-1.2-only with its existing notices"
  },
  "reproducible_model_checks": {
    "script": "check_models.py",
    "results": "model-check.json",
    "finite_groups": 10,
    "original_algebra_groups": 7,
    "algebra_script": "check_algebra.py",
    "all_original_mathematical_controls_retained": true,
    "portable_changes": "Local input/output paths and current source-structure guard; unused historical source/state branch removed from preparation.",
    "passed": true
  },
  "added_endpoint_checks": {
    "script": "check_endpoint.py",
    "results": "endpoint-checks.json",
    "groups": 3,
    "passed": true,
    "scope": "Exact balanced dilation derivatives and wrong-scaling control, both off-diagonal exponents including low shells, and finite shell matrices with a failed unstructured-summation control."
  },
  "endpoint_companion": {
    "source": "endpoint-half-order-bound.md",
    "sha256": "e1cc8c0ead16146183259b4631e0d732e8e9e761792d8e9b4d0010dbc43bf0dc",
    "proofs": "E0–E4"
  },
  "figures": [
    {
      "path": "figures/complex-fio-models.svg",
      "sha256": "2cb3f37aff449c9095ff6e737be44e6a5d499f04461b2a2f3cb7ac0c8dc56fa4",
      "original_bytes_unchanged": true,
      "reproducible_source": "figures/draw_complex_fio_models.py"
    },
    {
      "path": "figures/endpoint-shells.svg",
      "sha256": "4799d8b27411065a084b3e55111e74f7f9db33003a578c844d396e7618d97214",
      "reproducible_source": "figures/draw_endpoint_shells.py",
      "data": "figures/endpoint-shells-data.json",
      "scope": "Exact frozen metric ellipse and finite display of proved infinite-shell majorants; these are bounds, not measured operator norms."
    }
  ],
  "font_notices": [
    "figures/notices/LICENSE_DEJAVU.txt",
    "figures/notices/LICENSE_STIX.txt",
    "figures/notices/BAKOMA_SECTION.txt"
  ],
  "linked_component_rights": "All earlier components retain their own licences and complete notices; the earlier AN-03 packet selection remains GFDL.",
  "all_seventeen_original_exercise_solutions_retained": true,
  "exercise_changes": "Provider wording only in Exercises 14 and 17; all mathematical calculations and conclusions retained.",
  "display_change": "Stray comma corrected to thin spacing in the conjugate-transpose notation of the whole Hermitian form.",
  "proof_review": [
    "Reconnect exact current earlier programme lesson: (../20261005-restored-positive-ideals/positive-lagrangian-ideals-and-distributions.md)",
    "Reconnect exact current earlier programme lesson: (../20261005-restored-quadratic-forms/quadratic-hamilton-maps-and-positive-complex-planes.md)",
    "Reconnect exact current earlier programme lesson: (../20261005-restored-analytic-composition/clean-composition-of-fourier-integral-operators.md)",
    "Supply the exact endpoint bridge using the already included complete finite-derivative proof.",
    "Correct the geometric name of the excess variable in the zero-damping example; its base coordinate is constrained to zero.",
    "Correct stray comma in the transpose spacing; the Hermitian quadratic form is unchanged.",
    "Put convexity in the inverse-coordinate image, where the mean-value argument actually uses it.",
    "Identify the complete local endpoint provider.",
    "Replace an unclosed transitive general-metric import by a complete local proof of precisely the required compact-base endpoint; retain metric calculations and credit.",
    "Use the proved left-quantized theorem directly.",
    "Bind the operator series to the actual uniform compact-support constant.",
    "Update Exercise 14 provider wording, retaining its complete geometric calculation.",
    "Retain the exact Planck-factor conclusion in Exercise 14 without relying on an unused general quantization theorem.",
    "Update Exercise 17 to the complete current endpoint provider.",
    "Correct the bibliographic edition to the exact admitted copy.",
    "Bind the final source note to the complete current analytic proof.",
    "Retain all transverse composition hypotheses, complete ideal proofs, order constants and global support conditions.",
    "Retain both full directions of the universal L2 criterion, the exact real-versus-complex distinction and all semipositive cases.",
    "Supply complete balanced dilation, full off-diagonal Fourier kernel, both Schur marginals and finite neighboring-shell summation from the existing exact E23 proof.",
    "Bind every result used to current programme proofs; all 118 original targets are accounted for, including seventeen full solved exercises.",
    "Retain the original exact illustration and add a correctly labelled scale/shell-bound illustration, with reproducible sources and font notices.",
    "Read the full fourteen-section original lesson, all seventeen solutions, all 118 target entries, the full prior proof preparation, both original check scripts and the original figure source.",
    "Read admitted H IV PDF 54–63 / printed 43–52 in full; book citations and proof-source use remain admitted.",
    "Checked the complex shear polynomial, real base realization, normal critical matrix, arbitrary-phase complex transpose argument and exact flat residual elimination.",
    "Checked every noncomparable shell regime, all endpoint derivatives, finite proper matching covers, the actual mixed Jacobian and the cutoff/Fubini distributional identity.",
    "Checked the exact packet powers, moving-frequency domination, Riesz representation, product-test detection, both transport obstructions and actual nonzero model.",
    "Read the precise positive-plane nullspace proof and checked both positivity inequalities in the mixed projection, actual critical graph and local matching uniqueness/properness.",
    "Checked the full real derivative-map injectivity, convex image box, all critical-value gradients and both radial weights.",
    "Checked all exponential derivatives, the converse on every ray, self-dual metric and both center-comparison cases.",
    "Read the existing current AN-03 metric route at the stated comparison locators and the complete already included E23 packet proof; the broader transitive metric calculus is not certified by this restoration.",
    "Proved the compact-base endpoint from that actual E23 component, including fixed finite derivatives, low shells, full separation constants, both Schur bounds, strong neighboring convergence and norm convergence of the far terms.",
    "Checked exact original conic Hessians and ranks, whole positive model, Gaussian/delta constants, norm sharpness, quartic degeneracy and all seventeen complete solutions.",
    "Inspected the original model image and the corrected new endpoint image; final reader render inspection remains a separate upload gate.",
    "Ten retained finite model groups and three added endpoint controls pass. Their numerical/symbolic checks support the complete proofs and do not certify general theorems."
  ],
  "changes": [
    "Reconnect exact current earlier programme lesson: (../20261005-restored-positive-ideals/positive-lagrangian-ideals-and-distributions.md)",
    "Reconnect exact current earlier programme lesson: (../20261005-restored-quadratic-forms/quadratic-hamilton-maps-and-positive-complex-planes.md)",
    "Reconnect exact current earlier programme lesson: (../20261005-restored-analytic-composition/clean-composition-of-fourier-integral-operators.md)",
    "Supply the exact endpoint bridge using the already included complete finite-derivative proof.",
    "Correct the geometric name of the excess variable in the zero-damping example; its base coordinate is constrained to zero.",
    "Correct stray comma in the transpose spacing; the Hermitian quadratic form is unchanged.",
    "Put convexity in the inverse-coordinate image, where the mean-value argument actually uses it.",
    "Identify the complete local endpoint provider.",
    "Replace an unclosed transitive general-metric import by a complete local proof of precisely the required compact-base endpoint; retain metric calculations and credit.",
    "Use the proved left-quantized theorem directly.",
    "Bind the operator series to the actual uniform compact-support constant.",
    "Update Exercise 14 provider wording, retaining its complete geometric calculation.",
    "Retain the exact Planck-factor conclusion in Exercise 14 without relying on an unused general quantization theorem.",
    "Update Exercise 17 to the complete current endpoint provider.",
    "Correct the bibliographic edition to the exact admitted copy.",
    "Bind the final source note to the complete current analytic proof.",
    "Retain all transverse composition hypotheses, complete ideal proofs, order constants and global support conditions.",
    "Retain both full directions of the universal L2 criterion, the exact real-versus-complex distinction and all semipositive cases.",
    "Supply complete balanced dilation, full off-diagonal Fourier kernel, both Schur marginals and finite neighboring-shell summation from the existing exact E23 proof.",
    "Bind every result used to current programme proofs; all 118 original targets are accounted for, including seventeen full solved exercises.",
    "Retain the original exact illustration and add a correctly labelled scale/shell-bound illustration, with reproducible sources and font notices."
  ],
  "all_alternative_proofs_preserved": true,
  "bounded_lesson_P514_closed": true,
  "human_review_claimed": false,
  "full_course_complete": false,
  "public_release_authorized": false
}