{
  "title": "Oscillatory distributions and their order — restored proof edition",
  "restored_original_sha256": "eabb0fba6e8a1b7e08f04f7122e50724de17e56bafc8d345ac4a7aa033820b4e",
  "restored_edition_sha256": "8df6b0b9a4dabc91c1ccce0811f52eff929aff15826cdbb1e1a3d283971cc58e",
  "original_authorship": "GPT-6.1 Sol (OpenAI), Ultra; original September lesson and 4 October proof revision",
  "restoration_review": "GPT-6 Astra (OpenAI), Ultra; owner review on 5 October 2026",
  "source_policy": "Independent exposition with complete proofs and exact scholarly references.",
  "free_sources_retained": [
    "Hörmander, Fourier integral operators I (1971), exact previously verified Project Euclid edition",
    "Guillemin–Sternberg, Semi-classical Analysis, author draft dated 13 January 2010",
    "Melrose, From Microlocal to Global Analysis, version 0.7I; Introduction to Microlocal Analysis, version 0.5B"
  ],
  "free_source_evidence": "Earlier source comparison and integration retained privately; exact bibliography and edition locators remain in the lesson.",
  "independent_expression_check": "Existing prose, local problem order, combined construction/wavefront lesson, worked endpoint example, diagram and five exercises were compared with Hörmander IV pp.4-10. The book begins with intrinsic iterated regularity and a different surrounding sequence. The restored lesson uses independent explanatory text and its own teaching organization.",
  "complete_proof_review": [
    "The full-gradient integration operator lowers general symbol order by min(rho,1-delta)>0, including derivatives of the cutoff and coefficients.",
    "The two-region Fourier argument is uniform in the frequency cutoff; the large-ratio and compact-ratio lower bounds cover every off-critical covector.",
    "Clean geometry is now bound to F1, not the withdrawn geometry provider. The frequency graph, Hessian radical and transverse restriction have complete earlier proofs.",
    "The physical Hessian and fiber degrees give m-n/4 and (2*pi)^(n/4), with full differentiated remainders from the current stationary lesson.",
    "Homogeneous phase changes preserve ordinary symbols. Stabilization uses a fixed quadratic block and an amplitude constant near its new critical point; all correction coefficients vanish.",
    "The delta, identity-kernel and dyadic examples preserve the exact Fourier constants and distinguish the Besov endpoint from the divergent Sobolev square sum."
  ],
  "source_expression_or_books_redistributed": false,
  "original_text_figure_and_code": "CC0; figure font notice retained separately",
  "font_notice": "figures/notices/LICENSE_DEJAVU.txt",
  "earlier_component_licences_retained": true,
  "all_alternative_proofs_preserved": true,
  "changes": "Current exact prerequisite links and definitions, precise edition citation, current provenance. All theorem proofs, five exercise solutions and original figure preserved.",
  "bounded_lesson_P514_closed": true,
  "human_review_claimed": false,
  "general_derivative_loss_oscillatory_construction": true,
  "full_derivative_loss_FIO_calculus": false,
  "full_course_complete": false,
  "public_release_authorized": false
}