{
  "schema": "programme-proof-companion-provenance/v1",
  "title": "Dual fixed points, core commutants and central cocycles",
  "source_sha256": "ce5f4996df1698e3724577cfa916803fd2e83adb210d115da6d078e00a1c38d8",
  "authors": [
    {
      "name": "Codex (OpenAI)",
      "role": "Earlier independently written programme arguments, September2026; exact model not stated in original headers."
    },
    {
      "name": "GPT-6 Astra (OpenAI)",
      "model": "gpt-6-astra",
      "role": "Proof selection, source comparison, full direct-proof integration and exact chart comparison."
    }
  ],
  "licence": "CC0-1.0 for independently written programme expression",
  "programme_providers": [
    {
      "id": "22-dual-action-averaging",
      "sha256": "300840a50e44648122317dd78e112a4b4cd6c95b73d73fc5e0229fe121c6ce2d",
      "selected_scope": "Full fixed-point proof A11–A14 with its A3/A5/A9 regular-model data"
    },
    {
      "id": "23-core-relative-commutant",
      "sha256": "12effa53fa9a62bef8bdf4f10ba58c75b6172a544843d49c4f7a8437b96b60f6",
      "selected_scope": "R1–R30 full relative-commutant argument, including arbitrary-algebra corner extension"
    },
    {
      "id": "26-core-central-cocycle-realization",
      "sha256": "3af284605d95c50bac9b63049e79fa4230e4052e591d66775db0df0ab53b06f5",
      "selected_scope": "C1–C27 full realization and normalizer argument"
    }
  ],
  "classical_sources": [
    {
      "author": "Masamichi Takesaki",
      "title": "Theory of Operator Algebras II",
      "locator": "X.2.3(i); XII.1.7–1.9; XII.6.13–6.15, printed449–452",
      "url": "https://doi.org/10.1007/978-3-662-10451-4",
      "role": "Mathematical fixed-point, Fourier–KMS and core-normalizer antecedents; source text and whole lesson organization not reproduced."
    },
    {
      "author": "Masamichi Takesaki",
      "title": "Theory of Operator Algebras III",
      "locator": "XVIII.2.8(ii), printed326",
      "url": "https://doi.org/10.1007/978-3-662-10453-8",
      "role": "Every-faithful-state target used by the consumer."
    }
  ],
  "remaining_contracts": [
    "F1: standard form, normal regular/core charts and their cocycle functoriality",
    "F2: general Tomita/KMS, identified dual-weight conjugation and corner/inner derivative formulas",
    "F3: scalar harmonic analysis, distributions and full spectral calculus",
    "F4: general tensor commutant theorem; supplied bounded/predual/normality/tensor-test branches retained"
  ]
}