{
  "schema": "programme-proof-companion-provenance/v1",
  "title": "Removing a specified unitary from a discrete trace-scaling action",
  "source_sha256": "c719a8fa8ae1b83680d5a73067a81a364b74ae5964213429423907aa49b2b2f9",
  "authors": [
    {
      "name": "GPT-6 Astra (OpenAI)",
      "model": "gpt-6-astra",
      "role": "Discrete counting-weight and Fourier argument, classical source comparison and mathematical exposition."
    }
  ],
  "licence": "CC0-1.0 for independently written programme text",
  "construction": "Recorded OA-FLOW linking-algebra, counting-weight and Fourier proof; exact general projection consequences and scalar-composite semifiniteness supplied locally.",
  "classical_sources": [
    {
      "author": "Masamichi Takesaki",
      "title": "Theory of Operator Algebras II",
      "locator": "XII.1.11, printed378–379",
      "url": "https://doi.org/10.1007/978-3-662-10451-4",
      "use": "primary real-action proof compared; not mislabeled as an integer-action statement."
    },
    {
      "author": "Masamichi Takesaki",
      "title": "Theory of Operator Algebras III",
      "locator": "XVII.3.12, printed283",
      "url": "https://doi.org/10.1007/978-3-662-10453-8",
      "use": "proof invokes stability after outer conjugacy."
    },
    {
      "author": "Masamichi Takesaki",
      "title": "Theory of Operator Algebras I",
      "locator": "V.2.15; V.2.6–V.2.9; V.4.6(i)",
      "use": "Classical antecedents of center-valued traces, finite comparison and scalar trace existence; T1 is supplied in the trace companion."
    }
  ],
  "programme_providers": [
    {
      "title": "Recognizing a weight by its fixed density",
      "scope": "PT01–PT08; spectral, modular and extended-positive prerequisites remain explicit.",
      "source_sha256": "185caa784e814eb9ab97b21616507d528842280694f83f4e318a04a967c10f33"
    },
    {
      "title": "Operator-valued weights",
      "scope": "OVW04, normal scalar composition.",
      "source_sha256": "a16279e54f6d9bb9077f92d505d67d26813fe4a01ffb1cd563209896a782fe63"
    },
    {
      "title": "Operator-valued weight rigidity",
      "scope": "OR03–OR04, conditional modular-transfer assembly.",
      "source_sha256": "3bd2a037e1567d336aec429208df0c5f345b42e21a9ceea28b19d89f19005f00"
    },
    {
      "title": "Operator-valued weights and scalar composition",
      "scope": "O9 and HC-2; general modular inputs.",
      "source_sha256": "acbae0988d9e8c6012533f593a32671565b6d9fc6d10d13b0071c8e033af657c"
    },
    {
      "title": "Wandering projections",
      "scope": "Wandering-projection construction.",
      "source_sha256": "d969d25f8ff1620062b205c05a9331dbcc943e6a07e98e4eaed22b31b59d0193"
    },
    {
      "title": "Removing noncentral cocycles from a trace-scaling action",
      "scope": "Real actions; projection comparison, linking algebra, Fourier generation and local trace comparison.",
      "source_sha256": "f9d25ea0ea03baae34d1d26ed7c963c558db6930d263c9663c0263a9cb4a86ba"
    },
    {
      "title": "Discrete decomposition of type III lambda factors",
      "scope": "Counting weights, Fourier series and the half-open spectral cut.",
      "source_sha256": "29d118d6fdd742470b4ae0ecb843eb7779a45b132535e3a62b7ea60d331f31a4"
    }
  ],
  "remaining_contracts": [
    "W1",
    "W2",
    "W3"
  ],
  "trace_foundations": {
    "source": "trace-existence-foundations.md",
    "reader": "../trace-existence-foundations.html#t1",
    "scope": "T1 scalar-trace existence, finite center-valued trace, and norm-closed unitary averaging; arbitrary centers and Hilbert cardinality.",
    "proofs": [
      "GS1–GS3",
      "FCT0–FCT8",
      "CA1–CA3"
    ],
    "remaining_general_inputs": [
      "W1",
      "W2",
      "W3"
    ]
  }
}