{
  "schema": "programme-source-record/v1",
  "title": "Gluing comparisons of isotropy actions",
  "source": "src/gluing-comparisons-of-isotropy-actions.md",
  "reader": "gluing-comparisons-of-isotropy-actions.html",
  "source_sha256": "521f0912cb438e0972ae34843a88820fa98612918073941ba2229fa2646d2238",
  "authors": [
    {
      "name": "GPT-6.1 Sol (OpenAI)",
      "contribution": "Gluing exposition, finite constructions, diagrams and eight solved exercises."
    },
    {
      "name": "GPT-6 Astra (OpenAI)",
      "contribution": "Predual completeness, trace lower semicontinuity and exact prerequisite exposition."
    }
  ],
  "license": "CC0-1.0 for original programme expression; human works retain their own rights.",
  "scope": "Gluing of actual phase-compatible isotropy comparisons over a supplied finite Borel exhaustion. The unitary cocycle, trace gauge and chosen inner implementers are retained. Predual completeness and finite gluing are proved here; initial isotropy classification, construction of compatible phases and",
  "human_sources": [
    {
      "authors": "Vaughan F.R. Jones and Masamichi Takesaki",
      "title": "Actions of compact abelian groups on semifinite injective factors",
      "year": 1984,
      "url": "https://doi.org/10.1007/BF02392378",
      "open_text": "https://archive.ymsc.tsinghua.edu.cn/pacm_download/117/6360-11511_2006_Article_BF02392378.pdf",
      "scope": "Section2.5,printed242–245; Appendix,printed253–256.",
      "role": "Comparison pairs and relative density; the classical finite-exhaustion cohomology method, with its credited Bures–Connes–Krieger–Sutherland ancestry."
    },
    {
      "authors": "Colin E. Sutherland and Masamichi Takesaki",
      "title": "Actions of discrete amenable groups and groupoids on von Neumann algebras",
      "year": 1985,
      "url": "https://ems.press/journals/prims/articles/3261",
      "scope": "Section4,printed1107–1112.",
      "role": "Characteristic-compatible isotropy and moving-arrow comparisons; residual characteristic-character correction."
    }
  ],
  "programme_sources": [
    {
      "source": "src/characteristic-compatible-inner-approximations.md",
      "source_sha256": "71530ed6f8e2ce69c6a99a6297f6b921d483e08c33ca2ef5e237832027ea8db0",
      "scope": "Theorem5.1; Sections1–2 topology and comparison-pair operations."
    },
    {
      "source": "foundations/bounded-topology-foundations.md",
      "source_sha256": "d06bff624d30c09efdb83de081ab3684cfd014b6d8a79bdace59e0c391159d1b",
      "scope": "FoundationF concrete predual,CP-04 throughCP-07."
    },
    {
      "reader": "../OA-ERGODIC/reader/ancillary-actions-and-unitary-corrections.html",
      "source_sha256": "1499a0b236788ce75ff2789536c39d0098642a037c6b6dd0bc8467e24b7bc123",
      "scope": "Lemma1.1,only for the alternative standard-form realization,with its canonical implementation prerequisite."
    }
  ],
  "figures": [
    {
      "path": "figures/finite-class-unitary-gluing.svg",
      "sha256": "20f6dfa1401b90af410ded90670e7d252b5191a9d656b939b19aeca6bf3f8863"
    },
    {
      "path": "figures/finite-class-unitary-gluing.png",
      "sha256": "2691ecfa5d4a3fb20f8569b8cfbca9353175c6fcff98f094115adf31c996b5fc"
    },
    {
      "path": "figures/draw_finite_class_unitary_gluing.py",
      "sha256": "c89d3ec9c1213aaab439bfeb7931de9df338a82cd6b2d55595bb2bf6764abecf"
    },
    {
      "path": "figures/mixed-isotropy-covariance.svg",
      "sha256": "1ed467ace840bbd7296459e168691f81ff2407f6cbf7fd22bb3f15dffc76b199"
    },
    {
      "path": "figures/mixed-isotropy-covariance.png",
      "sha256": "652e2dd028c70328edd223b7a9a5a40ecbfd0d96f9ff40db7010c3701143d0c0"
    },
    {
      "path": "figures/draw_mixed_isotropy_covariance.py",
      "sha256": "66fc2f1bd829368d250941285cecccb321e33fd6e989f08a23a1c013525c31b4"
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  ]
}