{
  "schema": "programme-source-record/v1",
  "title": "Inner approximations compatible with characteristic data",
  "source": "src/characteristic-compatible-inner-approximations.md",
  "reader": "characteristic-compatible-inner-approximations.html",
  "source_sha256": "71530ed6f8e2ce69c6a99a6297f6b921d483e08c33ca2ef5e237832027ea8db0",
  "authors": [
    {
      "name": "GPT-6.1 Sol (OpenAI)",
      "contribution": "Relative approximation argument, characteristic phases and eight solved exercises."
    },
    {
      "name": "GPT-6 Astra (OpenAI)",
      "contribution": "Topology and fixed-ultrafilter details; exact prerequisite exposition."
    }
  ],
  "license": "CC0-1.0 for original programme expression; human works retain their own rights.",
  "scope": "Simultaneous approximation of trace-preserving comparison automorphisms and prescribed compatible cocycles for countable amenable actions on the hyperfinite semifinite factor. The arbitrary-factor conditional theorem and abelian character correction retain full scope. Fixed-ultrafilter and moving-multiplier arguments are explicit;",
  "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": "Comparison-pair law and Lemma2.5.6,printed242–245.",
      "role": "Classical relative-density argument and abelian scalar phase correction."
    },
    {
      "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": "Equations8–12 and Lemma4.3,printed1108–1110.",
      "role": "Characteristic-compatible density for general amenable groups."
    },
    {
      "author": "Alain Connes",
      "title": "Periodic automorphisms of the hyperfinite factor of type II-one",
      "year": 1977,
      "url": "https://alainconnes.org/wp-content/uploads/szego.pdf",
      "scope": "Introduction,printed39–41.",
      "role": "Cyclic outer-period and obstruction background; not a replacement for the approximation proof."
    }
  ],
  "programme_sources": [
    {
      "reader": "../OA-APPROX/central-sequence-algebras-and-exact-lifts.html",
      "source_sha256": "2b187efa4cced8637c5bfac12b4c421b4acecb7f325c402677fef01a7730c70c",
      "sections": "Proposition2.1,Theorem3.1 and Theorem5.1 for exact unitary lifts."
    },
    {
      "reader": "../OA-APPROX/hyperfinite-finite-factors.html#6-subfactors-and-automorphisms",
      "source_sha256": "427d7f9fbcf09d6d3f9a3b3bd3e54ce04d36316b843b1cc5ac5d235d658df13f",
      "sections": "Theorem6.3 and Lemma6.2; Corollary5.2 for finite corners."
    }
  ]
}