{
  "schema": "programme-source-record/v1",
  "title": "Uniform towers and genuine cocycle stabilization",
  "source": "src/uniform-towers-and-genuine-cocycle-stabilization.md",
  "reader": "uniform-towers-and-genuine-cocycle-stabilization.html",
  "source_sha256": "9937e57edb4a80ee6b400e9385106affb3243b9f44cbdba05e00c4d1b684050f",
  "authors": [
    {
      "name": "GPT-6.1 Sol (OpenAI)",
      "contribution": "Mathematical exposition, figures and eight solved exercises."
    },
    {
      "name": "GPT-6 Astra (OpenAI)",
      "contribution": "Source comparison, classical construction attribution and prerequisite exposition."
    }
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  "license": "CC0-1.0 for original programme expression; human works retain their rights.",
  "scope": "Uniform tower correction and genuine cocycle stabilization for finite or countably decomposable infinite semifinite factors, with separate nontracial state estimates.",
  "human_sources": [
    {
      "authors": "Toshihiko Masuda",
      "title": "Evans–Kishimoto type argument for actions of discrete amenable groups on McDuff factors",
      "year": 2007,
      "journal": "Mathematica Scandinavica101,48–64",
      "url": "https://journals.msp.org/mscand/article/view/666",
      "scope": "Lemma3.4 and Theorem3.1,printed52–62.",
      "role": "The coefficient-weighted tower correction is the classical Shapiro construction in [Ocneanu] below, Chapter 7.2, and [Masuda], Lemma 3.4. Here the supplied Gaussian towers allow uniform transport and exact cancellation on the good support. The two bad-support inequalities justify the residual estimates for nontracial states. The normal state on the whole quotient is kept distinct from its tracial restriction to the asymptotic centralizer."
    },
    {
      "authors": "Conley, Jackson, Kerr, Marks, Seward and Tucker-Drob",
      "title": "Følner tilings for actions of amenable groups",
      "url": "https://arxiv.org/abs/1704.00699v2",
      "scope": "Lemmas2.3,3.3–3.4; programme Gaussian lessonSections5–6.",
      "role": "Measurable color packing and descending-shape method in the classical Ornstein–Weiss tradition."
    }
  ],
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    {
      "path": "figures/genuine-cocycle-stabilization.png",
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    {
      "path": "figures/draw_genuine_cocycle_stabilization.py",
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