{
  "schema": "programme-source-record/v1",
  "title": "Two-sided convergence and transported cocycle limits",
  "source": "src/two-sided-convergence-and-transported-cocycle-limits.md",
  "reader": "two-sided-convergence-and-transported-cocycle-limits.html",
  "source_sha256": "3aeec9dbcc0fa05da9c0409c515d5485229b61e17cd4c08f99e7a8be7106a204",
  "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."
    }
  ],
  "license": "CC0-1.0 for original programme expression; human works retain their rights.",
  "scope": "Two-sided convergence of automorphisms and transported cocycles, including the one-sided shift obstruction.",
  "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 forward and inverse conjugator tests and convergence of the cumulative cocycles occur in [Masuda] below, pp.60–62. This lesson isolates the required general convergence statements, supplies the predual inverse-map argument and the moving-input estimate, and examines the unilateral-shift and scalar-phase obstructions. These details explain the classical convergence mechanism; they do not make that mechanism a new construction."
    }
  ],
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      "sha256": "656b5a9f1cc45b2450ff307bc8b7acf72357b068b3c516f309418c275fb5abc6"
    },
    {
      "path": "figures/two-sided-convergence-obstruction.png",
      "sha256": "8cb8129abbdac13862312715f19fbb4bf3ed4ff78f6a2d1955ff115ec80f8b77"
    },
    {
      "path": "figures/draw_two_sided_convergence_obstruction.py",
      "sha256": "9a9ef688de3565bf5a31ebbf5aebcb1aef536bfa6e4cfbbdbbeb8aed2cf7097c"
    }
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    {
      "source": "src/central-towers-and-unitary-cocycles.md",
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    {
      "source": "src/controlled-amenable-cohomology-and-finite-inner-comparisons.md",
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      "source": "src/from-approximate-cocycles-to-exact-coboundaries.md",
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    {
      "source": "src/generator-tests-for-cocycle-stabilization.md",
      "source_sha256": "ef4df56c8cd15fe282f60d5e352aa1b7fa470de0592537eaf76f36acc68ec8da"
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    {
      "source": "src/unitary-two-cocycles-and-approximate-action-comparison.md",
      "source_sha256": "226c5df30cbeaf43ce5dc40ffc8b89dd158e10fac94aa34a419eca35cbdfc0c5"
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