{
  "schema": "programme-source-record/v1",
  "title": "Quotient associators and reconstruction of comparisons",
  "source": "src/quotient-associators-and-genuine-comparison-reconstruction.md",
  "reader": "quotient-associators-and-genuine-comparison-reconstruction.html",
  "source_sha256": "18c4fa98c2cca6bff10a73eaa5d418be91fd027cf808fa945a7431c64533d646",
  "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": "The quotient scalar associator, exact reconstruction, a common-coboundary comparison and the approximate joint input for general associators.",
  "human_sources": [
    {
      "authors": "Toshihiko Masuda",
      "title": "Unified approach to classification of actions of discrete amenable groups on injective factors",
      "year": 2010,
      "url": "https://arxiv.org/abs/1006.1176v1",
      "scope": "arXivv1, Sections3–6,pp6–17.",
      "role": "Quotient lifts, their quasi-associativity and simultaneous coefficient comparison are developed in [Masuda], Sections 3–4. Here actual inner implementing unitaries and the left-section convention give the scalar formula (2.5). The pentagon, gauge identities and reconstruction are written out with that convention. Section 5 treats a common coboundary; the general common-associator comparison is [the following lesson](joint-quotient-comparisons-with-a-common-associator.md), Theorem 1.1."
    }
  ],
  "figures": [
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      "sha256": "dd29932c7d8b8ee5dc4f6de3e6da8ab8086cc01a3ef02a84161a1a3c949bdb83"
    },
    {
      "path": "figures/quotient-associator.png",
      "sha256": "7df0e6b777bf5e98357d7fe21f82c8486ccf1854c71fe53595db8d9d27d74f41"
    },
    {
      "path": "figures/draw_quotient_associator.py",
      "sha256": "59904e4ccaf1b2c3c045b1ec21604d91e906cef48b27035e8aafea52d4d2f70c"
    }
  ],
  "programme_sources": [
    {
      "source": "src/alternating-comparisons-with-convergent-cocycles.md",
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    },
    {
      "source": "src/characteristic-compatible-inner-approximations.md",
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    },
    {
      "source": "src/finite-outer-period-and-obstruction.md",
      "source_sha256": "ba6d3b9d9d84b21a647400ac87aab30574b7d780ba28d3efff458110c213858c"
    },
    {
      "source": "src/joint-quotient-comparisons-with-a-common-associator.md",
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    },
    {
      "source": "src/near-identity-two-cocycle-correction-on-the-original-factor.md",
      "source_sha256": "9f4ad1ae6137ffa09774acc1952d54e5bee5f37cd74f1d9bbd9da1779cffe832"
    },
    {
      "source": "src/quotient-comparison-with-matched-inner-phases.md",
      "source_sha256": "7b03f44627fdf2ca90c4cf3bfc2636a767663f2a8e48d294189a833fe949bb4d"
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    {
      "source": "src/trace-scaling-on-the-hyperfinite-semifinite-factor.md",
      "source_sha256": "948c9151e55f8e01192f6068e74827cd49c635707465fcf4596650c658670f60"
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}