{
  "schema": "programme-source-record/v1",
  "title": "Quotient comparison with matched inner phases",
  "source": "src/quotient-comparison-with-matched-inner-phases.md",
  "reader": "quotient-comparison-with-matched-inner-phases.html",
  "source_sha256": "7b03f44627fdf2ca90c4cf3bfc2636a767663f2a8e48d294189a833fe949bb4d",
  "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": "Approximate original-factor comparisons and a genuine ultrapower cocycle with prescribed inner-subgroup values.",
  "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": "The simultaneous action and coefficient comparison is the classical construction in [Masuda], Section 4, especially Lemmas 4.2–4.7. The matched inner values cancel the mixed defects before quotient cohomology is used. This lesson writes that mechanism with actual inner implementing unitaries in a semifinite factor and a left-coset section. The result at this stage is a genuine ultrapower cocycle; its coordinate representatives satisfy the full law in the limit."
    },
    {
      "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": "Theorem1.2 and Section4,printed1092and1107–1112.",
      "role": "Full characteristic invariants and measured groupoid comparison."
    }
  ],
  "figures": [
    {
      "path": "figures/inner-subgroup-quotient.svg",
      "sha256": "1235703c110dd8569c4df4c6b1af2662a708cd35d1353fd72531b35a667e0932"
    },
    {
      "path": "figures/inner-subgroup-quotient.png",
      "sha256": "d7050ce6e5700bcf02d6dd2c23222c0b6c9dbdf70e707a0a6ef7a25a03c5fa61"
    },
    {
      "path": "figures/draw_inner_subgroup_quotient.py",
      "sha256": "1edefb1fbf895666fb5db61e70803788583743b4fdd386e11bb53bc156e41331"
    }
  ],
  "programme_sources": [
    {
      "source": "src/aligning-traces-and-inner-phases.md",
      "source_sha256": "cd96eb52ede38af7f5743aa02fe30e578072910bf7b1684a596e3c18ee4af485"
    },
    {
      "source": "src/characteristic-compatible-inner-approximations.md",
      "source_sha256": "71530ed6f8e2ce69c6a99a6297f6b921d483e08c33ca2ef5e237832027ea8db0"
    },
    {
      "source": "src/controlled-amenable-cohomology-and-finite-inner-comparisons.md",
      "source_sha256": "855621ffd309a58e84e27ff4a6e7f77cb6e776bace5fcb9106b5db1952a9eae1"
    },
    {
      "source": "src/gaussian-models-and-amenable-towers.md",
      "source_sha256": "7ea40159e16b17b753f158db4b31f1f684391f4700797aaf848bca7639e7e37b"
    },
    {
      "source": "src/joint-quotient-comparisons-with-a-common-associator.md",
      "source_sha256": "4f168bb0ab5bb84e07603dfa976a0e67974863511670b46e9550c8da96b6c95a"
    },
    {
      "source": "src/quotient-associators-and-genuine-comparison-reconstruction.md",
      "source_sha256": "18c4fa98c2cca6bff10a73eaa5d418be91fd027cf808fa945a7431c64533d646"
    },
    {
      "source": "src/trace-scaling-on-the-hyperfinite-semifinite-factor.md",
      "source_sha256": "948c9151e55f8e01192f6068e74827cd49c635707465fcf4596650c658670f60"
    },
    {
      "source": "src/two-sided-convergence-and-transported-cocycle-limits.md",
      "source_sha256": "3aeec9dbcc0fa05da9c0409c515d5485229b61e17cd4c08f99e7a8be7106a204"
    },
    {
      "source": "src/unitary-two-cocycles-and-approximate-action-comparison.md",
      "source_sha256": "226c5df30cbeaf43ce5dc40ffc8b89dd158e10fac94aa34a419eca35cbdfc0c5"
    }
  ]
}