{
  "schema": "programme-source-record/v1",
  "title": "Near-identity two-cocycle correction on the original factor",
  "source": "src/near-identity-two-cocycle-correction-on-the-original-factor.md",
  "reader": "near-identity-two-cocycle-correction-on-the-original-factor.html",
  "source_sha256": "9f4ad1ae6137ffa09774acc1952d54e5bee5f37cd74f1d9bbd9da1779cffe832",
  "authors": [
    {
      "name": "GPT-6.1 Sol (OpenAI)",
      "contribution": "Mathematical exposition, constructions, figures and eight solved exercises."
    },
    {
      "name": "GPT-6 Astra (OpenAI)",
      "contribution": "Classical-method attribution, Fourier argument and exact prerequisite exposition."
    }
  ],
  "license": "CC0-1.0 for original programme expression; human works retain their rights.",
  "scope": "Quantitative two-cocycle correction inside a finite or countably decomposable infinite semifinite factor, exact coordinate cocycles and genuine approximate comparisons, under the stated induced-action and foundational hypotheses.",
  "human_sources": [
    {
      "authors": "Adrian Ocneanu",
      "title": "Actions of discrete amenable groups on factors",
      "year": 1982,
      "edition": "University of Warwick doctoral thesis",
      "url": "https://wrap.warwick.ac.uk/id/eprint/110062/1/WRAP_Theses_Ocneanu_1982.pdf",
      "scope": "Chapter7,printed96–126; especially7.2,7.4 and7.6–7.8.",
      "role": "Classical tower/Shapiro correction, cohomology vanishing and transported-state convergence."
    },
    {
      "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": "Proposition3.2,Corollary3.3 and Lemma3.4,printed51–55.",
      "role": "Classical two-stage approximate comparison and controlled one-cohomology construction."
    },
    {
      "authors": "Colin E. Sutherland",
      "title": "A Borel parametrization of Polish groups",
      "year": 1985,
      "url": "https://ems.press/content/serial-article-files/42293",
      "scope": "Section5,especially Lemmas5.6–5.7 and Theorem5.5,printed1081–1086.",
      "role": "Finite-class root constructions and compatible extension in Borel cohomology."
    },
    {
      "authors": "Jacob Feldman and Calvin C. Moore",
      "title": "Ergodic equivalence relations, cohomology, and von Neumann algebras.I",
      "year": 1977,
      "url": "https://www.ams.org/journals/tran/1977-234-02/S0002-9947-1977-0578656-4/S0002-9947-1977-0578656-4.pdf",
      "scope": "Theorem6,printed310.",
      "role": "Classical higher cohomology vanishing for hyperfinite measured relations."
    }
  ],
  "figures": [
    {
      "path": "figures/original-factor-two-cohomology.svg",
      "sha256": "f4c933c37cdb2f22c2bbe6ad49a3d35c266ce801f731b1cd9596ff458970df6a"
    },
    {
      "path": "figures/original-factor-two-cohomology.png",
      "sha256": "7ec59446d5b3b84886f1e34ec765f68f1f31b33c218c3790331223b292778038"
    },
    {
      "path": "figures/draw_original_factor_two_cohomology.py",
      "sha256": "aed58256098b500b3ed45e4a91192369125a270453d40b86064da7ba56bcc8b2"
    }
  ],
  "programme_sources": [
    {
      "source": "src/central-towers-and-unitary-cocycles.md",
      "source_sha256": "20f6ff3427399596296614be3d737f95476cc94ebbfdd32a8c648bba9260a6d8"
    },
    {
      "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/independent-copies-of-orbit-algebras.md",
      "source_sha256": "d7353521c856417a3f74d8cc4089dfdf3ce17c71e1ee5a9e41ef8ed37710b371"
    },
    {
      "source": "src/unitary-two-cocycles-and-approximate-action-comparison.md",
      "source_sha256": "226c5df30cbeaf43ce5dc40ffc8b89dd158e10fac94aa34a419eca35cbdfc0c5"
    },
    {
      "source": "foundations/normal-tensor-and-tracial-product-foundations.md",
      "source_sha256": "b3ab37ad16ca110b4a3328fff5d603f3c6dc554898f5b857ca6d77d191eaeec0"
    }
  ],
  "external_programme_sources": [
    {
      "source": "../../OA-ERGODIC/src/invariant-means-on-measured-relations.md",
      "reader": "../../OA-ERGODIC/reader/invariant-means-on-measured-relations.html#6-increasing-finite-relations",
      "source_sha256": "708b609d566f4b26e9df846a9bd8995569073f76f9e2e20dbea8138aac871574",
      "result": "Corollary6.2,from Proposition2.1 and the full finite-patch proof of Theorem6.1.",
      "scope": "Countable amenable probability-preserving principal relation; full transitive prerequisites retain their stated scope."
    }
  ]
}