{
  "schema": "programme-source-record/v1",
  "title": "Alternating comparisons with convergent cocycles",
  "source": "src/alternating-comparisons-with-convergent-cocycles.md",
  "reader": "alternating-comparisons-with-convergent-cocycles.html",
  "source_sha256": "9fbac2729c3dc58c96e9331e1919216542db199c108e2c860d126937a944b8ee",
  "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 classical alternating comparison for centrally nontrivial amenable actions on finite or countably decomposable infinite semifinite factors, under the stated foundations. Nontrivial inner isotropy and measured-field classification have additional scope.",
  "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 action-preserving gauge, two-step finite preparation, alternating comparison rows, transported old-cocycle states, and both parity limits are the construction of [Masuda], Theorem 3.1, pp.55–62. Sections 3–4 below spell out the support estimate and a two-term cumulative bound; Sections 5–6 express the two parity cases through one row index. These are explanations of the classical proof strategy. The theorem does not claim a new comparison method."
    }
  ],
  "figures": [
    {
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      "sha256": "908a727bea3a8b4594c7ae6602789404b91c14d638b5b81a4ea9de03714b5f6b"
    },
    {
      "path": "figures/alternating-comparison.png",
      "sha256": "39ca60bea5e4111f612bb18beb035fceddb4126cc76e0aa38ab4c70ee1fb343d"
    },
    {
      "path": "figures/draw_alternating_comparison.py",
      "sha256": "64cc2395ac78dcc644963f9a1deaef0646fe9ae5be4b2e80ebebde62cb464dca"
    }
  ],
  "programme_sources": [
    {
      "source": "src/generator-tests-for-cocycle-stabilization.md",
      "source_sha256": "ef4df56c8cd15fe282f60d5e352aa1b7fa470de0592537eaf76f36acc68ec8da"
    },
    {
      "source": "src/near-identity-two-cocycle-correction-on-the-original-factor.md",
      "source_sha256": "9f4ad1ae6137ffa09774acc1952d54e5bee5f37cd74f1d9bbd9da1779cffe832"
    },
    {
      "source": "src/two-sided-convergence-and-transported-cocycle-limits.md",
      "source_sha256": "3aeec9dbcc0fa05da9c0409c515d5485229b61e17cd4c08f99e7a8be7106a204"
    },
    {
      "source": "src/uniform-towers-and-genuine-cocycle-stabilization.md",
      "source_sha256": "9937e57edb4a80ee6b400e9385106affb3243b9f44cbdba05e00c4d1b684050f"
    },
    {
      "source": "foundations/bounded-topology-foundations.md",
      "source_sha256": "d06bff624d30c09efdb83de081ab3684cfd014b6d8a79bdace59e0c391159d1b"
    },
    {
      "source": "foundations/normal-tensor-and-tracial-product-foundations.md",
      "source_sha256": "b3ab37ad16ca110b4a3328fff5d603f3c6dc554898f5b857ca6d77d191eaeec0"
    }
  ]
}