{
  "schema": "programme-source-record/v1",
  "title": "Choosing and gluing measurable action comparisons",
  "source": "src/choosing-and-gluing-measurable-action-comparisons.md",
  "reader": "choosing-and-gluing-measurable-action-comparisons.html",
  "source_sha256": "4052173b8674a5c79cd29c18d2601271b926823e168fa518389a337770bcd03f",
  "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": "Completed-measure selection, invariant Borel reduction and exact gluing on a supplied constant hyperfinite semifinite field with a finite orbit exhaustion.",
  "human_sources": [
    {
      "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": "The passage from isotropy comparison to measurable groupoid comparison is the method of [ST], Section 4. Its proof retains a further mixed scalar character and cancels it using a model action. The programme gluing theorem used here instead assumes actual phase-compatible isotropy pairs and retains their entire unitary coordinates through the finite exhaustion. Its equations (6.3)–(6.7) prove the mixed identity needed for the genuine whole-groupoid cocycle. The selector below supplies exactly those stronger initial data."
    }
  ],
  "figures": [
    {
      "path": "figures/measurable-comparison.svg",
      "sha256": "ebbcb133d4d88a74aa68461c1f1bfaf8a64b49d6971cba856947042942df0c73"
    },
    {
      "path": "figures/measurable-comparison.png",
      "sha256": "14c06ca387ab7833d8bde4014add21eaf431d16cf6f2a7ce8b65d86121bb55d3"
    },
    {
      "path": "figures/draw_measurable_comparison.py",
      "sha256": "0923b979eac3d3aecd42dd1caaa280225bd1a4ec445a6e2be2dd019cc935711a"
    }
  ],
  "programme_sources": [
    {
      "source": "src/characteristic-classification-of-semifinite-actions.md",
      "source_sha256": "7a2af11e0a9c8b1997d63bcc8c5254a3eb10a6c3807c737c94427163b6d53dfa"
    },
    {
      "source": "src/gluing-comparisons-of-isotropy-actions.md",
      "source_sha256": "521f0912cb438e0972ae34843a88820fa98612918073941ba2229fa2646d2238"
    },
    {
      "source": "src/joint-quotient-comparisons-with-a-common-associator.md",
      "source_sha256": "4f168bb0ab5bb84e07603dfa976a0e67974863511670b46e9550c8da96b6c95a"
    },
    {
      "source": "src/trace-scaling-on-the-hyperfinite-semifinite-factor.md",
      "source_sha256": "948c9151e55f8e01192f6068e74827cd49c635707465fcf4596650c658670f60"
    }
  ]
}