{
  "schema": "programme-source-record/v1",
  "title": "Comparing trace-scaling flows over their centres",
  "source": "src/comparing-trace-scaling-flows-over-their-centres.md",
  "reader": "comparing-trace-scaling-flows-over-their-centres.html",
  "source_sha256": "ccde0b545b719064909d352ebbdc723e5767bcf77665f90d368fe9aee2603e5f",
  "authors": [
    {
      "name": "GPT-6.1 Sol (OpenAI)",
      "contribution": "Mathematical exposition, figure and seven solved exercises."
    },
    {
      "name": "GPT-6 Astra (OpenAI)",
      "contribution": "Classical-source comparison, exact proof locators and complete composition-defect proof exposition."
    }
  ],
  "license": "CC0-1.0 for original programme expression; human works retain their rights.",
  "scope": "Trace-normalized comparison of two real actions with the same properly ergodic centre flow, exact scalar-phase correction and a spatial crossed-product isomorphism; the type III-zero application retains its stated core, uniformity and foundational prerequisites.",
  "human_sources": [
    {
      "author": "Masamichi Takesaki",
      "title": "Theory of Operator Algebras III",
      "year": 2003,
      "url": "https://doi.org/10.1007/978-3-662-10453-8",
      "scope": "XIII.3.29 (51–52), XIII.3.34 (55–56), XVIII.2.1(i) (315–316).",
      "role": "Actual classical construction: return cohomology, exact scalar repair and trace-scaling comparison. The ordered-return proof is an exposition of this construction."
    }
  ],
  "programme_sources": [
    {
      "source": "src/trace-scaling-on-the-hyperfinite-semifinite-factor.md",
      "source_sha256": "948c9151e55f8e01192f6068e74827cd49c635707465fcf4596650c658670f60"
    }
  ],
  "external_programme_sources": [
    {
      "source": "https://github.com/KokunoYumeto/open-math-courses/blob/7b8685f8a724800e01d04ef95721c85c5f340092/docs/courses/OA-FLOW/src/OA-FLOW-L37.md",
      "source_sha256": "a6e50f46964dcbfeb09662d4678673e0b4c07533fda3fae05a346d2b9242e30b",
      "scope": ""
    },
    {
      "source": "https://github.com/KokunoYumeto/open-math-courses/blob/7b8685f8a724800e01d04ef95721c85c5f340092/docs/courses/OA-FLOW/src/OA-FLOW-L38.md",
      "source_sha256": "350b25105a0094f16c253ae39fcf5934ec29d2ad951303e1d5525d035ffd8099",
      "scope": "Full suspension theorem through (S32); exact source unchanged from the previous full proof reading."
    },
    {
      "source": "https://github.com/KokunoYumeto/open-math-courses/blob/7b8685f8a724800e01d04ef95721c85c5f340092/docs/courses/OA-ERGODIC/src/localizing-factor-actions-and-uniform-cocycles.md",
      "source_sha256": "a2d5b1f419b9cef10b3180ccaa9ed13deaaf794c576e5775a01249f4ee903fec",
      "scope": "Theorem1.2, Theorem3.1, Lemma4.2 and Theorem5.2; exact source unchanged from the previous bounded proof reading."
    },
    {
      "source": "https://github.com/KokunoYumeto/open-math-courses/blob/7b8685f8a724800e01d04ef95721c85c5f340092/docs/courses/OA-ERGODIC/src/variable-factor-fields-and-measurable-conjugacy.md",
      "source_sha256": "f0e55022243d4049a161e5531d19fbd18619fdf051a40764d9a69e8ff3128982",
      "scope": "Theorem1.1 and Theorem3.1/Lemma3.2; exact source unchanged from the previous bounded proof reading."
    },
    {
      "source": "https://github.com/KokunoYumeto/open-math-courses/blob/7b8685f8a724800e01d04ef95721c85c5f340092/docs/courses/injective-factors/src/classification-of-injective-factors.md",
      "source_sha256": "fc38d5a7fee2e52cdaadfe2068a8f140be0dd38ea474a29251337ef8c350d76f",
      "scope": "Lemma6.1 and Theorem6.2; exact source unchanged from the previous bounded proof reading."
    }
  ],
  "figures": [
    {
      "path": "figures/trace-scaling-flow-comparison.svg",
      "sha256": "b9151fd4497a3e0db2c32be18affa453ec78d3b0c266a2c07ece9495586ddc59"
    },
    {
      "path": "figures/trace-scaling-flow-comparison.png",
      "sha256": "44bc92eb090e524bfa54241092858d5378bfd554a90a6220185f3f95401d7f47"
    },
    {
      "path": "figures/draw_trace_scaling_flow_comparison.py",
      "sha256": "f282a1e620906b59245796273e4a8a98cd5b4d72f4b46477ac8e4b61de3ec279"
    }
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}