{
  "schema": "programme-source-record/v1",
  "title": "Normal tensor tests and tracial GNS identifications",
  "author": "GPT-6 Astra (OpenAI)",
  "license": "CC0-1.0 for original programme expression; human sources retain their own rights",
  "source_sha256": "b3ab37ad16ca110b4a3328fff5d603f3c6dc554898f5b857ca6d77d191eaeec0",
  "scope": "Normal product functionals at arbitrary Hilbert cardinality; faithful countable tracial products and compatible GNS identifications; normal tensor homomorphisms with exact kernels and ranges; normal completely positive dilations and tensor maps, and predual limits of tensor automorphisms.",
  "programme_sources": [
    {
      "title": "Normal representations and finite corners of tracial factors",
      "reader": "../../OA-APPROX/normal-representations-and-finite-trace-corners.html",
      "source_sha256": "6a242f98ad6fd996268686d596265b65b7803d01024a5ca963feb67f95a98e43",
      "sections": "NA3–NA4: normal representations as amplified subrepresentations; bounded positive roots and normal GNS coefficients."
    },
    {
      "title": "Bounded calculus, concrete preduals, density and faithful normal ranges",
      "reader": "../../OA-APPROX/constant-car-reviewed-weight-foundations.html",
      "source_sha256": "6a90c0d3826cc835fb6cc5af11c3314e50a4988d3c68997b739724ddaf5bae55",
      "sections": "CF1–10, CP1–6, BD1–5, ST1–2 and ST-C: bounded calculus, concrete preduals, density and faithful normal ranges."
    },
    {
      "title": "Spatial tensor products of von Neumann algebras",
      "author": "Claude Opus 5.5 (Anthropic)",
      "sections": "Theorems9.2 and10.1(1)–(2)"
    },
    {
      "title": "Infinite tensor products",
      "reader": "../../OA-APPROX/infinite-tensor-products.html",
      "sections": "Sections2,4–5 and10.3–10.4; pointed-product and Hilbert tensor constructions"
    },
    {
      "title": "Strong stability and tensor absorption",
      "reader": "../../OA-APPROX/strong-stability-and-tensor-absorption.html",
      "sections": "Theorem3.1 supplies the separate ambient summable-splitting hypotheses"
    }
  ],
  "human_sources": [
    {
      "author": "Bruce Blackadar",
      "title": "Operator Algebras: Theory of C*-Algebras and von Neumann Algebras",
      "edition": "Revised author edition,8February2017",
      "url": "https://bruceblackadar.com/Mathematics/Cycr.pdf",
      "sections": "III.2.2.4–III.2.2.8,printed266–268",
      "role": "Normal dilation, normal cp tensor maps and amplified representations; historical tensor-provider reference"
    },
    {
      "author": "Masamichi Takesaki",
      "title": "Theory of Operator Algebras III",
      "url": "https://doi.org/10.1007/978-3-662-10453-8",
      "sections": "XIV.1.1–XIV.1.14 andXIV.4.10",
      "role": "Construction source of the earlier infinite-product provider"
    }
  ],
  "scope_limits": [
    "The tracial product construction uses specified faithful normal tracial states; the normal tensor-map theorems require neither states nor traces.",
    "Normal homomorphism and completely positive tensor maps do not imply that arbitrary commuting subalgebras give an ambient spatial tensor decomposition.",
    "Modular-weight, core, centralizer, cohomology and full factor-classification results retain their own hypotheses."
  ]
}