{
  "schema": "programme-proof-companion/v1",
  "title": "Trace existence and central averaging",
  "source": "foundations/trace-existence-foundations.md",
  "reader": "trace-existence-foundations.html",
  "license": "CC0-1.0",
  "scope": "Finite center-valued traces, normal corner-trace extension, semifinite scalar traces and simultaneous norm averaging, with arbitrary centers, Hilbert dimensions and increasing nets. The accompanying bounded-topology and tracial-normality proofs supply the stated analytic foundations.",
  "authors": [
    {
      "name": "GPT-6.1 Sol (OpenAI)",
      "contribution": "FCT, CF, PC and norm-averaging exposition"
    },
    {
      "name": "GPT-6 Astra (OpenAI)",
      "contribution": "Faithful representations, bounded interfaces, scalar-trace proof and companion integration"
    },
    {
      "name": "Claude Opus 5.5 (Anthropic)",
      "contribution": "Earlier programme exposition of corner-trace extension and semifinite trace existence"
    }
  ],
  "programme_sources": [
    {
      "title": "The normalized trace with its full center retained",
      "source": "../../OA-FLOW/src/OA-FLOW-FCT.md",
      "sections": "FCT0–FCT8"
    },
    {
      "title": "Continuous calculus, positivity and Hilbert spaces",
      "source": "../../OA-FLOW/src/OA-FLOW-CF.md",
      "sections": "1–8"
    },
    {
      "title": "Projection comparison and the countably decomposable type III case",
      "source": "../../OA-FLOW/src/OA-FLOW-PC.md",
      "sections": "PC0–PC7"
    },
    {
      "title": "Concrete predual balls and faithful ultraweak representations",
      "source": "../../OA-FLOW/src/OA-FLOW-ST12.md",
      "sections": "ST1–ST2"
    },
    {
      "title": "Central averaging and maximal ideals",
      "source": "../../OA-FOUND-REMAINDER/src/central-averaging-and-maximal-ideals.md",
      "sections": "Definitions and 1–3"
    }
  ],
  "analytic_foundations": [
    "bounded-topology-foundations.md",
    "tracial-normality-foundations.md"
  ],
  "human_sources": "Bibliographic citations and their mathematical roles appear in the companion source notice. Human-source expression retains its own rights.",
  "source_sha256": "d7912327394fc462f52c1fdb97d962ab7f2f64e2eb2eedd98ee613bf30b63dd8"
}