{
  "schema_version": 1,
  "problem_number": "OWR-3392-002",
  "title": "Exchangeability and Trivial Tails Do Not Imply the Coordinate Intersection Property",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "For every prime p >= 5, we construct a minimal exchangeable sequence of trace-preserving embeddings of L(C_p) into a hyperfinite finite von Neumann algebra whose tail algebra is scalar but whose canonical filtration fails the intersection axiom for noncommutative factorizations. The intersection of the algebras on {0,1} and {1,2} has dimension p^2, while the algebra on {1} has dimension p. The example comes from an explicit class-three nilpotent group: a central coordinate is recovered by a triple commutator using any auxiliary index, but not from its single generator. We also identify the least enlargement of the coordinate algebras that does form a factorization. Thus the obstruction concerns retaining the given singleton ranges; it does not assert that the ambient algebra admits no factorization with enlarged coordinates. This is an unrefereed, AI-assisted preprint with a self-contained proof and exact reproducibility code. It makes no absolute priority claim.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.OA",
    "math.PR",
    "math.GR"
  ],
  "keywords": [
    "OWR-3392-002",
    "math.OA",
    "math.PR",
    "math.GR"
  ],
  "manuscript_version_date": "2026-10-22",
  "publication_date": "2026-10-23",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-23",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/owr-3392-002/",
  "pdf_url": "https://eulersolve.org/papers/owr-3392-002/paper.pdf?v=351b3b524a1b",
  "doi": "10.5281/zenodo.23587385",
  "zenodo_record_url": "https://zenodo.org/records/23587385",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "For every prime p>=5, a minimal exchangeable L(C_p) sequence with scalar tail has a canonical pair-algebra intersection of dimension p^2 instead of the singleton dimension p; its least enlarged factorization is explicit. This is a self-audited, AI-assisted, unrefereed preprint. No independent certification, formal proof verification or absolute-priority claim is made.",
  "files": {
    "paper.pdf": {
      "sha256": "351b3b524a1b100254c5f69463dcf73a6fb947cd982235527622263029c7cb65"
    },
    "source.zip": {
      "sha256": "a165db07e96b01c77af9ccaeab705c775f8a41075d17ba2ee088021f4229b8f6"
    },
    "verification_report.md": {
      "sha256": "aae7223efa5f38f84129f198d0f0c190996098b19e55769a3ba657904390e2b8"
    }
  },
  "ai_use_disclosure": "AI-assisted tools supported research, computation, proof development, and manuscript preparation. The author remains responsible for all claims and the final text."
}