{
  "schema_version": 1,
  "problem_number": "OWR-3392-012",
  "title": "Orbit Generation Does Not Ensure GNS Descent of Markov Dilations",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "We construct a general dilation of the Ornstein-Uhlenbeck Markov semigroup whose ambient commutative von Neumann algebra is generated by the initial algebra and its nonnegative time shifts, but whose GNS representation kernel is not invariant under those shifts. The dilation endomorphisms are normal, injective and point-strongly continuous, and its expectation is normal. Thus orbit generation alone does not permit passage of a given dilation to the GNS module of its expectation. The construction uses a bounded density built from independent Gaussian bridge signs. For each prescribed integer m, this density leaves conditional observations at any m times unchanged while producing the obstruction. An exact support criterion identifies kernel invariance in the commutative setting. This is a complete counterexample to the explicit orbit-generation formulation; it does not classify stronger sufficient minimality conditions, contradict weak corner dilation theorems, or preclude a different module dilation of the same semigroup. The manuscript is unrefereed, and no absolute priority claim is made.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.OA",
    "math.PR"
  ],
  "keywords": [
    "OWR-3392-012",
    "math.OA",
    "math.PR"
  ],
  "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-3392-012/",
  "pdf_url": "https://eulersolve.org/papers/owr-3392-012/paper.pdf?v=8f4c1bdbc997",
  "doi": "10.5281/zenodo.23587469",
  "zenodo_record_url": "https://zenodo.org/records/23587469",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "For every fixed m>=1, an explicit normal point-strongly continuous orbit-generated general OU dilation matches at most m coordinate observations but has noninvariant GNS left kernel; an exact commutative support criterion is also proved. 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": "8f4c1bdbc997386b5a8b9a7ec03339850834842697696dca6dcfdbf4acd42194"
    },
    "source.zip": {
      "sha256": "28139b6123536d25d324972ea7be2ab225a4af579c6e62406daa16fefeb1316f"
    },
    "verification_report.md": {
      "sha256": "7501507f0477a523cb759e09cb1b5b5bb876595f0b074003ffdf0df6b800b133"
    }
  },
  "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."
}