{
  "schema_version": 1,
  "problem_number": "OWR-12868-001",
  "title": "Cohomology Annihilators of Truncated Polynomial Rings",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "We compute every cohomology-annihilator ideal and its least nonnegative stabilization index for S[x]/(x^n), where n >= 2 and S is a polynomial or formal power-series ring over any field. In base dimension zero, the eventual ideal is (x^floor(n/2)) and the index is 1. In base dimension one, the ideal is (x^(n-1)) and the index is 2 in every characteristic; this formula holds over every nonfield principal ideal domain. In base dimension d >= 2, the ideal is (x^(n-1)), with index d+1, when n is invertible in the field; it is zero, with index 0, when the characteristic divides n. Maps through projectives are described by an explicit transfer. A classical symmetric-power nilpotent operator gives a trace and colon-ideal obstruction in positive characteristic, and finite-free induction treats every divisible truncation degree. The field comparison also yields strict failures of equality under polynomial extension and localization. Version 1.1 extends version 1.0 to every characteristic dividing n and to formal power-series bases in every dimension. It is a revision of the same manuscript, not a separate work. The broad noether-algebra question in OWR-12868-001 remains unresolved. The preprint is AI-assisted, self-audited and unrefereed; no independent review, proof-assistant certification, or absolute priority claim is asserted.",
  "result_type": "COMPLETE_PROOF",
  "categories": [
    "math.AC",
    "math.RA"
  ],
  "keywords": [
    "cohomology annihilator",
    "truncated polynomial ring",
    "modular characteristic",
    "stabilization index",
    "transfer",
    "OWR-12868-001"
  ],
  "manuscript_version_date": "2026-10-19",
  "publication_date": "2026-10-19",
  "publication_date_kind": "first public online release",
  "version": "1.1",
  "date_modified": "2026-10-19",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.1",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/owr-12868-001/",
  "pdf_url": "https://eulersolve.org/papers/owr-12868-001/paper.pdf?v=e364cf686a24",
  "doi": "10.5281/zenodo.23482971",
  "zenodo_record_url": "https://zenodo.org/records/23482971",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Complete calculations for polynomial and formal power-series bases over arbitrary fields, in all dimensions and characteristics, and for all nonfield principal ideal domains. The broad noether-algebra research question remains unresolved. Classical Friedlander-Pevtsova and Avramov-Buchweitz-Iyengar constructions are credited, as is the known Iyengar-Takahashi double-line calculation. Finite diagnostics supplement the written proof. AI-assisted, self-audited and unrefereed; no independent review, formal certification, dataset-maintainer acceptance or absolute priority is claimed.",
  "files": {
    "paper.pdf": {
      "sha256": "e364cf686a24e723e95b7b4867b9306ff2d4e7a551414dd40557e740bce7167f"
    },
    "source.zip": {
      "sha256": "627a3c6ae32625eeb9c5b6e084d53943465805be5bbae0e99f86b00d36fd3e6d"
    },
    "verification_report.md": {
      "sha256": "6734ba5aa4a2d16eea8d28009990b8264e8ab31afc045ea1911f17ffbc394cc8"
    }
  },
  "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."
}