{
  "schema_version": 1,
  "problem_number": "OWR-7155441-003",
  "title": "Normalized Maps of Arbitrary Arity to Wound Unipotent Groups",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "For every integer n>=2, we construct a field k of characteristic two, a single closed point x of the projective line, and a nonconstant morphism from n copies of its complement to a smooth geometrically connected commutative k-wound unipotent group of dimension 2^n-1. The morphism is zero on every coordinate slice through infinity, while the residue field L always satisfies [L:kL^2]=2. The proof uses a determinant and the parameter-parity decomposition of a product of additive polynomials. For n>=3, this disproves the primitivity-bound assertion in Conjecture 5 of Oberwolfach Report 20/2021, exactly frozen UnsolvedMath record OWR-7155441-003, under either the printed index or logarithmic normalization. The n=2 case recovers the explicitly credited earlier paper DOI 10.5281/zenodo.23683405; the new result covers arbitrarily many factors at the same residue-field index. The fields and targets vary with n, the boundary points are not geometrically irreducible, and the base-field imperfection equals n. No claim is made about fixed-field unboundedness, base-field-imperfection thresholds, central-series assertions, corrected all-conjugate invariants or other characteristics. This four-page English unrefereed preprint was developed with AI assistance and self-audited. Exact polynomial checks supplement the written all-n proof; independent review, formal proof-assistant verification and absolute priority are not claimed.",
  "result_type": "COMPLETE_COUNTEREXAMPLE",
  "categories": [
    "math.AG"
  ],
  "keywords": [
    "OWR-7155441-003",
    "wound unipotent groups",
    "rigidity",
    "determinants",
    "characteristic two"
  ],
  "manuscript_version_date": "2026-10-27",
  "publication_date": "2026-10-27",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-27",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/owr-7155441-003/",
  "pdf_url": "https://eulersolve.org/papers/owr-7155441-003/paper.pdf?v=4abb63c90705",
  "doi": "10.5281/zenodo.23684182",
  "zenodo_record_url": "https://zenodo.org/records/23684182",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "For every n>=2, an explicit characteristic-two determinant construction gives a nonconstant normalized morphism from n copies of a one-point complement in P1 to a smooth geometrically connected commutative wound group, with residue-field index [L:kL^2]=2. Every n>=3 refutes Conjecture5 of OWR20/2021 p1108, under either its printed index or logarithmic normalization. This resolves frozen OWR-7155441-003 negatively. The arbitrary-n determinant construction refutes Conjecture5 of OWR20/2021 under both printed index and logarithmic normalizations. The two-factor predecessor is explicitly credited. The fields, points and groups vary with n; no claim is made about geometric-irreducibility variants, fixed-field unboundedness or thresholds using the base field imperfection. This preprint is AI-assisted, self-audited and unrefereed; no independent or formal verification or certified novelty or absolute-priority claim is made.",
  "files": {
    "paper.pdf": {
      "sha256": "4abb63c90705b7567b7f5ce29aa488c825bdae31af9883dd48cb10e706354c89"
    },
    "source.zip": {
      "sha256": "72ded4af26d4af34a2fc8899ec785d7ede5796e937720a4a4d3f66ff90a692ae"
    },
    "verification_report.md": {
      "sha256": "3bc2073723f329aa6090244543b877aa726277286b478395abbb4a63f2c27e59"
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  },
  "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."
}