{
  "schema_version": 1,
  "problem_number": "OWR-7155441-002",
  "title": "A Characteristic-Two Counterexample to Rigidity for a Punctured Projective Line",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "We construct a characteristic-two counterexample to the two-factor rigidity assertion in Conjecture 4 of Rosengarten's contribution to Oberwolfach Report 20/2021, exactly the frozen UnsolvedMath record OWR-7155441-002. Over k=F_2(s,t), let X be the projective line with the single degree-four closed point defined by T^4+sT^2+t removed. We give an explicit nonzero morphism X times X to a smooth connected commutative k-wound unipotent group of dimension three, zero on both coordinate slices through infinity. Four rational functions and one polynomial identity give the construction; irreducibility, woundness and global regularity are proved directly. We also give two choices of embeddings of the factors of one finite reduced algebra whose composita have imperfection one and two, disproving the embedding-independence assertion in Proposition 2.5 of arXiv:2307.04649v4. The closed point is not geometrically irreducible; no claim is made about that restricted variant, characteristic different from two, corrected invariants or unrelated applications. This four-page English unrefereed preprint was developed with AI assistance and self-audited. Exact polynomial checks supplement the written proof; independent review, formal proof-assistant verification and absolute priority are not claimed.",
  "result_type": "COMPLETE_COUNTEREXAMPLE",
  "categories": [
    "math.AG"
  ],
  "keywords": [
    "OWR-7155441-002",
    "characteristic two",
    "wound unipotent groups",
    "rigidity",
    "punctured projective line"
  ],
  "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-7155441-002/",
  "pdf_url": "https://eulersolve.org/papers/owr-7155441-002/paper.pdf?v=c84ec0f991d9",
  "doi": "10.5281/zenodo.23683405",
  "zenodo_record_url": "https://zenodo.org/records/23683405",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Complete characteristic-two counterexample to Conjecture4 of Rosengarten, OWR20/2021 p1107, exactly frozen OWR-7155441-002. Over F_2(s,t), remove the single degree-four point T^4+sT^2+t and map the square of its complement nontrivially to the smooth connected commutative wound group v0=v0^2+s v1^2+t v2^2+st v3^2, vanishing on both infinity slices. An explicit field tower also disproves embedding independence in Proposition2.5 of arXiv:2307.04649v4. This explicit characteristic-two counterexample refutes the full frozen Conjecture 4 of OWR20/2021. It makes no claim about other characteristics or a geometrically irreducible boundary variant. The source-package includes exact polynomial checks and a separate counterexample to the stated embedding-independence assertion in arXiv:2307.04649v4, Proposition 2.5. 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": "c84ec0f991d902c0f9559e9f0bda98b88c2469ff9ea133b0607c0a672e2edf19"
    },
    "source.zip": {
      "sha256": "22fd3b598a85f6ccacc08f1b49bb9a27e6d87e3f997c7477032f9e3b8042aba9"
    },
    "verification_report.md": {
      "sha256": "54e55aa82909c4b35b86a517e0353dcbd82ddcb6108b4861b894f2f119be4168"
    }
  },
  "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."
}