OWR-7155441-003 · Complete counterexample

Normalized Maps of Arbitrary Arity to Wound Unipotent Groups

Manuscript 27 October 2026 · Online 27 October 2026

math.AGUnrefereed preprint

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.

Record

Affiliation
Mercury Software GmbH
Result
Complete counterexample
Categories
math.AG
Manuscript
27 October 2026
Online release
27 October 2026
Version
1.0
License
Creative Commons Attribution 4.0 International

Files and verification

The PDF is the canonical reading copy. The source archive contains the LaTeX manuscript, bibliography, reproducibility material, and audit documents without build artefacts.

Citation

Alper Ferudun, “Normalized Maps of Arbitrary Arity to Wound Unipotent Groups,” EulerSolve Research Papers, OWR-7155441-003, 2026. https://doi.org/10.5281/zenodo.23684182.

BibTeX
@misc{ferudun2026arbitraryarityrigidity,
  author = {Ferudun, Alper},
  title = {Normalized Maps of Arbitrary Arity to Wound Unipotent Groups},
  year = {2026},
  howpublished = {EulerSolve Research Papers},
  url = {https://eulersolve.org/papers/owr-7155441-003/},
  doi = {10.5281/zenodo.23684182},
  note = {OWR-7155441-003; unrefereed preprint}
}

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