Normalized Maps of Arbitrary Arity to Wound Unipotent Groups
Manuscript 27 October 2026 · Online 27 October 2026
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
- Contact
- [email protected] · GitHub
- 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}
}