Published October 27, 2026 | Version 1.0

Normalized Maps of Arbitrary Arity to Wound Unipotent Groups

Authors/Creators

  • 1. Mercury Software GmbH

Description

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.

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