A Characteristic-Two Counterexample to Rigidity for a Punctured Projective Line

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.