A characteristic-two counterexample to dévissage for local deformation functors

A negative answer to Byszewski's unrestricted fibre-product question for local deformation functors (Oberwolfach Report 54/2008, p.3039; 2009 thesis Question 6.4.4; arXiv:1112.0352v1, Question 4.4). For the weakly ramified additive F4 action t → t/(1+at) and its F2 subgroup, restriction–induction cannot factor formally smoothly over any prorepresentable recipient, regardless of tangent dimension. The proof uses actual unframed deformation classes, with nilpotent constant coordinate changes allowed, and an exact zero-kernel tangent restriction calculation. The variant imposing prorepresentability of the subgroup and quotient deformation functors remains unaddressed. The additive action, involution parameter-shift conjugacy and tangent-cohomology framework are established prior ingredients. Recipient tangent collapse is credited as an elementary consequence of Byszewski–Cornelissen (2009), Proposition 6.1, with the direct matrix calculation of Proposition 4.1 reproduced. The contribution is combining these ingredients to exclude the proposed unrestricted factorization. A bounded priority audit located no matching negative assertion in inspected primary bodies; it does not certify exhaustive originality or continued openness through 2026. The deposit includes the proof, TeX source, source/priority supplement, authored independent adversarial reviews and portable exact arithmetic verification (Python 3.10 or later; standard library only). Finite diagnostics support identities and selected controls; the written proof supplies full formal-series and arbitrary-natural-map claims. AI tools were used extensively in solving, verifying, source auditing and preparation. This is an unrefereed preprint with AI adversarial reviews; no formal proof-assistant certificate, conventional human peer review or journal acceptance is claimed.