An elementary counterexample to a Nullstellensatz for finite-type link invariants

We give a principal-ideal counterexample to the arbitrary-ideal actual-link Nullstellensatz in the ordinary uncompleted complex algebra of all finite-order finite-type link invariants. With g the sum of squared pairwise linking numbers and f=g(4g-1), the nonempty common zero set is the algebraically split links, but g does not lie in the radical of fV. A character on the entire algebra is obtained by formal evaluation of the standard twist-restriction polynomial at one half. The result applies for every fixed component count m at least two and for all finite-component links; the source's separate indexed linking-number ideal in the labelled theory is not decided. This is an elementary application of older polynomiality, explicitly credited to Stanford-Trapp, Eisermann and Stoimenow. A bounded primary-source audit found no explicit equivalent earlier counterexample in the inspected bodies, without claiming historical firstness, a new polynomiality method, or guaranteed novelty. The included audit discloses uninspected final-version/body limits. The deposit includes the self-contained research note, LaTeX source and exact-rational verification materials. AI tools were used extensively in developing, drafting, auditing and adversarially checking the result. This preprint is unrefereed and has not undergone conventional human peer review.