The \b7IP\b7rat-characteristic factor conjecture for rationally independent polynomial systems

Let $P=(p_1,\b7\dots,p_r)$ be a system of rationally independent polynomials, and let $Z_k(X)$ denote the factor appearing in the definition of an $\b7IP\b7rat$-characteristic factor for $P$. Characteristic factor conjecture. There exists some $k=k(P)$ such that $Z_k(X)$ is an $\b7IP\b7rat$-characteristic factor for $P$. This conjecture would extend the characteristic-factor theory to systems in which exactly one polynomial may be linear; the paper notes that the case of the system $bfn,n^2\}$ has been verified, while the general assertion remains unresolved.