Genericity conjecture for effective minimal-critical-point assumptions

Let $F({\mathbf z})\in\mathbb{Z}(z_1,\dots,z_n)$ be a rational function, and let (A5) denote that the Jacobian matrix of the relevant system of equations (GenSys1)–(GenSys5) has full rank at its solutions, while (J2) denotes that the Jacobian matrix of (GenSys1)–(GenSys6) is non-singular at its solutions. Genericity conjecture. Assumptions (A5) and (J2) hold generically. The source proves genericity of assumption (A4), but leaves these two Jacobian conditions as the conjectural part needed for the effective minimal-critical-point analysis.