Where $f_+(x,\theta) = \Sigma_{n \ge 0} a_n x^{p^n} + \alpha \theta, f_-(x,\theta) = \Sigma_{n \ge 0} b_n x^{p^n} + \beta \theta$$f_+(x,\theta) = \Sigma_{n \ge 0} a_n x^{p^n} + \alpha \theta, f_-(x,\theta) = \Sigma_{n \ge 0} b_n x^{p^n} + \beta \theta$. We claimed that the correct "strictness" condition is $gr(df) = Id$ where $gr$ is the associated graded w.r.t. the $\mathbb{Z}/2$-filtration. In coordinates this condition translates to: