The anti-telescope parabola conjecture for $Z$

Let $\widehat Z$ be the telescope of the $v_2$-self-map on $Z$. Let $x_i=h_{i,0}^2$. Parabola conjecture, height 2. The differentials of the preceding height-$2$ differentials conjecture are nontrivial, and every remaining $v_2$-parabola contains permanent-cycle elements. Consequently, the $v_2$-periodic homotopy of $Z$ is generated by the families

$$v_2^m h_{3,0}^{\bar\epsilon_3}\widetilde h_{2,1}^{\epsilon_2}h_{3,1}^{\epsilon_3},\qquad m\geq0,\quad \epsilon_j\in\{0,1\},$$

and the $v_2$-parabolas are supported by

$$h_{3,0}^{\bar\epsilon_3}\widetilde h_{2,1}^{\epsilon_2}h_{3,1}^{\epsilon_3}x_3^{\bar\epsilon_3}x_4^{\bar\epsilon_4}\cdots, \qquad \epsilon_j,\bar\epsilon_j\in\{0,1\}.$$

This is presented as a maximally anti-telescope version of the earlier parabola conjecture and remains conjectural.