The tmf-ASS differentials conjecture for $Z$, part 2

In the $\mathrm{tmf}$-Adams spectral sequence for $Z$, let $\epsilon_j,\bar\epsilon_j\in\{0,1\}$ and let $m\gg0$. Differentials conjecture, part 2. The $v_2$-families

$$v_2^m\widetilde h_{2,1}^{\epsilon_1}h_{3,0}^{\epsilon_2}h_{3,1}^{\epsilon_3}\widetilde h_{4,1}$$

support differentials hitting the $v_2$-parabolas supported by

$$\widetilde h_{2,1}^{\epsilon_1}h_{3,0}^{\epsilon_2}h_{3,1}^{\epsilon_3}x_3^2.$$

Also, the $v_2$-parabolas supported by

$$\widetilde h_{2,1}^{\epsilon_1}h_{3,0}^{\epsilon_2}h_{3,1}^{\epsilon_3}\widetilde h_{4,1}x_3^{k_3}x_4^{\bar\epsilon_4}x_5^{\bar\epsilon_5}\cdots$$

support differentials hitting the parabolas

$$\widetilde h_{2,1}^{\epsilon_1}h_{3,0}^{\epsilon_2}h_{3,1}^{\epsilon_3}x_3^{k_3+2}x_4^{\bar\epsilon_4}x_5^{\bar\epsilon_5}\cdots.$$

The conjecture extends the earlier differentials conjecture by including the $d_4(h_{4,1})=v_2x_3^2$ pattern; the existence and nontriviality of these differentials are open.