The tmf-ASS differentials conjecture for $Z$, part 1

Let $x_j=h_{j,0}^2$. In the $\mathrm{tmf}$-Adams spectral sequence for $Z$, use indices $i\geq3$, $l\geq i+3$, $m<2^{i+1}-1$, $k_j\geq0$, and $\epsilon_j,\bar\epsilon_j\in\{0,1\}$. Differentials conjecture, part 1. There are differentials

$$\begin{aligned} d_3(&v_2^m h_{3,0}^{\bar\epsilon_3}x_i^{k_i+1}x_{i+1}^{k_{i+1}}x_{i+2}^{\bar\epsilon_{i+2}}x_{i+3}^{\bar\epsilon_{i+3}}\cdots x_{l-1}^{k_{l-1}}x_l^{k_l}\cdots \\&\qquad\widetilde h_{2,1}^{\epsilon_2}h_{3,1}^{\epsilon_3}\widetilde h_{4,1}^{\epsilon_4}h_{l,1}h_{l+1,1}^{\epsilon_{l+1}}h_{l+2,1}^{\epsilon_{l+2}}\cdots)\\ &=v_2^{m+1}h_{3,0}^{\bar\epsilon_3}x_i^{k_i+1}x_{i+1}^{k_{i+1}}x_{i+2}^{\bar\epsilon_{i+2}}x_{i+3}^{\bar\epsilon_{i+3}}\cdots x_{l-1}^{k_{l-1}+2}x_l^{k_l}\cdots\\ &\qquad\widetilde h_{2,1}^{\epsilon_2}h_{3,1}^{\epsilon_3}\widetilde h_{4,1}^{\epsilon_4}h_{l+1,1}^{\epsilon_{l+1}}h_{l+2,1}^{\epsilon_{l+2}}\cdots+\cdots. \end{aligned}$$

The conjecture proposes the indicated $d_3$-differentials; after them, only bounded torsion or specified surviving families remain.