MRS differentials conjecture

Let $y(h)$ be the spectrum under consideration, and let $h_{2h+i-j,j}$, $b_{h+i,j}$, and $q_h$ denote the classes and coefficient appearing in its localized Adams spectral sequence. MRS differentials conjecture. In the localized Adams spectral sequence for $y(h)$, each class $h_{2h+i-j,j}$ survives to the $(2p^j)^{\mathrm{th}}$ page, $b_{h+i,j}$ survives to the $(2p^{h-1}+1)^{\mathrm{st}}$ page, and there are differentials

$$d_{2p^j}(h_{2h+i-j,j})=q_h b_{h+i,h-1-j}^{p^j}$$

for each $i>0$ and $0\leq j\leq h-1$. This is the expected pattern of differentials truncating the polynomial generators on the localized Adams $E_2$-page; the source attributes it to MRS, and the subsequent collapse behavior is treated separately.