The localized Adams differentials conjecture for $Z$

Consider the localized Adams spectral sequence

$$v_2^{-1}\prescript{\mathrm{ass}}{}{E}_2^{*,*}(Z)\Rightarrow\pi_*\widehat{Z},$$

with $E_2$-term $\mathbb{F}_2[v_2^{\pm},\widetilde{h}_{2,1},h_{3,0},h_{3,1},h_{4,0},h_{4,1},\ldots]$. Differentials conjecture. In this spectral sequence,

$$d_2(h_{4,0})=v_2\widetilde{h}_{2,1}^2,\qquad d_2(h_{i,0})=v_2h_{i-2,1}^2,\qquad d_4(h_{i,1})=v_2h_{i-1,0}^4.$$

These differentials are proposed as the localized analogue of the Mahowald–Ravenel–Shick differentials conjecture; the paper explains their expected origins but does not establish them.