Unresolved Bockstein differential on γ/τ^7 h0^3 h4^2 in coweight 6, stem 30
Determine whether the element γ/τ^7 h_0^3 h_4^2 (coweight 6, stem 30) is hit by a Bockstein differential, specifically by establishing either a Bockstein d_9 from γ/(ρ^9 τ) h_2 c_1 (coweight 7, stem 31) to γ/τ^7 h_0^3 h_4^2 or a longer Bockstein differential originating from γ/(ρ^k τ) h_2 c_1; resolve this remaining uncertainty in the computed range.
References
In the range under consideration in this manuscript (coweights from $-2$ to $8$, stems up to $30$), there is one possible Bockstein differential that we have not established. It is possible that the element $\frac{\gamma}{\tau7} h_03 h_42$ in coweight $6$ and stem $30$ is hit by a differential. More precisely, either there is a Bockstein $d_9$ differential from $\frac{\gamma}{\rho9 \tau} h_2 c_1$ in coweight 7 and stem 31 to $\frac{\gamma}{\tau7} h_03 h_42$ or else $\frac{\gamma}{\rhok \tau} h_2 c_1$ supports a longer Bockstein differential. The uncertain status of the element $\frac{\gamma}{\tau7} h_03 h_42$ is indicated in \cref{fig:Ext} by an open square.