The BPGL\langle 2 \rangle motivic Adams spectral sequence collapse claim

Let $F$ be a field of low cohomological dimension. Consider the motivic Adams spectral sequence based on $\operatorname{BPGL}\langle 2 \rangle$, and let $n$ be a positive integer. The BPGL\langle 2 \rangle spectral sequence claim. The $E_1$-page can be computed by appropriate lifts of the differentials in the motivic Adams spectral sequence based on $\operatorname{H}\mathbb{Z}$. In particular, when $F=\mathbb{C}$ or $F=\mathbb{R}$, the motivic Adams spectral sequence based on $\operatorname{BPGL}\langle 2 \rangle^{\otimes n}$ collapses at the $E_2$-page. This is presented as a particular investigation motivated by the broader question of whether differentials for motivic finite-presentation spectra are determined by those for $\operatorname{H}\mathbb{Z}$; the parser supplies no evidence resolving the claim beyond its formulation.