The proposed relations for the coefficient ring of the 2-typization of the universal Abel formal group law

Let $\mathcal{F}_{Ab}$ be the universal Abel formal group law, and let its $2$-typization have coefficient ring presented as a quotient of the localized Brown–Peterson coefficient ring $BP_* = \mathbb{Z}_{(2)}[v_1,v_2,\ldots]$. Write $R$ for the ideal of relations and let $|v_i|=2(2^i-1)$. For indices $1\leq i<j$ and $1\leq i'<j'$, let $P$ denote a monomial not divisible by any $v_1v_{i'}^2v_{j'}^2$. The proposed relations. The coefficient ring is isomorphic to

$$\Lambda=\mathbb{Z}_{(2)}[v_1,v_2,\ldots]/R,$$

and all generating relations have the form

$$v_1v_i^2v_j^2\sim P,\qquad 1\leq i<j.$$

These relations are motivated by explicit low-degree computations of the kernel of the classifying map for the $2$-typized Abel formal group law; the parser supplies no evidence that the proposed presentation has been proved or disproved, so its status remains open.