The finite-dimensional presentation conjecture for the elliptic Bloch group

Let $E$ be a cubic curve in $P^2$. For a point $p\in P^2$ and three lines $l_1,l_2,l_3$ through $p$, let $A_i:=l_i\cap E$ and define

$$\{p;l_1,l_2,l_3\}:=A_1\ast A_2^-+A_2\ast A_3^-+A_3\ast A_1^-.$$

Let $\tilde R^*_3(E)\subset I^4_E$ be the subgroup generated by these elements and by those linear combinations of $\{a\}_3+\{-a\}_3$ that lie in $I^4_E$, and let $R^*_3(E)$ be the relation subgroup used to define the elliptic Bloch group. Elliptic Bloch relations conjecture. One has

$$\tilde R^*_3(E)=R^*_3(E).$$

The claim would show that the displayed geometric relations generate all the relations defining the elliptic Bloch group, giving a finite-dimensional geometric analogue of the five-term presentation for the classical Bloch group. The source provides a lemma showing only the inclusion $\tilde R^*_3(E)\subset R^*_3(E)$, so equality remains open here.