Yagi–Yoshinaga's filtered VG-algebra reconstruction conjecture

Let $\mathcal{A}$ and $\mathcal{B}$ be real central hyperplane arrangements, and let $R$ be an integral domain with $\operatorname{char}R\neq 2$. Write $\mathrm{VG}(\mathcal{A})_R=R^{\mathrm{Ch}(\mathcal{A})}$ and $\mathrm{VG}(\mathcal{B})_R=R^{\mathrm{Ch}(\mathcal{B})}$ for their Varchenko–Gelfand algebras equipped with the filtrations generated by products of at most $p$ Heaviside functions. Let $\mathcal{T}(\mathcal{A})$ and $\mathcal{T}(\mathcal{B})$ denote their tope graphs. Yagi–Yoshinaga's conjecture. If

$$\mathrm{VG}(\mathcal{A})_R\cong \mathrm{VG}(\mathcal{B})_R$$

as filtered $R$-algebras, then

$$\mathcal{T}(\mathcal{A})\cong \mathcal{T}(\mathcal{B}).$$

This conjecture asserts that, over an integral domain of characteristic different from $2$, the filtered Varchenko–Gelfand algebra determines the tope graph and hence the underlying oriented-matroid chamber structure up to isomorphism. The result is known for arrangements generic in codimension $2$, while the non-generic case remains open because odd rank-two pencils can produce additional degree-one idempotents, or generalized Heaviside functions.