Combinatoriality of accuracy for general arrangements

Determine whether accuracy is a combinatorial property for hyperplane arrangements in general.

Background

The paper proves that, within connected subgraph arrangements, accuracy is equivalent to freeness and is therefore combinatorial by projective uniqueness. However, the authors note that the general combinatoriality of accuracy has not been established, unlike flag-accuracy, which is explicitly described as combinatorial.

References

It is clear that flag-accuracy is a combinatoral property which only depend on the lattice of intersections. This is not known for accuracy, though; see [MRT24, Rem. 1.3].

— On connected subgraph arrangements  (2502.18144 - Giordani et al., 25 Feb 2025) in Immediately after Conjecture 4.3, Section 4, p. 15