Flag-accuracy conjecture for connected subgraph arrangements

Let $G$ be a connected graph, and let ${\mathscr A}_G$ denote its connected subgraph arrangement. A free arrangement is flag-accurate if it is accurate and the tuple of flats witnessing accuracy can be chosen to form a flag in its intersection lattice. Flag-accuracy conjecture. The arrangement ${\mathscr A}_G$ is free if and only if it is flag-accurate. Flag-accuracy is known for several families, including path and cycle graphs, and computationally for the indicated almost-path cases up to rank $8$; the equivalence for all connected subgraph arrangements remains open.