The homotopy-type conjecture for connected central arrangements

Let ${\mathcal A}$ be a central hyperplane arrangement with connected underlying matroid, and let $C({\mathcal A})$ denote its complement. Homotopy-type conjecture. The homotopy type of $C({\mathcal A})$ determines the underlying matroid of ${\mathcal A}$. The question asks whether homotopy-equivalent complements of central arrangements with connected underlying matroids must have the same combinatorial structure; the paper presents counterexamples outside this restricted setting but does not resolve the stated problem.