Uniqueness of minimal orders for even Clifford algebras

Let $Q$ be a conic bundle and let $\operatorname{Cl}_0(Q)$ be its even Clifford algebra. Consider orders Morita equivalent to $\operatorname{Cl}_0(Q)$ and having the same rank and second Chern class. Uniqueness conjecture. The even Clifford algebras $\operatorname{Cl}_0(Q)$ are the only such orders. This is a conjecture about the uniqueness of the minimal second Chern class representative in the relevant Morita equivalence class; the source does not state whether it has been resolved.