Coincidence conjecture for maximal bi-invariant orders on Hermitian Lie groups

Let $G$ be the Hermitian Lie group considered above, with maximal bi-invariant order, maximal continuous bi-invariant order, and, when $G$ is of tube type, geometric order. Coincidence conjecture. The maximal and maximal continuous bi-invariant orders coincide. In particular, in the tube type case, both coincide with the geometric order. The preceding theorem gives inclusions between these orders, and the conjecture asks whether the remaining inclusions are equalities; the source presents this as an open question.