Involution-stable maximal-order conjecture

Let $\mathbb{C}_n$ be the Clifford algebra with generators $i_1,\ldots,i_{n-1}$, and let $\mathbb{Z}[i_1,\ldots,i_{n-1}]$ be the indicated Clifford order. A maximal order is closed under the involutions when it is preserved by the involutions considered in the source. Involution-stable maximal-order conjecture. There always exists a maximal order containing $\mathbb{Z}[i_1,\ldots,i_{n-1}]$ which is closed under the involutions. The conjecture is motivated by calculations, and the source states that the corresponding questions remain open for general quadratic forms.