The mixed-characteristic Q-sequence conjecture

Let $R$ be a complete local domain of mixed characteristic. A Q-sequence is a sequence with the quasilength property used in the definition of robust algebras. Mixed-characteristic Q-sequence conjecture. Every system of parameters of $R$ is a Q-sequence; equivalently, $R$ is robust as an $R$-algebra. The text states that this conjecture would imply the direct summand conjecture, but supplies no resolution status.