Monotonicity and CM-monotonicity for valuations

Let $d719$ be a $d4aa$-valuation for any $d4aa$.

Monotonicity conjecture. $d719$ is monotone if and only if $d719$ is CM-monotone.

This conjecture asks whether the equivalence between monotonicity and CM-monotonicity, proved in the paper for $d719$ an $d4d9^d$-valuation, holds for valuations over any coefficient structure $d4aa$.