A flip for a partition into at most $p$ parts is obtained from the original graph by a fixed transduction: color the parts with $p$ unary predicates and flip the adjacency between the chosen pairs of colors. This bounded-flip image of a class is transduced by it, and monadic dependence is preserved under transductions. Every $s$-definable flip is a flip for the partition into atomic types over at most $s$ vertices, which has at most $3^s$ parts.

The argument is carried out for the graph classes of the archive and their monadic dependence, and transferred to the graph classes used here.