Determine whether two-color critical multiplicity is monotonically increasing

Determine whether the two-color critical multiplicity $m_2(s)$ is monotonically increasing as the clique size $s$ increases.

Background

Monotonicity of $m_2(s)$ is identified as a separate unresolved question in the paper. The proposed structural conjecture for extremal colorings would imply this monotonicity, so establishing the conjecture would resolve the question as a consequence.

The issue concerns the sequence of minimum guaranteed numbers of monochromatic $K_s$ subgraphs in colorings of $K_{R_2(s)}$. Although the paper derives improved upper bounds for several small values, it does not establish a general ordering of these critical multiplicities.