Asymmetric density criterion for Ramsey-infinite ordered graph pairs

Let $H$ and $H'$ be ordered graphs with asymmetric $2$-density parameters satisfying $m_2(H)\geq m_2(H')$. Let $m(F)$ denote the relevant density of a graph $F$, and let $R_<(H,H')$ be the family of Ramsey graphs of $(H,H')$. Asymmetric density conjecture. If

$$m(F)>m_2(H,H')$$

for every $F\in R_<(H,H')$, then $(H,H')$ is Ramsey infinite. This is proposed as an asymmetric extension of the paper's symmetric density result; the cited random-Ramsey results provide partial motivation, while the ordered statement remains open.