The reduced-power maximality conjecture for SOP3

Let $T$ be a theory with elimination of quantifiers, and let $\trianglelefteq_{{\rm rp}}$ denote the reduced-power maximality relation for pairs $(T,\Delta)$. The notation ${\rm SOP}_3$ denotes the strict order property of level $3$.

Reduced-power maximality conjecture. $(T,\Delta)$ is $\trianglelefteq_{{\rm rp}}$-maximal if and only if $(T,\Delta)$ has the ${\rm SOP}_3$.

This conjecture seeks to characterize the theories maximal for atomic saturation of reduced powers. The source presents it as a natural question after establishing that ${\rm SOP}_3$ implies reduced-power maximality; its resolution is not supplied.