Cross-Cutting Exposure as an Engine of Radicalization: Platform Design, Attention, and Geography in a Stochastic Multiplex Model of Opinion Dynamics

Do social-media platforms polarize because they hide disagreement, or because they expose people to it? We study a continuous-time model in which agents diffuse in physical space by Brownian motion while interacting through an adaptive, algorithmically curated digital network under a finite attention budget. When influence is purely assimilative (bounded confidence), opinion-blind long-range exposure heals locality-induced fragmentation and algorithmic homophily builds echo chambers. Once influence includes a repulsive response to strongly opposed views, the ranking of platform designs inverts: a neutral, uncurated platform drives maximal polarization with opinions pinned at the extremes; a controversy-seeking engagement algorithm is nearly as radicalizing; and strong algorithmic homophily paradoxically shields the population from extremism. A two-bloc reduction shows that the stationary cross-bloc attention fraction set by the engagement kernel controls the radicalization rate and a finite-horizon crossover ${\lambda }_c(T)$ in the digital attention share—consistent with simulations, with no parameters fitted to the onset data. Radicalization is thus rate-limited, not threshold-limited. Across repulsion parameters, kernels, and sizes up to $N=1600$, uncurated exposure sets the saturation level of radicalization. A mobility–attention phase diagram shows that once the platform owns most of an agent’s attention, physical mobility becomes irrelevant. Under opinion-independent mobility we detect no geographic opinion structure; a Schelling-type homophilic drift of strength $\chi$ restores it only above a Péclet threshold $\chi \mathrm{\ell }\mathrm{/}D\sim 1$. The model offers a mechanism for field observations in which curated cross-cutting exposure increased polarization, and implies that exposure-diversity interventions can have either sign depending on the prevalence of negative influence.