Recommendation-Mediated Diffusion of Stance-Bearing Information in Online Social Networks: A Dynamic Message-Passing Analysis of the UEAI Model

Recommendation systems change both the amount and allocation of exposure opportunities, making their effects on diffusion difficult to separate. We develop a discrete-time unexposed–exposed–active–inactive (UEAI) model that links static stance consistency, target-specific recommendation visibility and active-prevalence feedback. For this model, we derive sparse dynamic message-passing (DMP) equations. Exact per-time-step matching of degree-weighted potential edge-opportunity budgets isolates allocation changes. We prove that equal budgets can produce different expected new adoptions. Paired Monte Carlo (MC) simulations on Barabási–Albert and stochastic block model networks show a positive median network-level advantage in final cumulative adoption under dynamic recommendation over uniform budget-matched allocation. Constructive counterexamples establish that a shared local non-backtracking stability boundary need not determine finite-network stochastic early-growth boundaries or macroscopic cascade transitions. Across four synthetic network families, numerical boundary estimates vary with topology, seed and observation criteria. DMP approximates final adoption and active-fraction trajectories. In some parameter tests, however, its predicted change in the dynamic-minus-matched adoption advantage has the opposite sign to the MC result. The framework supports comparisons of recommendation allocation at equal potential budgets and requires propagation boundaries to be interpreted according to their distinct physical criteria.