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Adv."],"published-print":{"date-parts":[[2026,10,9]]},"abstract":"<jats:p>Understanding how contagion unfolds on large, heterogeneous networks is essential for predicting and controlling spreading processes, yet structural complexity often obscures the mechanisms governing transmission across scales. Here, we show that contagion is naturally organized around dense local structures that become dynamical spreading units once infection saturates within them. Building on this principle, we introduce iterative structural coarse-graining (ISCG), a framework that compresses large networks into interpretable multiscale representations while retaining the contagion dynamics of the original system. In this saturation regime, these representations reproduce macroscopic outbreak sizes, node-level infection risks, and spatiotemporal infection trajectories across scales. Beyond this regime, ISCG enables controlled trade-offs between dynamical fidelity and structural compression. The resulting multiscale representations support mechanism-driven intervention strategies, including influence maximization, immunization, and surveillance, that consistently outperform adaptive centrality\u2013based methods. 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