Propagation, Persistence, and Defense Across Scales: A Mechanism-Based Framework from Molecular Replicators to Network Cascades

Terms such as transmission, contagion, replication, persistence, cascade, and self-protection are used across molecular biology, epidemiology, ecology, social science, economics, technology, and physics. Their mathematical similarities are real, but the underlying entities and causal mechanisms can be radically different. This paper develops a mechanism-based Propagation-Persistence-Defense framework, abbreviated PPD, for comparing these systems without assuming that they share one ontology. The framework separates four questions: whether a state can propagate to new substrate units, whether it can amplify or reproduce, whether it can persist, and whether it induces or carries secondary mechanisms that causally increase future persistence. It introduces a multicomponent state description, an operator-level propagation threshold based on the spectral radius of a local next-generation map where such a map is meaningful, a causal persistence-gain diagnostic for putative protective mechanisms, and a seven-category taxonomy distinguishing passive stability, environment-induced shelter, host-mediated protection, selected adaptation, collective emergence, cognitive intention, and engineering. The framework is evaluated against prions, viroids, viruses, mobile genetic elements, bacteria and biofilms, parasites, cancer, plants, animal societies, invasive species, cultural and informational diffusion, financial contagion, technological failures, wildfire-like physical spread, cosmic-ray showers, and supernova-triggered star formation. The strongest conclusion is deliberately limited: cross-domain unification is defensible at the level of causal architecture, feedback, network topology, branching, and threshold behavior, but not at the level of biological identity. Heredity, variation, and selection sharply separate adaptive propagators from merely cascading physical processes. The paper provides formal propositions, counterexamples, falsification criteria, an evidence hierarchy, a consistency ledger, and a research program for empirical testing. It therefore presents a framework and research program rather than a claimed universal law of harmful transmission.