Compression Without Collapse: A Cross-Scale Framework for Layered Emergence

Emergent layers persist by compressing detail without collapsing into it. This paper develops a conditional framework for layered emergence. Its central claim is not that compression alone explains emergence, but that when a higher-level layer has lower descriptive capacity than its lower-level support, must remain systematically related to that support, and must preserve distinctions relevant to a higher-level burden, an admissible compression interface is structurally required. Compression is defined as selective preservation under capacity reduction. The paper argues that stable higher-level description requires a relevance-governed interface that filters some lower-level distinctions while preserving those needed for prediction, control, identity, coordination, meaning, or another layer-specific function. The paper also introduces triadic pattern amplification as a precondition for admissible compression. Before a lower-level pattern can be preserved across scale, it must become sufficiently distinguishable from background variation, bound through internal cohesion or criterion-mediated membership, and identity-stable across relevant transformations. The framework is developed through two conditional lemmas, a taxonomy of compression failures, and cross-domain applications from information theory, statistical mechanics, renormalization, biology, cognition, machine learning, language, and social systems. The result is a disciplined account of layer preservation under capacity reduction: higher-level layers do not float free of their substrates, and they do not drown in them. They remain related without becoming identical.