General Theory of Hierarchical Generation

Abstract

This paper introduces a minimal axiomatic framework for hierarchical generation. Each hierarchical layer is defined by its natural scale, which measures the magnitude of its internal rate of change. Differentiation with respect to this natural scale produces a nested generative structure that explains the emergence of hierarchical depth, abstraction, and complexity. A dissipation term naturally appears as the part of a hierarchy that cannot be extracted through scale‑normalized differentiation. This dissipation accumulates in deeper layers and acts as semantic sedimentation, linking hierarchical generation to meaning formation. The framework presented here is fully abstract and model‑independent. A subsequent paper will develop concrete realizations of hierarchical generation in physical, informational, and semantic systems.