Information Projection and the Hierarchical Dynamics of Physical Events

Physical events change the states of their participants and the organization that conditions subsequent events. This paper develops hierarchical event dynamics as a mathematical description of this generative relation. Starting from the event and capsule concepts of information-projection theory, the study formulates the construction in terms of state spaces, conditional path laws, constitutive dynamics, observation maps, and physical balances. A typed capsule specifies either a persistent physical object or a selected observation region. Relative to that capsule, upper conditions constrain admissible continuations, self-level states carry the present response, and lower organization supplies continuous influences and threshold transitions. Selection, quality, and propagation organize nine event roles whose conditional covariance is connected to physical state variation through domain-specific response maps. Under explicit measurability, well-posedness, causality, and balance hypotheses, the constitutive dynamics induces a normalized joint law of event mark, reached state, and realized path. Exact predictive sufficiency characterizes when a retained state preserves the declared joint future law. A composition result preserves completed history under normalized prospective responses, while physical and modular closure theorems distinguish identity and successor transfer from compatible fields, boundary fluxes, and scale-dependent readout. A finite marked-lifecycle criterion treats asynchronous local events and their instantaneous exchanges. Bead--track and regional-atmosphere descriptions expose the shared organization and distinct constitutive content of these constructions. Quantum instruments and astronomical worldtube balances then provide precise interfaces for evaluating retained history, operational prediction, and persistent organization. The resulting theory connects event formation to the production of future conditions: a realized path leaves physical information that participates in the next event law. Controlled comparisons of joint records make this connection testable within each specified physical realization.