Expansion, Constraint, and Information: A Unified Structural Framework in Temporal Rate Ontology

Temporal Rate Ontology (TRO) proposes that the primitive structure of physical reality consists of ordered succession among events, from which spacetime geometry, temporal rates, and observable quantities arise as representational encodings. This paper develops a unified structural interpretation of three phenomena typically treated separately: cosmological expansion, gravitational constraint, and apparent information loss. The central claim is that these correspond to distinct regimes of a single underlying quantity: continuation multiplicity, the number of admissible future developments of a given structure over a finite horizon. We formalize continuation multiplicity, introduce constraint-weighted selection dynamics governed by an exponential kernel, and establish a general non-injectivity result for coarse observables on directed acyclic growth structures (Proposition 3.1). The central new formal result, Proposition 5.1 (Degeneracy Amplification), provides a rigorous derivation connecting transport suppression under constraint to increasing observable equivalence class size: under a Lipschitz continuity assumption on the observable and an explicit structural metric, we prove that constraint drives observationally distinct continuation paths together, making apparent information loss a structural consequence rather than a postulate. Cosmological scaling compatibility is established as a structural consistency result. The framework introduces no new dynamical laws and remains consistent with General Relativity at the representational level.