Information and Computation as Continuation Structure: A Temporal Rate Ontology Formulation

Information and computation are traditionally formulated in terms of symbolic states evolving over time, with probability and state space taken as primitive. In this work, we develop a structural reformulation within Temporal Rate Ontology (TRO), in which ordered succession and admissible continuation structure are primary. In this setting, information is not fundamental but arises from the distinguishability of continuation structures under observational projection, while computation corresponds to constrained navigation through admissible continuation space. We introduce a horizon-bounded continuation multiplicity ΦH and define a corresponding logarithmic measure that plays the role of structural entropy. We identify the unique structurally natural probability assignment over admissible extensions as the linear continuation measure at selectivity parameter β = 1 of the Principle of Maximal Freedom (PMF), and prove that Shannon entropy emerges from this assignment under explicit structural conditions. We further show that the full PMF family at arbitrary β generates the Rényi entropy family as derived descriptions. Classical notions including algorithmic complexity and Landauer’s principle are recovered as special cases. The framework yields a substrate-independent account of computation and provides a unified structural perspective on information, irreversibility, and complexity.