Axiomatic Structure of Computational Universes:\\ Discrete Configurations, Update Relations, and the Unified Time Scale Framework

Under the assumptions of finite information density and local reversible updates, we provide a unified axiomatic definition for the ``computational universe.'' The core object is a quadruple U_{comp} = (X,T,C,I), where X is the discrete configuration space of the entire universe, T \subset X \times X is the one-step update relation, C is the single-step cost (time, energy, or gate count), and I is a state function characterizing ``information quality.'' We introduce axioms of locality, finite metricity, and (generalized) reversibility, proving that classical Turing machines, cellular automata, and reversible quantum cellular automata can all be embedded as special cases within this framework. Furthermore, we prove that under the unified time scale hypothesis (i.e., the existence of a single-step cost function compatible with physical scattering time scales), the configuration graph (X,T,C) induces a ``complexity geometry'' in appropriate limits, whose geodesic distances are equivalent to a continuous version of traditional time complexity. Finally, we characterize relationships between different computational universes via simulation mappings, constructing a category CompUniv with computational universes as objects and structure-preserving simulations as morphisms, proving that the classical Turing universe, classical cellular automaton universe, and quantum cellular automaton universe form equivalent full subcategories within this category. As the first work in the ``Computational Universe Theory'' series, this paper aims to provide a minimal discrete and physicalizable axiomatic foundation, establishing a unified benchmark structure for subsequent complexity geometry, information geometry, and the category equivalence between physical and computational universes.