A Generalized Discrete-Cyclic Framework for Fundamental Physical Structure

This paper presents a generalized discrete-cyclic framework for the mathematical representation of periodic physical systems. The central proposition of the research is that several problems conventionally treated as independent may originate, in part, from a common structural limitation in the representation of cyclic quantities. Temporal measurement, angular parametrization, periodic phase, discrete state organization, and selected cosmological problems are therefore examined within a unified mathematical architecture. The framework is based on a fundamental distinction between a numerical coordinate and the physical state represented by that coordinate. In a cyclic system, two different numerical labels may correspond to the same structural state. This permits periodic phenomena to be described through equivalence relations, cyclic closure, discrete refinement, and invariant transformations.