Relaxation-Driven Cyclic Cosmology (RDCC): A Minimal Mathematical Framework

This document presents the minimal mathematical foundation of the Relaxation‑Driven Cyclic Cosmology (RDCC) framework. Unlike phenomenological cosmological models, RDCC is formulated as a structural, globally CPT‑symmetric description of the universe, in which time, causality, and entropy arise only after projection into a sector with a fixed thermodynamic arrow. The global spacetime is timeless, non‑separable, and invariant under CPT conjugation, while apparent cosmic evolution emerges as a sectoral relaxation process governed by a single complex scalar field and a minimal structural asymmetry parameter. The text defines the global degrees of freedom, the role of the relaxation field, the meaning of cyclicity without global time, and the interpretation of the CPT fixpoint as a structural boundary rather than a dynamical bounce. It also clarifies the sectoral nature of causality, the status of the speed of light, and the limits of observability within a single time‑oriented sector. This work does not introduce new particles, modified gravity, or additional mechanisms. Instead, it provides a mathematically consistent and ontologically minimal scaffold for understanding RDCC as a theory architecture. Phenomenological extensions, interpretative companions, and conceptual developments are treated in separate documents. Related RDCC publications and conceptual extensions are available via Zenodo:https://zenodo.org/records/18204087 Michael [email protected]