R-layer Mode Theory Volume 0: CUP Structure, Information Flow, and Higher-Layer Projection Dynamics

This Volume 0 develops the foundational dynamical framework of the R-layer Mode Theory (RLMT), in which four-dimensional spacetime is interpreted as a projection of a higher-dimensional information manifold. Matter (MUP), antimatter (AUP), and their associated projection modes arise as distinct 4D manifestations of a single higher-layer structure. AUP modes retain partial access to higher-dimensional degrees of freedom, providing a geometric origin for quantum nonlocality, tunneling, and entanglement as traces of inter-layer connectivity. The volume introduces the Core–Umbra–Penumbra (CUP) structure as a primordial information container and formulates the projection geometry that generates matter–antimatter asymmetry, torsion-induced amplification, and localized “Small Bang” events. Information circulates between layers through projection, uplift, and reprojection processes, preserving total information while generating observable signatures in curvature evolution, temperature history, and mode conversion. We derive the basic evolution equations for CUP splitting, AUP/MUP conversion, curvature decay, and higher-layer information flow. The hierarchical R-layer structure is presented as a unified information-geometric framework capable of connecting early-universe dynamics, dark information, and higher-dimensional geometry. This volume forms the conceptual and mathematical foundation for all subsequent volumes of the R-layer Mode Theory, including tensor perturbations, entanglement wedges, cosmological predictions, and quantum-gravity effective actions.