Detailed Exposition of the 0-Sphere Model Framework for Gravitational-Like Phenomena: Supplementary Note to "Geometrical Confinement of Energy in the 0-Sphere Model"

Description[35 Supplement] This document is a supplementary theoretical exposition of the 0-Sphere model, an emergent-force framework in which gravitational-like behavior arises from internal phase synchronization and energy redistribution, without introducing additional force mediators. The 0-Sphere model interprets gravitational phenomena as a consequence of conserved energy flow between internal Zitterbewegung dynamics and coherent translational motion, rather than as a fundamental interaction or spacetime curvature. This supplement clarifies the conceptual, topological, and mathematical structure of the model to support reproducibility and cross-disciplinary evaluation. This supplementary document provides…