Topological Ring-Network Cosmology (TRNC): A Framework for Path-Dependent Observation and Emergent Gravitational Structure

Topological Ring-Network Cosmology (TRNC) is a speculative theoretical framework that investigates whether the global topological organization of spacetime may play an active role in physical observation and gravitational phenomena. While General Relativity successfully describes gravity through local spacetime geometry, TRNC explores the possibility that an additional layer of global topological connectivity may influence how physical information propagates between an event and an observer. The framework introduces the Topological Propagation Principle (TPP), which proposes that the observable description of a physical event may depend not only on the properties of the event and the local geometry of spacetime, but also on the global topological class of the information propagation pathway. To formalize this idea, a hypothetical Topological Connectivity Field, denoted by C(x)C(x)C(x), is introduced as an additional structural variable describing the large-scale connectivity of spacetime. Within this framework, the article further explores the hypothesis that effective gravitational mass may contain an emergent component associated with spatial variations of the connectivity field. A phenomenological mathematical formulation is proposed as an initial foundation for future theoretical development, numerical simulations, and observational investigation. TRNC is not presented as a replacement for General Relativity or existing cosmological models. Instead, it is intended as an exploratory extension that examines whether global topological connectivity could represent an additional physical degree of freedom relevant to gravitation, spacetime structure, and information propagation. The framework emphasizes mathematical consistency, compatibility with established local physics, and the importance of future experimental and computational tests capable of evaluating its predictions