Cosmology from Two Axioms 7; A Unified Framework of Topology and Spacetime Structure under Information Dynamics Axioms

This paper systematically expounds a theoretical framework—Information Dynamics—based on two core axioms: information conservation and the computability of physical processes. It aims to provide a unified underlying description fortopological quantum states of matter and spacetime geometric structures. Takinginformation as the fundamental carrier, and utilizing mathematical tools such ascomplexity geometry, higher category theory, and persistent homology, the framework constructs a self-consistent logical system from basic principles to the evolution of specific physical systems. Research indicates that this framework can notonly naturally derive quantum dimensions with special algebraic features and sizeresonant topological orders but also formulate the evolution of spacetime structuresas a computable problem of multi-scale topological data analysis. The article further delineates specific testable pathways for this theory in quantum simulationand cosmological observations, forming a complete research paradigm that bridgesthe microscopic and macroscopic scales and connects mathematical theory withexperimental verification.