Geometrization of Manifold J: A Unified Framework of Information Geometry and Renormalization Group Flow

This paper establishes an information-geometric framework that connects therenormalization group (RG) flow in quantum field theory with the topology ofthe background spacetime. The core thesis is that the attractor structure on therenormalization group manifold is constrained by the information capacity quantization conditions borne by the background topology. By coupling the holographicprinciple with the renormalization group flow equations of effective field theory, itis demonstrated that there exists a correspondence between topological invariantsand information twisters. Based on three fundamental assumptions—informationconservation, physical computability, and the holographic principle—this framework interprets the renormalization group flow process as a quantum computationprocess limited by the information capacity of spacetime, thereby providing a computable implementation path for the emergence mechanism of spacetime topology.