∞-Groupoid Cosmology G; First-Principles Derivation of Cosmological Structure Based on Axioms of Information Conservation and Computability

This paper starts from a minimalist axiomatic system and attempts to provide aself-consistent theoretical framework for the large-scale structure of the universe andits potential multiplicity. The core of the system consists of two fundamental axioms: information conservation and the computability of physical processes. By introducing ∞-groupoids as the mathematical framework for describing the quantuminformation state of the universe and defining the information potential difference asa dynamical variable within this framework, this paper deduces that cosmic evolution must be accompanied by discrete CPT-symmetric branching processes, therebyintrinsically generating a series of mutually mirrored universe pairs. This processcorresponds mathematically to semantic layer transitions of ∞-groupoids. Furthermore, through renormalization analysis of observable dimensions under holographicboundary conditions, the theory predicts a series of discrete phase transition pointsin the history of cosmic evolution, corresponding to shifts in information processing paradigms. This framework not only logically and self-consistently explains thepotential origin of multiverse structures, but also derives a series of parameter-free,unique predictions that can be tested by next-generation astronomical observations,including a specific index for the evolution of the cosmological constant, odd-evenmodeoscillations in the primordial gravitational wave power spectrum, and step-likefeatures in the holographic boundary noise temperature.