∞-Groupoid Cosmology E; Emergence of Spacetime and Matter from the Self-Referential Structure of ∞-Groupoids

This paper, based on the two fundamental axioms of “information conservation”and “computability,” proposes a unified cosmological framework with ∞-groupoidsas its mathematical skeleton. This framework views the physical universe as acategory-theoretic object with infinite-order self-referential structure, its evolutiondriven by discrete information transitions (∆µ = ln2). We prove that “successful universes” capable of emerging four-dimensional Lorentzian spacetime and theStandard Model structure correspond to a class of ∞-groupoids with specific stable homotopy order (π/√3) and coherent higher-order commutativity; while thevast majority of “failed universes” correspond to ∞-groupoids that are topologically trivial, chaotic, incoherent, or frozen in incorrect symmetries. This paper further points out that although successful universes constitute a set of measure zeroin the parameter space, their cardinality within the infinite-order self-referentialhypergraph is uncountably infinite (≥ ℶω). Consequently, their existence is not alow-probability event but a syntactic necessity under infinite self-reference. Finally,we list observable predictions of this framework (such as odd-mode oscillations inthe primordial gravitational wave power spectrum and specific parameters for CMBnon-Gaussianity) and indicate that future multi-messenger astronomical observations (e.g., LISA, SKA-2, CMB-S4) can provide rigorous tests for the theory.