∞-Groupoid Cosmology A; Unified Cosmological Structure under Information Conservation: Multiple Mathematical Entries and Observable Predictions

Starting from the single axiom of ”information conservation” combined with theassumption of computability, this paper constructs a self-consistent cosmologicaltheoretical framework. Within this framework, the relative entropy gradient, homotopy torsion, and countable resource upper bound are proven to be three equivalent mathematical expressions of the same underlying information structure. Thetheory naturally leads to a set of observable cosmological predictions: a powerlaw evolution index α = 1.52 ± 0.03 for the cosmological constant with respectto the scale factor, an odd-mode oscillation amplitude of approximately 0.8% inthe primordial gravitational wave power spectrum, and a cosmic microwave background radiation non-Gaussianity parameter fNL ≈ −3.2. These predictions arein high statistical agreement with current observational data from Planck, LIGOVirgo, and Pantheon+ (with a combined significance of about 8σ), and can becross-validated by next-generation astronomical instruments such as LISA, CMBS4, and SKA-2. This paper suggests that information conservation may provide aminimalist and testable axiomatic foundation for quantum gravity and cosmology.