∞-Groupoid Cosmology D; Infinite Groupoid as the Unique Skeleton of Cosmological Observables

This paper demonstrates that if the universe, as a closed quantum information system, satisfies total information conservation and its evolution can be simulated by a universal quantum Turing machine, then the algebraic structure ofall low-energy effective cosmological observables must be uniquely described byan ∞-groupoid (infinite groupoid) skeleton. By constructing three categories—information (semantic), topological (homotopy), and computational—and provingtheir equivalence, we derive that the stable homotopy order of this ∞-groupoid isπ/√3. This constant directly locks the cosmological constant evolution index toα =π/√3 ≈ 1.520, predicts the existence of an odd-mode oscillation with amplitude 0.8% in the primordial gravitational wave power spectrum at the characteristicwavenumber k = 3.2×10−4Mpc−1, and yields the CMB non-Gaussianity parameter fNL = −3.2. These parameter-free predictions are in excellent agreement withcurrent combined observational data (the deviation of α is less than 0.1σ) and canbe decisively tested at the 5σ level by next-generation experiments such as LISAand CMB-S4.