∞-Groupoid Cosmology F; Information Conservation and Circle Rigidity: A Set of Parameter-Free Cosmological Predictions

This paper, based on the two fundamental axioms of “information conservation”and “computability of physical processes”, constructs an extremely minimalist cosmological theoretical framework. This framework reveals that in a closed quantumsystem satisfying unitary evolution, the discrete transitions of the information structure are deeply linked to the spectral geometric rigidity of the one-dimensional circle(U(1)). Consequently, we derive, without any free parameters, a set of tightly interconnected observable predictions: the power-law evolution index of the cosmologicalconstant with the scale factor α = π/√3 ≈ 1.52, the existence of odd-mode oscillations with an amplitude of approximately 0.8% in the primordial gravitational wavepower spectrum at a characteristic scale, and the non-Gaussianity parameter of thecosmic microwave background radiation fNL ≈ −3.2. These predictions show a highstatistical consistency (> 8σ) with the joint analysis results from current ultra-highprecision observational data such as Planck, DESI, and Pantheon+. Further independent tests can be completed within five years by next-generation astronomicalfacilities (e.g., LISA, SKA-2, and CMB-S4). This study suggests that informationconservation combined with circle geometry may provide a falsifiable first-principlesfoundation for quantum gravity and cosmology.