R-layer Mode Theory LXXI-com: — The SU(2) Cosmic Information Cycle: Geometry, Topology, Complexity, and Observational Signatures

This volume presents the compressed edition of R-layer Mode Theory LXXI, establishing the SU(2) cosmic information cycle as a unified framework for cosmology. The universe is described as a self-organizing SU(2) information system in which geometry, gravity, matter, structure formation, and late-time acceleration emerge from a single non-Abelian information field.

The work develops the SU(2) information geometry, where the spacetime metric arises as the Hessian of SU(2) complexity, and Berry curvature and Chern–Simons topology generate curvature and topological charge. Entanglement entropy leads to emergent gravity, while monotonic SU(2) complexity defines the arrow of time.

Inflation is interpreted as an information ignition phase driven by topological transitions. SU(2) dark matter arises as topological relics with wave-like behavior and solitonic halo cores. Dark energy emerges from topological entropy and an infrared fixed point of the SU(2) RG flow, predicting a slightly phantom equation of state w≈−1.02 to −1.00.

The model yields distinctive observational signatures in CMB polarization (E/B/V modes), large-scale structure, gravitational waves, BAO, supernovae, and 21cm probes. This compressed edition provides a concise but complete presentation of the SU(2) cosmic information cycle and its observational consequences.