R-layer Mode Theory LXXI: — The SU(2) Cosmic Information Cycle: Full Extended Edition

This is the full extended edition of R-layer Mode Theory (RLMT) Volume LXXI, presenting the complete formulation of the SU(2) cosmic information cycle. The universe is modeled as a closed SU(2) information system whose evolution is governed by non-Abelian geometry, topology, entropy, complexity, and renormalization-group flow. The extended edition contains the full mathematical development of SU(2) information geometry, including the Hessian construction of the emergent metric, Berry curvature, Chern–Simons topology, entanglement entropy, and the SU(2) complexity growth law. It provides the complete derivation of SU(2) inflation from topological transitions, the formation and dynamics of SU(2) dark matter relics, and the emergence of SU(2) dark energy from an infrared fixed point. This version includes all appendices, mathematical foundations, perturbation theory, topological sector analysis, numerical schemes, and full derivations omitted from the compressed edition. It serves as the definitive reference for the SU(2) cosmic information cycle and its unified description of inflation, dark matter, dark energy, and observational signatures across CMB, LSS, GW, BAO, SNe, and 21cm probes.