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

This Version 2 release presents a substantially improved and fully rigorous formulation of the SU(2) Cosmic Information Cycle within the R-layer Mode Theory (RLMT) program. The universe is modeled as a self-organizing SU(2) information system whose geometry, curvature, entropy, and renormalization-group (RG) flow jointly generate the observed cosmological epochs: inflation, dark matter, dark energy, and late-time structure formation. Major improvements in this version include: • Rigorous derivation of all key equations. A new Appendix F provides first-principles derivations of the emergent metric from the SU(2) complexity functional, the instanton-induced topological energy density, the SU(2) RG flow and IR fixed point, and the correspondence with SU(2) gauge-flation and chromo-natural inflation. The meaning of the information coordinates θ and the projection map π:𝓜→M is clarified. • Explicit connection to existing literature. The revised text now includes detailed links to standard SU(2) Yang–Mills theory, instanton physics, Chern–Simons topology, Fisher/Hessian information geometry, and non-Abelian inflationary models. • Determination of free parameters from first principles. The effective SU(2) coupling g_eff(μ), the topological charge Q_topo, and the critical exponent γ are constrained by SU(2) RG structure and topological quantization. • Quantitative predictions with uncertainty estimates. The model yields falsifiable predictions for CMB parity violation (EB, BV), halo core radii, gravitational-wave signatures, BAO phase shifts, a phantom-like dark-energy equation of state w_IR = −1.02 ± 0.01, and 21cm brightness-temperature modifications. • Structural and consistency improvements. All labels, references, and appendix structures have been corrected. The document now forms a coherent and mathematically consistent presentation of the SU(2) information universe. This version supersedes Version 1 and is intended as the definitive reference for the SU(2) Cosmic Information Cycle. Version note: This Version 2 release includes rigorous derivations (Appendix F), explicit links to existing SU(2) Yang–Mills and topological literature, improved parameter determination, and updated numerical predictions for CMB, LSS, GW, BAO, SNe, and 21cm.