Emergent Near-3D Geometry as a Renormalization Group Attractor in Causal Information Networks

A computational framework in which geometry emerges from adaptive causal information networks. Using a common-ancestor connectivity rule, the system self-organizes into a stable near-3D geometric phase with nontrivial renormalization group behavior, scheme-independent coarse-graining stability, and massless transverse-traceless collective modes. The work derives a running coupling law R∝ρ−1/3R \propto \rho^{-1/3}R∝ρ−1/3, identifies a geometric fixed point, and explores conditional connections between entanglement structure and emergent gravity. Supported by large-scale numerical simulations and spectral analysis.