Nonlinear Stability of Emergent Hyperbolic Causal Structure from Bures Gradient Flows

This research presents the Informational Geometry of Emergent Spacetime (IGES) framework, which derives fundamental physical laws from the principle of minimizing quantum information degradation. The study encompasses both theoretical stability analysis and experimental validation using high-energy physics data. First, by simulating Information Open-systems Flow (IOF) on the Bures manifold, we demonstrate that an effective hyperbolic causal structure emerges as a dynamically stable nonlinear attractor. Using finite-dimensional dephasing models, it is shown that the spectral gap and Onsager symmetry ensure the global stability of the emergent light-cone. Second, the framework is empirically tested against Pb-Pb collision data at √sNN = 5.02 TeV from the ALICE experiment (Run 3) at CERN. Bayesian MCMC inference reveals that the IGES-predicted transport coefficients—specifically a shear viscosity-to-entropy ratio of η/s = 0.283 ± 0.015 and a significantly reduced response coefficient of κ = 0.311 ± 0.010—are in excellent agreement with experimental observations. These findings provide the first empirical evidence that information-geometric principles govern the macroscopic dynamics of the quark-gluon plasma.