Causal Microdynamics and Spectral Realization of the Retarded Kernel in CETΩ

Description: This work develops the Causal Microdynamics and Spectral Realization of the Retarded Kernel within the CETΩ (Causal-Informational Theory of Everything) framework. It establishes the microphysical foundation of the nonlocal retarded kernel K^{-1}(\Box_R) as emerging from causal-informational interactions among discrete events in a quantum-causal network. The study derives the kernel’s Stieltjes-positive spectral density \rho(\mu), demonstrating that it defines a ghost-free, analytic and fully covariant propagator consistent with energy positivity and causal retardation. The resulting microdynamics describe how the texon field arises as the averaged excitation of causal connectivity, linking information flow to spacetime curvature and quantum coherence. This formulation unifies gravitational, quantum, and informational dynamics under a single causal law, showing that classical spacetime and quantum correlations are emergent from the same spectral structure. It also provides explicit realizations of the kernel in both cosmological and black-hole backgrounds, verifying causal stability, unitarity, and the recovery of General Relativity in the local limit. The results demonstrate that CETΩ provides the first self-consistent, retarded, and analytically complete realization of quantum gravity based on informational causality. Keywords: CETΩ theory, causal microdynamics, retarded kernel, Stieltjes spectral representation, nonlocal gravity, texon field, quantum-causal network, causal information, covariant propagator, causal completion of gravity.