The Causal–Informational Completion of Gravity

We present CETΩ, a unified framework that completes gravity through a causal–informational

principle. The theory reconciles general relativity and quantum mechanics within a strictly four-

dimensional, nonlocal, and causal formulation. At its core lies an analytic and retarded kernel

K−1(□R), derived from a discrete causal network, which governs the propagation of the gravitational

and scalar sectors. A scalar field, the texon, emerges as the effective excitation of causal connectivity

and accounts simultaneously for dark matter and dark energy without introducing extra degrees of

freedom or breaking locality.

The formalism ensures analyticity, spectral positivity, and holographic completeness: the kernel

admits a Stieltjes representation with positive spectral density ρ(µ) ≥0, guaranteeing unitarity

and causal propagation. At cosmological scales, CETΩ predicts stable inflationary dynamics with

ns = 0.966–0.970, tensor-to-scalar ratio r = 0.004–0.015, and running αs ≃−(0.8–2) ×10−3

,

consistent with Planck data. Black hole ringdown frequencies deviate by |δω/ω|∼10−4 from general

relativity, within the detectable range of next-generation gravitational-wave observatories. The

theory remains falsifiable within the causal parameter window M∗ ∈[10−5

,10−4] m−1, where M∗

sets the mean causal correlation length of the texonic field.

CETΩ thus provides a complete, causal, and informational foundation for spacetime dynamics,

recovering Einstein gravity in the infrared while extending its validity to the quantum and cosmological

domains.