Framework: Modular Curvature, Informational Flow, and High-Density States in CET$

This work presents the completed formulation of the modular–informational sector of the CETΩ v3.1 framework, including the explicit construction of the modular curvature \mathcal{M}_\Omega, the informational coordinate \psi, and the full structure of high-density modular phases. The framework integrates Tomita–Takesaki modular theory, noncommutative geometry, and spectral methods to define a consistent extension of GR+QFT in ultradense and highly entangled regimes. The modular curvature is constructed in generic curved backgrounds, its spectral properties are derived, and its role in the CETΩ spectral operator is fully developed. Complete numerical implementations of CETΩ high-density phases are presented, including neutron-star interiors with informational cores, early-universe cosmology with modified acoustic scales, and modular-channel dynamics in quantum systems. The work also provides observational and experimental diagnostics that distinguish CETΩ predictions from standard physics, including mass–radius curvature signatures, tidal deformabilities, cosmological sound-horizon shifts, and modular-channel observables. This document constitutes a fully realized, self-contained reference for the CETΩ v3.1 informational framework and its geometric, dynamical, and phenomenological consequences.