Canonical Formalism of Informational Gravity in the IFUF/IST Framework: Symbol Table, Action Principle, and Equations of State

This work presents a canonical and self-contained formalization of the Information-First Unified Framework (IFUF) / Information Structure Theory (IST). The framework introduces a scalar informational background field u(x), a structural sector with baryonic and dark residual components modulated by a coherence field C(x), and an exchange coupling enforcing conservation of informational content between structured and unstructured reservoirs. We derive the field equations, Newtonian and galactic limits for rotation curves, halo hydrostatic equilibrium leading to NFW-like profiles, and a relativistic completion via an effective metric coupling. A comprehensive global symbol table and an appendix on equations of state (EOS) are included for clarity. This document serves as the canonical reference for IFUF/IST, connecting mathematical formalism, physical interpretation, and astrophysical observables such as galaxy dynamics, lensing, and cosmological redshift.