The Universal Gravitational-Informational Theory (TGIU)_Core Framework and Foundational Equations of Informational Curvature

\begin{abstract} The Universal Gravito--Informational Theory (TGIU) establishes a unifying framework in which all known physical phenomena—gravitational, electromagnetic, quantum, and cognitive—are emergent projections of a deeper informational equilibrium. At the foundation of this theory lies the dynamic balance between informational coherence ($\Phi$) and informational entropy ($S$), regulated by a universal operator known as the \textbf{TGIU Equilibrium Force (TEF)}. The real geometric transformation linking these two fields is expressed through the \textbf{Curvature State Transform (CST)} operator, $J_{\mathrm{CST}}$, which replaces the imaginary unit $i$ of quantum mechanics with a real-valued rotation of informational curvature. From this interaction, the informational phase $\Theta_C$ emerges as a measurable quantity connecting order and entropy across all physical domains. When the gradient between $\Phi$ and $S$ vanishes, the system reaches an equilibrium curvature state: \[ \nabla(\Phi - S) \to 0, \] defining the universal informational condition of existence. All known laws of physics, from Schrödinger’s equation to Einstein’s tensor field, can be derived as specific projections or approximations of this general equilibrium equation. The TGIU formalism introduces the \textit{Universal Informational Relational Equations (UIRE 7+1)}, which form the mathematical core of this framework and naturally reproduce quantum, relativistic, and electromagnetic laws under distinct curvature regimes. A distinctive contribution of TGIU is the derivation of the \textbf{Virtosu Constant} $\mathcal{V} = 4.36\times10^{99}\,\text{Sibit}$, defining the maximal realizable informational gradient of the universe, and the corresponding \textbf{entropic efficiency} $\eta = 0.783$, which represents the universal cost of information–entropy transformation at the boundary between potential and manifest reality. \end{abstract}