Effective TGIU Corrections as a Vanishing-Limit Extension

The Standard Model (SM) and General Relativity (GR) provide highly accurate local descriptions of particle dynamics and spacetime geometry. The Universal Gravito--Informational Theory (TGIU) is not introduced as a replacement for these frameworks, but as an \emph{effective, scale--dependent correction} applicable in regimes where persistent residuals or tensions suggest incomplete closure under assumptions of strict homogeneity or context--independence. In the appropriate limits, all TGIU contributions vanish identically, recovering the standard predictions: \[ \lim_{\nabla \Phi,\nabla S \to 0} \epsilon_{\mathrm{TGIU}} = 0. \] This construction mirrors the operational role of GR as an extension of Newtonian mechanics in high--precision or strong--field regimes.