Unified Invariant Structural Theory

AbstractThis paper introduces Unified Invariant Structural Theory, in which an invariantidentity is treated as a primitive structural object. An invariant identity is a quantitypreserved under admissible structural transformations:I(T (x)) = I(x).This invariance forms a single structural framework from which optimization, equilib-rium, energy, force, geometry, and curvature arise as invariant structural realizations.In particular, optimization appears as a special case in which invariant identity isexpressed through equilibrium-type conditions and admissibility preservation