A Unitary Algebraic Framework for Linear Inequality Systems: The Trojan Chain

This paper introduces a unitary algebraic framework for the resolution of linear inequality systems, utilizing the R^2 linear plane as a foundational instantiation. By moving away from traditional geometric shading, the Trojan Framework utilizes a tripartite process - the Chain Operator, the Boundary-Enclosure Operator, and the Interior-Point Solver - to map 2D constraints into a multi-branched structural map. The methodology achieves a deterministic Linear time complexity, O(n), for standard Linear R^2 systems, providing a mathematically rigid and computationally optimal backbone for R^n resolution.