The Anchoring Law for Finite Reflected Arithmetic Lattices: Midpoint-Curvature Decomposition and Defect-Controlled Localization

This paper develops an asymptotic anchoring theory for finite reflected arithmetic lattices. It combines arithmetic lattice structures, reflection symmetry, spectral coefficients, and reflected-energy interactions to explore midpoint behavior and localization effects in finite-dimensional settings. A central contribution is the formulation of the Anchoring Law, which identifies the dominant role of the odd sector in generating asymptotic growth while showing that reflected-prime contributions act mainly as logarithmic corrections. The theory yields explicit midpoint-curvature relations and provides conditions under which quartic midpoint curvature emerges. The work offers a self-contained framework for studying reflected arithmetic structures and defect-controlled localization mechanisms.